CRC Handbook of Irrigation Technology. Vol. 1 9780849332319, 0849332311, 9780849332326, 084933232X, 0849332338, 9781315893549, 9781351072649

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CRC Handbook of

Irrigation Technology Volume I Editor

Herman J. Finkel, Ph.D. Director, Finkel & Finkel Ltd. Consulting Engineers Haifa, Israel

Boca Raton London New York

CRC Press, Inc.

CRC Press is an imprint of the Taylor &Boca Francis Raton, Group, an informa business Florida

First published 1982 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 Reissued 2018 by CRC Press © 1982 by CRC Press, Inc. CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright. com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a notfor-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging in Publication Data Main entry under title: Handbook of irrigation technology. Includes bibliographies and index. 1.  Irrigation engineering. I. Finkel, Herman J. TC805.H25   627’ .52   80-26417 ISBN 0-8493-3231-1 (v. 1) ISBN 0-8493-3233-8 (v. 2) A Library of Congress record exists under LC control number: 80026417 Publisher’s Note The publisher has gone to great lengths to ensure the quality of this reprint but points out that some imperfections in the original copies may be apparent. Disclaimer The publisher has made every effort to trace copyright holders and welcomes correspondence from those they have been unable to contact. ISBN 13: 978-1-315-89354-9 (hbk) ISBN 13: 978-1-351-07264-9 (ebk) Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

CONTENTS Volume I The Importance and Extent of Irrigation in the World Soil-Water Relationships Plant-Water Relationships Water Requirements of Crops and Irrigation Rates Soil Salinity and Water Quality Hydraulics of Open Channels Measuring Channel Flow Pipe Flow Sprinkler Irrigation Drip Irrigation Pumps and Pumping Gravity Irrigation Index

Volume I1 Land Grading Drainage of Irrigated Fields Criteria for the Choice of Irrigation Method Health Hazards of Irrigation Economics and Costing of Irrigation Automated Computerized Irrigation Irrigation Management and Scheduling The Irrigation of Cotton Irrigation of Sugar Crops Irrigation of Oil Crops Irrigation of Cereal Crops Irrigation of Alfalfa Irrigation of Citrus Index

THE EDITOR Herman J. Finkel, Ph.D., is Director of Finkel and Finkel, Consulting Engineers, and Emeritus Professor of Agricultural Engineering of the Technion-Israel Institute of Technology, Haifa, Israel. Dr. Herman J . Finkel is a graduate of the Department of Agricultural Engineering of the University of Illinois (1940) and holds a Ph.D. from the Faculty of Agriculture of the Hebrew University, Jerusalem. After years of experience in the United States with the U.S. Corps of Engineers, the U.S. Soil Conservation Service, and private consulting engineering firms, he moved to Israel where he became the Chief Engineer of the newly formed Israel Soil Conservation Service. This work emphasized water resource development and irrigation. In 1952 he founded the Faculty of Agricultural Engineering at the Technion, Israel Institute of Technology, and served as its head and Dean intermittently for 24 years. During this time he taught and did research in the fields of irrigation and soil and water. From 1969 through 1972 he served as Academic Vice-President for the Technion. During this period, Dr. Finkel maintained an active consulting practice and served as an expert in irrigation for FAO, other international agencies, and private consulting firms in 24 countries of Latin America, the Caribbean, Africa, the Middle East, and the Far East. This activity was divided among design, project evaluation, and training of local staff. He also served on a number of missions of UNESCO and the World Bank on educational planning for the developing countries, as an expert on agricultural and technical education. Since 1972 he has been the head of the consulting firm of Finkel and Finkel, located in Haifa, Israel. This firm has done design work in Israel as well as in Iran, the Caribbean, and Latin America. Dr. Finkel is the author of numerous articles both in his profession and in the more distant fields of history and archeology as well.

ADVISORY BOARD Amnon Benami, Ph.D. Faculty of Agricultural Engineering Technion-Israel Institute of Technology Haifa, Israel

Israela Ravina, Ph.D. Faculty of Agricultural Engineering Technion-Israel Institute of Technology Haifa. Israel

Dov Nir, D. Sc. Faculty of Agricultural Engineering Technion-Israel Institute of Technology Haifa, Israel

Zeev Nir, D. Sc. Faculty of Agricultural Engineering Technion-Israel Institute of Technology Haifa, Israel

CONTRIBUTORS Amnon Benami, Ph.D. Faculty of Agricultural Engineering Technion-Israel Institute of Technology Haifa, Israel Herman J. Finkel, Ph.D. Director, Finkel and Finkel, Ltd. Haifa, Israel Peter Neumann, Ph.D. Plant Physiologist and Senior Lecturer Soil and Fertilizers Division Faculty of Agriculture Engineering Technion-Israel Institute of Technology Haifa, Israel

Dov Nir, D. Sc. Faculty of Agricultural Engineering Technion-Israel Institute of Technology Haifa, Israel Zeev Nir, D. Sc. Faculty of Agricultural Engineering Technion-Israel Institute of Technology Haifa, Israel Israela Ravina, Ph.D. Faculty of Agricultural Engineering Technion-Israel Institute of Technology Haifa, Israel

TABLE OF CONTENTS Volume I The Importance and Extent of Irrigation in the World

...........................

1

Soil-Water Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Plant-Water Relationships

.................................................

49

Water Requirements of Crops and Irrigation Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Soil Salinity and Water Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Hydraulics of Open Channels ............................................... 93 Measuring Channel Flow PipeFlow

................................................. 145

..............................................................

......................................................

193

..........................................................

247

Sprinkler Irrigation DripIrrigation

171

Pumps and Pumping ..................................................... 299 Gravity Irrigation ........................................................ Index

339

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

Volume I

1

THE IMPORTANCE AND EXTENT OF IRRIGATION IN THE WORLD Herman J. Finkel

AGRICULTURAL PRODUCTION In a world of explosive demographic growth the agricultural production in general and the production of food in particular has not everywhere kept up with need. The per capita growth of production for various countries and regions is reported annually by the Food and Agriculture Organization of the United Nations. The 1977 edition gives the figures summarized in Table 1.' From this it can be seen that in 53 countries of the developing world the growth of agricultural production has not kept pace with the growth of the population. In many other countries the rate of agricultural growth has just barely kept up. Since, in many of these countries the prevailing levels of nutrition are below what is considered as adequate, an index of food production per capita even somewhat above 100 is unsatisfactory. Every means must therefore be sought to increase world agricultural production. In the arid and semiarid zones of the world one of the principal means to achieve this is irrigation.

ARID AND SEMIARID LANDS Arid and semiarid regions have been variously defined by climatologists. The most commonly accepted criterion has been the average annual rainfall. Areas with less than 200 mm have been considered to be arid, those from 200 to 500 mm are semiarid, from 500 to 750 are subhumid, and above 750 are humid. This classification, however simple, is misleading, from the point of view of irrigation requirements. There are zones in which the annual rainfall may be well above 750 mm, but which may, nevertheless, require irrigation because of the length of the dry season. Moreover, the longterm average annual rainfall may be a misleading figure if the climatic pattern is irregular, and the deviations in an individual year are large. It may be stated, therefore, that for purposes of irrigation planning, a semiarid region will be considered as one having an average dry season of 3 or 4 consecutive months, regardless of the total annual precipitation. Such an area would require supplementary or seasonal irrigation. The arid region would be taken as one in which the average dry season may last longer than 4 months, and in some years the drought may last throughout the year. This would require the installation of a perennial irrigation system. Another approach is that proposed by Thornthwaite.' He suggests a Moisture Index which is defined as the deficiency of average monthly precipitation compared to the average monthly potential evapotranspiration, summed up for the year. Expressed in millimeters of moisture, an annual deficit of from 20 to 40 defines a semiarid climate, and over 40 an arid climate. The average monthly precipitation is taken from the longterm climatological records, and the potential evapotranspiration is calculated as described in the chapter on Water Requirements of Crops. The extent of arid and semiarid lands in the world is illustrated in Table 2, which gives the percentage of land on which agricultural production is limited by drought. In Table 3 it is shown that of the 11.6 billion hectares of land in the 103 countries reporting, only 8.67% is cultivated. Of this about 20% is under irrigation. Some countries report 100% of their cultivated land under irrigation, and others have practically no irrigation. The reported irrigated areas in each country should be taken with caution as the date and method of estimation were not identical for all the countries.

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C R C Handbook of Irrigation Technology

IRRIGATION NEEDS IN THE DEVELOPING COUNTRIES The Food and Agriculture Organization of the United Nations has proposed targets for irrigated areas in the developing market economies for the year 1990. These, together with the existing irrigated areas in 1975, are summarized in Table 4. As can be seen from this table there is a projected addition of some 22 million hectares of new irrigation and 45 million hectares of improvements of existing irrigation in the developing regions of the world.

WATER REQUIREMENTS The water use in the world in 1967, and the projected use in 2000 are summarized in Table 5. It is seen that the proportion of the water supply of the world used for irrigation is expected to vary from 70% in 1967 to a projected 51% in the year 2000. Although the annual rate of growth of irrigation will be about 2.1%, the growth of urban domestic and industrial demand will grow at rates from 4 to 5%/year. These projections indicate that a formidable effort will have to be made in the coming two decades to develop water resources and to construct and improve irrigation systems if the population of the world is to be fed at some minimum acceptable standard of nutrition.

Table 1 PER CAPITA INDEX OF FOOD AND AGRICULTURAL PRODUCTION FOR THE YEAR 1976 (BASED ON 1961-65 = 100)' Country or region World Developed countries Western Europe European economic community Belgium-Luxembourg Denmark France Germany, Federal Republic of Ireland Italy Netherlands United Kingdom Other Western Europe Austria Finland Greece Iceland Malta Norway Portugal Spain Sweden Switzerland Yugoslavia U.S.S.R. and Eastern Europe Eastern Europe

Food production per capita

Agricultural production per capita

Volume I

Table l (continued) PER CAPITA INDEX OF FOOD AND AGRICULTURAL PRODUCTION FOR THE YEAR 1976 (BASED ON 1961-65 = 100)' Country or region Albania Bulgaria Czechoslovakia German Democratic Republic Hungary Poland Romania U.S.S.R. North America, developed Canada United States Oceania, developed Australia New Zealand Developing countries Africa, developing North Western Africa Algeria Morocco Tunisia Western Africa Benin Gambia Ghana Guinea Ivory Coast Liberia Mali Mauritania Niger Nigeria Senegal Sierra Leone Togo Upper Volta Central Africa Angola Cameroon Central African Empire Chad Congo Gabon Zaire Eastern Africa Burundi Ethiopia Kenya Madagascar Malawi Mauritius Mozambique Rhodesia Rwanda Tanzania

Food production per capits

Agricultural production per capita

3

4

CRC Handbook o f Irrigation Technology

Table l (continued) PER CAPITA INDEX OF FOOD AND AGRICULTURAL PRODUCTION FOR THE YEAR 1976 (BASED ON 1961-65 = 100)' Country or region Uganda Zambia Southern Africa Botswana Lesotho Swaziland South Africa Latin America Central America Costa Rica El Salvador Guatemala Honduras Mexico Nicaragua Panama Caribbean Barbados Cuba Dominican Republic Haiti Jamaica South America Argentina Bolivia Brazil Chile Colombia Ecuador Guyana Paraguay Peru Uruguay Venezuela Near East, developing Near East in Africa Egypt Libya Sudan Near East in Asia Afghanistan Cyprus Iran Iraq Jordan Lebanon Saudi Arabia Syria Turkey Yemen, Arab Republic Yemen, Democratic Israel Far East, developing

Food production per capita

Agricultural production per capita

Volume I

Table l (continued) PER CAPITA INDEX OF FOOD AND AGRICULTURAL PRODUCTION FOR THE YEAR 1976 (BASED ON 1961-65 = 100)' Country or region

Food production per capita

Agricultural production per capita

South Asia Bangladesh India Nepal Pakistan Sri Lanka East South-East Asia Burma Indonesia Korea, Republic of Malaysia, peninsular Malaysia, Sabah Somalia Philippines Thailand Japan Asian central planned economy China Kampuchea, Democratic Korea, Democratic Peoples Republic Laos Mongolia Vietnam

Table 2 AREAS OF LAND LIMITED BY DROUGHT Region

% of land limited by drought

North America Central America South America Europe Africa South Asia North and Central Asia Southeast Asia Australia World

28

From State of Food and Agriculture, Food and Agriculture Organization, Rome, 1977. With permission of the Food and Agriculture Organization af the United Nations.

5

Table 3 EXTENT OF CULTIVATED AND IRRIGATED LAND IN THE WORLD

Name of country 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

Afghanistan Albania Algeria Argentina Australia Austria Belgium Bolivia Botswana Brazil Bulgaria Burma Cambodia Canada Ceylon Chile China, Mainland China, Republic of Colombia Costa Rica Cuba Cyprus Czechoslovakia Denmark Dominican Republic Ecuador El Salvador Ethiopia Fiji Finland

Total area (million ha)

Area cultivated (million ha)

Area irrigated (million ha)

Proportion of cultivated area to total area ("70)

Proportion of irrigated area to total area (Vo)

Proportion of irrigated area to cultivated area (V@)

31. France 32. Germany, Federal Rep 33. Ghana 34. Greece 35. Guatemala 36. Guyana 37. Haiti 38. Honduras 39. Hungary 40. India 41. Indonesia 42. Iran 43. Iraq 44. Israel 45. Italy 46. Ivory Coast 47. Jamaica 48. Japan 49. Jordan 50. Kenya 5 1. Korea, Republic of 52. Laos 53. Lebanon 54. Libya 55. Malagasy Republic 56. Malaysia 57. Malawi 58. Mali 59. Malta 60. Mexico 61. Morocco 62. Nepal 63. Netherlands 64. New Zealand 65. Nicaragua 66. Nigeria (northeastern state) (northwestern state)

Table 3 (continued) EXTENT OF CULTIVATED AND IRRIGATED LAND IN THE WORLD

Name of country 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97.

Norway Pakistan Panama Peru Philippines Poland Portugal Puerto Rico Rhodesia Romania, Social Republic of Saudi Arabia Senegal Sierra Leone Somalia South Africa (Union of) Spain Sudan Surinam Swaziland Sweden Switzerland Syria Tanzania Thailand Tunisia Turkey Uganda U.S.S.R. United Arab Republic United Kingdom U.S.

Total area (million ha)

Area cultivated (million ha)

Area irrigated (million ha)

Proportion of cultivated area to total area (qo)

Proportion of irrigated area to total area (qo)

Proportion of irrigated area to cultivated area (070)

98. 99. 100. 101. 102. 103.

Uruguay Venezuela Vietnam, Republic of Yemen Yugoslavia Zambia

Totals

18.693 91.205 17.326 19.500 25.654 75.272 11,632.008

2.000 5.219' 2.750

0.027 0.362 0.269

10.70 5.72 15.87

7.507 2.064 1,008.143

0.150 0.600 203.208

29.50 2.74 8.67

-

Figures from FAO Production Year Book 1968, Vol. 22, 1968. Arable land and land under permanent crops from FAO Production Year Book 1968, Vol. 22, 1968. From Holly, M., Water and the Environment, Irrigation and Drainage Paper No. 8, Food and Aariculture Organization, Rome, 1971. With permission of the Food and Agriculture Organization of the United Nations.

CRC Handbook o f Irrigation Technology

Table 4 IRRIGATION EXISTING IN 1975 AND TARGETS FOR 1990 IN THE DEVELOPING MARKET ECONOMIES4 Latin America

Africa

Near Esst

Asia

Total

Irrigation (in million ha) Equipped irrigation area, 1975 Targets, 1990 New irrigation Improvements to existing irrigation Minor Major Increased water demand (km3) Drainage (million ha) Equipped drainage area, 1975 Improvement targets, 1990 On irrigated land On nonirrigated land

Table 5 ESTIMATES OF WORLD WATER USE, 1967, AND PROJECTIONS TO 2000 Proportion of total use Total use

(Q'.)

Year 1967 (lwrn3) Agriculture Irrigation Livestock Rural domestic Other Urban domestic Industry and mining Total

Year UX)O

(IOW)

Projected rate of growth 1%7-UK)O (%/year)

1%7

UX)O

1,400,000 58,800 19,800

2,800,000 102,200 38,300

2.1 1.7 2.0

70 3 1

51 2 1

73,000 437,700

278,900 2,231,000

4.1 5.0

4 22

5 41

1,989,300

5,450,400

3.1

100

100

FAO, The State of Food and Agriculture 1977, Food and Agriculture Organization, Rome, 1977. With permission of the Food and Agriculture Organization of the United Nations.

REFERENCES 1. The State of Food and Agriculture, Food and Agriculture Organization, Rome, 1977. 2. Thornthwaite, C. W., An approach toward rational classification of climate, Geogr. Rev., 38, 55, 1948. 3. Holly, M..Water and the Environment, FAO Irrigation and Drainage Paper No. 8, Food and Agriculture Organization, Rome, 1971. 4. United Nations Water Conference, Water for Agriculture, Rome, 1977, Annex 1.

Volume I

11

SOIL-WATER RELATIONSHIPS Israela Ravina

MECHANICAL COMPOSITION OF THE SOIL Soil is a granular porous medium. The soil is composed of solid particles of many different sizes and shapes, and of different chemical compositions. The mechanical composition refers to the ultimate particles, and not to their arrangement as aggregates, a subject which is considered under soil structure. Classification of Soil Particles Size Generally particles which are larger than 2 cm are considered as stones, and particles between 2 cm and 0.2 cm or 2 mm are considered as gravel. Only particles smaller than 2 mm are considered as soil material. Their classifications according to different methods are given in Table 1.

Shape Sand and silt particles are of approximately spherical or cubical shape. They are weathering-resistant mineral of the rocks of which soil is formed. Their sharp edges are smoothed by chemical, physical, and mechanical processes. Clay particles are plate or lath-shaped depending on their crystal structure. Some of the clay fraction is amorphous. The particles are locked into intricate arrangements by different interparticle forces to form different structures. The different shapes and arrangements can be observed using scanning electron microscope techniques. Organic Matter All soils contain organic matter which affects the physical as well as the chemical state of the soil. Little is known about the biochemical and biophysical processes that occur in the organic fraction of soils. Some soils, called peats or mucks, are composed largely of organic materials (more than 20%). Soils containing less than 20% organic matter are classified as mineral soils. In arid zone soils the organic matter is usually not more than 0.5%, and in more humid areas soil organic matter is 2 to 5%. For practical purposes soil organic matter is best classified into residues and humus. The residues include parts of plants and animals in various stages of decomposition. The humus is the dark colored organic matter which is colloidal in nature, with very large specific surface area. Organic matter in soil performs many important functions. It is a major source of nitrogen and of many essential trace elements. It helps increase the solubility of inorganic soil minerals, thus releasing phosphorus, potassium, and other nutrients. It forms complexes with metal ions such as iron and manganese which are available to plants. Growth regulators and antibiotics are produced in the organic matter. The organic matter is a colloidal moderator binding sandy soils into aggregates, and loosing massive clayey soils to form a desirable aggregated structure. Generally, organic matter improves the physical conditions of the soil. Inorganic Constituents The sand fraction and most of the silt fraction are composed of primary minerals. These large particles are mainly broken-down rock fragments. The clay fraction and part of the silt fraction are composed mainly of secondary clay minerals and calcite. In arid and semiarid regions gypsum can also be found. The dominant primary min-

12

CRC Handbook o f Irrigation Technology

Table 1 TEXTURAL CLASSIFICATION O F SOIL PARTICLES

Dia. mm.

*

very coarse sand

Coarse sand Coarse sand

Coarse sand

Medium sand

Medium sand Fine

Dia. mm.

European

International

USDA

sand Fine

M~Y fine sand

,

sand

Fine sand Coarse silt

Medium silt

Silt Silt

Fine

silt

Coarse clay Clay

Clay

Medium clay Fine clay i

L

erals are quartz in sand and quartz and feldspars in fine sand and silt. Other primary minerals which are of great importance in soil fertility occur in small amounts. Mica, vermiculite, montmorillonite, and kaolinite are the main components of the clay fraction, which is in general of a colloidal nature. Specific Surface Area of Soil Particles The specific surface area is probably the outstanding characteristic of the soil system which results from the small size of the particles. The specific surface area is defined as the ratio of the surface area to the volume of the system. It is expressed as square centimeters per cubic centimeter or more generally as square meters per gram of soil. The specific surface area is a measure of the total interfaces in the system, and is important since most of the chemical and physical reactions occur at the interfaces. Consequently, the activity of the soil is approximately proportional to the specific surface. For particles of regular shape, the specific surface area can be easily calculated. It is found that the specific surface area varies inversely with the size of the particles. This is true for gravel, sand, silt, and the coarser clay fraction. However,

Volume I

Percent

13

sand

FIGURE 1. The soil texture triangle. (From Handbook No. 436, U.S. Department of Agriculture, Washington, D.C., 1975.)

clay particles are plate-shaped, and their thickness is very small relative to the other two dimensions. Their specific surface area is considerably larger than that of sand or silt. For example, the specific surface area of montmorillonite can be as high as 750 m2/g of clay. Thus the total surface area of medium or fine textured soils is due mainly to the clay fraction. Some approximate values of specific surface are as follows: Clay soils with over 50% clay Loam Sandy loams

200-300 m2/g 80-150 m2/g 50 m2/g or less

It is possible to estimate the surface area of a soil from the particle size distribution, but it is frequently easier and more accurate to estimate the specific surface area from measurements of adsorption. Soil Texture Particle size distribution represents a parameter that does not change very much over many years, and that is also related to the physical and chemical activity of the soil. Consequently, the relative proportion of the various ultimate grain size fractions in the soil has been adopted as a basic means of characterizing and classifying soils, and is called soil texture. The texture of a soil is usually named by the predominant size fraction, and the word "loam" is used whenever all three fractions occur in sizeable proportions. The U.S. Department of Agriculture has developed a system of texture designations which is generally accepted by agricultural engineers, and is usually presented by the so-called texture triangle (Figure 1). The sum of the percentages of sand, silt, and clay equals 100. If the percentages of any two fractions are known, the third can be found. The location of the intersection of any two particle fractions on the textural triangle will give the textural soil class.

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CRC Handbook o f Irrigation Technology

Table 2 SIGNIFICANCE OF SOIL TEXTURES

Feel Identification Internal drainage Plant-available water Drawbar pull Tillability Runoff potential Water detachability Water transportability Wind erodibility

Sand

Loam

Silt loam

Clay soil

Gritty Loose Excessive Low Light Easy Low High Low High

Gritty Cohesive Good Medium Light Easy Low-medium Medium Medium Medium

Silky Shows fingerprint Fair High Medium Medium High Medium High Low

Cloddy or plastic Gives shiny streak Fair to poor High Heavy Difficult Medium-high Low High Low

A knowledge of the texture of a soil is a guide in land evaluation. It must be kept in mind, however, that the textures of the entire soil profile are of importance and not only that of the surface layer. The relation of some soil properties to texture is given in Table 2. Mechanical Analysis The determination of the particle size distribution is called mechanical analysis. All methods of mechanical analysis involve two stages. The first is the complete dispersion into ultimate particles; the second is measuring the amounts of each size fraction.

Dispersion The ultimate soil particles are usually held together as aggregates by a binding agent, usually of colloidal material which may be clay, organic matter, iron and aluminum oxides, calcium carbonates, or silicates. The dispersion process must remove the binding colloids, or render them ineffective. The dispersion may be achieved by mechanical or chemical means. The mechanical means are shaking or stirring in cold or boiling water, agitating with air jets, and supersonic shaking. H 2 0 z , hydrogen peroxide, is used t o oxidize organic matter. Dilute hydrochloric acid can be used to dissolve carbonates and iron and aluminium oxides. (This procedure is not recommended for calcareous soils.) Chelating agents, such as sodium dithionates in citrate solution, may dissolve metal oxides. Adsorbed polyvalent cations, such as Ca, which cause aggregation, can be replaced with Na using s'odium hexametaphosphate, causing dispersion of the aggregates. The various methods of the mechanical analysis are summarized in Table 3. The large particles of the gravel and sand fractions can be determined by sieving with a 200 mesh which has an opening of 74 p and a 325 mesh with an opening of 44 p. Sedimentation The most wid'ely used technique for determining the size distribution of the dispersed soil suspension is by sedimentation based on Stokes' law: 2 r2g

v = - -

(P,

-P , )

9 rl

v is the settling velocity in centimeters per second, r is the equivalent radius of the particles in centimeters, g is the acceleration of gravity (981 cm/sec2), e, is the density of the solids (for soils it is 2.65 g/cm3), er is the density of the liquid, and q is its viscosity in dyn sec/cm2. Settling velocities are given in Figure 2.

Table 3 SOIL MECHANICS SPECTRUM

Diameter

Soil fraction

Gravel

mm.

-

2

2000

investigation

A

microns

--

Methods of mechanical analysis

Methods of

--

-

Coarse sand

- 0.2 Fine sand

-- 200 --

Screening

-

- 0.05 -- 50

-

- 0.02

-- 20

-

-0.002

-- 2

--2

I:

5000 -::4000-

Optical Microscope

-

Probbm zone

.

Silt

Coarse

cky

m

0'0°05

- Red viObt

- 0.0002 -- 02 ~ ~ l l ~ i -d0~ .l m day

-0.00002

True sdutiom

-

--

600-

-- 0.02 --

200-

- 0.06

- 0 . w - 0.005

--

50

--

40OOOOS- 0.002

--

20

-

X ray diffraction Electron mkroscope Limit of optical mkroscop Infrared qmctroSCOPY Limit of X-my diffraction and of &,ctron microscope

Sedimentation by gravity

-

-Sedimentation

bu

centrifuge

-

Limit of i n f m d SmsCoPY

The settling time of particles of a 0.002 mm diameter (upper limit of clay) for a distance of 10 cm in water is about 8 hr. while that for particles of 0.05 mm is only 40 sec. A very widely used method is the pipette method, which is described in Method 41 of U.S. Department of Agriculture Handbook 60. Another widely used method of determining the amount of each size fraction of particles smaller than 0.05 mm is the hydrometer method. Commercial hydrometers are available for this method, and are sold with detailed instructions as to their use.4a

16

C R C Handbook of Zrriga tion Technology

Diameter of FIGURE 2.

sol particles, hydraulic

equivalents, mm

Settling velocities of soil particles in water.

THE CLAY MINERALS The larger particles of the soil, gravel, sand, and silt make up the skeleton of the soil. The clay fraction is the active portion. The clay fraction of most soils contains large amounts of material that is in a colloidal state. The size limit of colloidal particles is often taken as 0.2 p. Thus colloidal material has a large surface area per unit mass. It is at the interface between the colloids and solution that much of the physical and chemical activity takes place. The clay minerals are probably the most important constituent of the clay fraction which determine the physical behavior of the soil. The various clay minerals differ greatly in their properties. Knowledge of the amount of clhy in the soil obtained by mechanical analysis reveals very little about the activity of the clay. This can be evaluated only after a qualitative identification of the clay minerals. The Structure and Classification of Clay Minerals The layered aluminosilicates are the most important minerals in the soil clay fraction. They are composed of two basic structural units: the silicon tetrahedron and the aluminum octahedron. The silicon tetrahedron consists of a silicon ion surrounded by four oxygen atoms which occupy positions corresponding to the corners of a tetrahedron (Figure 3A). The aluminum octahedron consists of an aluminum ion surrounded by six oxygen or hydroxyl ions which occupy positions corresponding to the corners of an octahedron (Figure 3B). The tetrahedra are joined at their basal corners and the octahedra are joined along their edges by means of shared oxygen atoms, thus forming

FIGURE 3. Basic structure of clay minerals. (A) Silicon tetrahedron; (B) Aluminurn octahedron.

tetrahedral and octahedral sheets only several angstroms thick. The crystalline clays are made up of these sheets in different combinations. Some clays are made up of alternating sheets of tetrahedra and octahedra. In these the ratio of tetrahedral sheets t o octahedral sheets is 1: l . In another group of clays the unit layer is made up of two sheets of tetrahedra enclosing an octahedral sheet as in Figure 4. Here the ratio of tetrahedra to octahedra sheets is 2: 1. Thus both faces of the unit layer are of the same structure, tetrahedral sheets, and the attraction between the unit layers is relatively weak. They can be separated by water molecules, and swell. During or after the formation of the crystal, there are substitutions of aluminum ions for silicon ions in some of the tetrahedra, and substitutions of magnesium or iron ions for aluminum ions in some of the octahedra (Figure 5). Since aluminum ions have a smaller positive charge than silicon ions, and magnesium ions have a smaller positive charge than aluminum ions, these substitutions produce a net negative charge in the clay crystals. This negative charge is balanced by the adsorption of positively charged cations. Different clays have different degrees of octahedral and tetrahedral substitutions. Thus, in some of the 2: 1 clays, potassium or magnesium cations are fixed between neighboring tetrahedral sheets and restrict their swelling. These and other factors result in the occurrence of many different types of clays which are classified into groups. The methods of identification of clay minerals and the characteristics of the various clay groups are important to the irrigation engineer but fall beyond the scope of the present volume. Electrical Properties of the Clay Fraction The clay particles carry an excess of negative charge, which is due mainly to the isomorphous substitutions in the crystal lattice, but which may also result from other mechanisms. The system as a whole, however, is electrically neutral, hence there is an attraction of cations from the surrounding solution and repulsion of anions. The re-

18

CRC Handbook o f Irrigation Technology

FIGURE 4.

Magnesium

Typical 2:1 clay structure.

Aluminium FIGURE 5 .

silicon

0 OxYWn

Formation of clay crystals.

sulting distribution of the ions in the adjacent solution is the product of interplay between the electrostatic attraction or repulsion forces on the one hand and the kinetic motion of the ions on the other hand. The charge on the particle surface and the swarm of the counter ions in the liquid phase constitute an electric double layer. The cations in the liquid phase, though attracted to the clay surface, are free to exchange with other ions, and are called both exchangeable and adsorbed cations. The total

amount of these cations is the cation exchange capacity, CEC, and is determined experimentally. The analytical methods for determining the CEC and the composition of the exchangeable ions are described in U.S. Department of Agriculture Handbook 60 (Methods 18, 19, 20).20 The various clay minerals have different values of CEC. The CEC of natural soils is thus dependent on the amount and type of clay. It is usually given in milliequivalents per 100 g soil ranging from about 60 meq/100 g in clayey soils rich in montmorillonite to a few meq/100 g in the coarse textured sandy soils.

The Electric Double Layer The equilibrium distribution of the ions away from the clay particle surface, or the configuration of the electric double layer and how it is changed by various factors is very important to the understanding of the behavior of soils, and especially of irrigated soils. A considerable amount of research work on the electric double layer theories has been published in the soil science literature. Some of the pertinent references are Kruytlo and van O l ~ h e n . A ' ~ more detailed discussion of the double layer phenomenon, however, lies beyond the scope of the present volume. Flocculation and Dispersion The processes of flocculation and dispersion of the clay are important in agricultural soils, because soil aggregates are formed in soils containing clays which flocculate. If the clays are not flocculated, but remain dispersed, the soil is said to be puddled and is sticky when wet, and hard and impermeable when dry. Crop growth is reduced in a puddled soil because of poor aeration, nutrition, and water relations. Whether or not soil colloids will flocculate depends upon the condition of the electric double layer. When two particles approach each other their diffuse counter-ion atmospheres begin t o interfere, and there will be a repulsion between the particles. The attractive force, originating from the Brownian movement, can overcome the repulsive force only when the particle can approach each other very closely and adhere. When the double layer is thick the clay particles are difficult to flocculate. The double layer will be thickest when the clay is Na-saturated and the solution is diluted. The addition of electrolytes will induce flocculation. The addition of divalent salt such as CaS04, will cause both an exchange of the Na with Ca and a suppression of the double layer. Trivalent salts are even more effective in flocculating the clays. Thus a procedure for improving alkaline-saline soils is the following: first leach the soil with a concentrated solution of a calcium salt. The clay remains flocculated. With efficient leaching the exchange of the sodium with calcium can be achieved. The concentration of the leaching water is gradually reduced until the soil solution concentration will reach the allowable limit. Shrinking and Swelling When dry soils are wetted they expand. Conversely a wet soil shrinks upon drying. The appearance of cracks in a dry soil and their disappearance after irrigation or heavy rains is field evidence of shrinking and swelling. The amount of swelling and shrinking depends on the amount and type of the clay in the soil. The more montmorillonite the soil contains the greater is the swelling. To some extent cycles of shrinking and swelling induce a good soil structure, but if the amount of shrinking and swelling is great some problems arise. A swollen soil is relatively impermeable to the passage of water. The cracks in a shrunken dry soil promote further drying. When a dry soil is wetted under constrained conditions it exerts great pressures, which can cause break-up of highways, structural foundations, and earth dams. The swelling of clays can be explained on the basis of the ionic distribution in the

20

CRC Handbook o f Irrigation Technology

electric double layer. When the clay particles are close, there is an interaction of the double layer of the particles. In the region of interacting double layers between two adjacent clay particles the concentration of ions is higher than in the external solution. This can be compared to osmosis. Water from the external solution tends to penetrate between the particles which are forced apart and the soil swells until there is no interaction between the double layers. If the particles are not free to move, a swelling pressure is built up. This pressure is related to the concentration between the particles, and can be calculated from the double layer theory. Here too, sodium clays will swell more than calcium clays, and when the soil solution concentration is high swelling is reduced.

Cation and Anion Exchange Since the soil colloids normally carry a net negative charge cations are attracted to the clay surfaces and anions are repelled The cations although attracted to the surface can be exchanged with cations in the bulk solution. Not all cations are held with the same force. Some are more specifically adsorbed and are less easily exchanged. For example, the higher the valency, the greater is the attractive force. The size of the ion in hydrated and nonhydrated states is also important. Generally in soils it is known that Li is held least strongly by the clay and thus easily exchanged. The ascending order of adsorption force is Li < Na < K < Rb < CS for the monovalent ions. The H+ ion is exceptional and is generally the most strongly held. The divalent ions are held more strongly than the monovalent and the order is Mg < Ca < Sr < Ba. Ion exchange equations describe the distribution of cations between the adsorbed and the solution phases. The exchange reaction is stoichiometric:

where A and B are ionic species, a and b are number of moles or valencies of A and B, respectively, and the dashes indicate ions in the adsorbed phase. The selectivity coefficient is given by

Thus, for example, if A are monovalent and B are divalent, in ideal solution the concentrations of the adsorbed and solution phases will relate as:

It can be seen from this equation that not only the proportion between the ions in the solution, but also the total concentration of the solution determine the ratio of the adsorbed phase. An important conclusion is that the clay prefers the counter ion of higher valence and that the preference increases with dilution of the solution. Anion exchange has also been observed in the soil. It has been suggested that the edges of the clay particles, particularly kaolinite, may carry positive charges, because of broken bonds, and a positive electric double layer is formed. Then the anion exchange is similar t o cation exchange. There may also be specific adsorption of anions to the colloids of the soil that may alter the apparent charge. The phosphate anions are apparently specifically adsorbed to clay minerals, and can enter into a limited amount of exchange. Some of the amorphous materials and the organic matter in soil may carry a positive charge at times and thus allow for anion exchange. The charge on some of these materials may be positive or negative depending on the pH of the soil solution.

Weight

Volume

Air - - - - -Water - ---

-

--

- - -

-

A

-

-

Weights and volumes in soil.

FIGURE 6.

SOIL WATER One of the most important ingredients of the soil is the moisture that fills the pores between the particles and aggregates. It is also one of the most dynamic properties. The water in soil is constantly moving by percolation, evaporation, use by plants, irrigation, infiltration, and other processes. Thus the water content of the soil may change in time and space. The relation between the water content and air content in the soil is very important for the production of crops. Thus, for example, if water is absent in the soil, though rich in essential nutrients, is barren, while excess water may turn the land into a worthless swamp. Water in soil contains dissolved salts which affect the soil properties as well as plant growth. It is therefore very important that water be of good quality. The problems of soil water quality will be treated in a separate chapter. Good irrigation will keep the soil water between lower and upper limits which d o not restrict plant growth, harm the soil, or waste water. Therefore an understanding of the behavior of soil water is fundamental. The terms soil water, soil moisture, and soil solution are used interchangeably. Volume Weight Relationships A soil unit can be schematically divided into its three phases using weights or volumes as given in Figure 6 . Soil porosity, n n =

Void volume Total volume

Vv -Vt

Void ratio, e e =

Void volume Volume of solids

-

- Vv Vs

S. .

O x K)5

-

:

- ~ '^

50

75

-

'

-

- 6

_

M

i

|

-1

Hygroscopic

^^

:j

I

: a5 5 - 10 - -

:

980

5

P

-~ x 10

^4J -- 31^23 F 4 J 5 - - 14,125

Z

IO

„

93 -

.

-

30.6

1

-j

-

-10 *c -

13.6

---

98

. -4.0*C

--

-

*"*

1

99

Unovoilable soil moisture

- t - 5 : J. " -* Colloiool 47 -

-I.I2°C

l|jp

-

- 4.B | ]

0.0002

Hygroscopic

. t3-^ . wmjng p^^4

l

5(

corffctint H

^°4) y J,oi*

Barelv

. r"^ '" " ' - -5 - ii i'i "1=-" " -0.2°C

2.7 - -

xlO 5

501 -

0,5

3-4 I

- -°rc i0-002

is.. »03 _. „ .. , _

-

-OX)4°C -

f|||

§S

[* ; Ii1! HfOTcZr,y

c.tt bllT

-

- 2.7 -

1 (t

J

;

H^ '

W

^

°05 -

"^ -|T:

-

.

!

0.098 -

„

" °'2

0.01 -Ifj5

Coarw sand

- 1 -

o

:

a009

? - O-001 x 10° NOTE! Zero tension can not be shown

-0 on this

scale

:

^

- :

1

g

:

-» - 2.0

-

1

moisture equival«nt

1 -

C

KiL.

Action porosity C limit

Subject damage

1 g

]

available

adjustment sluggish

'

i

:

~?«»

i

=

:

" '

Pine 3

??

:

10

-

R«W capacity

™W

£

i

-Maximum moisture hokfina '

capacity Saturation

CRC Handbook of Irrigation Technology

is F

Appearance

30

Table 4 SOIL MOISTURE DEFINITIONS

Volume 1

31

The water potential concept developed for a soil-water system can also be applied generally to the plant-water system. The two systems are often considered as a single soil-water-plant system. It can be seen that the general shapes of the water retention curves for the various soils (Figure 9) are similar although the amount of water retained at any potential varies according to the soil. Growth is undoubtedly related to the potential; thus there is a certain range of potential above which plants will wilt, whatever the soil type. It can also be seen from the curves in Figure 9 that at a certain moisture range the slope of the curve changes and the energy required to remove any additional water from the soil becomes very large. This occurs at moisture contents which are higher than the wilting moisture, where water is still available. Thus it can be assumed that the availability of water is not equal throughout all the range between field capacity and wilting moisture but that there is a certain moisture content below which plant growth may be considerably reduced. This is true not only because of the potential required, but also because the water movement at this range becomes very slow, as will be shown later.

MOVEMENT OF SOIL WATER Soil water moves in response to soil water potential differences. Water will move from points of higher water potential to points of lower water potential. As discussed above, depending on the soil type, the moisture content is different for the same potential; thus it is not generally true that water flows from high moisture content regions to low moisture content regions. Water can move as liquid, vapor, solid, or in any combination of the three phases. The flow is viscous as long as there is a continuous liquid phase, regardless of whether the soil is saturated or unsaturated. The vapor movement can be as diffusion, or mass flow. The viscous flow is important in wet soils, while the vapor movement is responsible for water transfer when the soil is dry. The potential differences causing water transfer are associated with the various contributions to the total potential. Thus we may define different groups of forces: (1) mechanical forces, such as gravitational, pressure, and capillary, and (2) diffusion forces such as vapor pressure gradients, concentration gradients, electrical gradients, and thermal gradients. Saturated Flow (Darcy's Law) Consider a soil section of cross section area A, and length L saturated with water. There is a piezometric head difference across the section Ah. The volume discharge of water Q was found experimentally by Darcysa as described by the following equation:

where Q is the discharge in cm3/sec, A is the cross area in cm2, L the length in cm, and the head difference h is given in cm. The proportionality coefficient K is called the hydraulic conductivity. The above equation can be written in a more general way which is applicable also for three dimensional flow as:

where q is the specific flux, i.e., discharge per unit cross section, and i is the hydraulic gradient (dimensionless). Thus the hydraulic conductivity K with dimensions of cm/ sec may be defined as the rate of flow through a unit cross section normal to the flow

32

CRC Handbook of Irrigation Technology

\

Reference

Screen datum level

i1 I

II

FIGURE 11. Diagram of an experiment to determine the hydraulic conductivity of a saturated vertical column of homogeneous soil when water flow is upward.

under a unit gradient. The hydraulic conductivity K depends both on the properties of the fluid (such as its viscosity) and on the soil (such as shape and size of pores). It is sometimes convenient to use the reciprocal of the hydraulic conductivity: R = 1/K which may be called the hydraulic resistivity. The hydraulic conductivity K is usually determined experimentally in a permeameter (Figure 11). It is theoretically unimportant whether water enters at the top and leaves at the bottom, or conversely. The heads h, and h2 are measured by two piezometers. In general the saturated hydraulic conductivity depends on many factors. It may vary in the field from point to point in nonuniform soils. It may vary in time or due to prolonged flow in unstable soil, when the structure is changing, in swelling and shrinking soils, or because of any other process affecting the geometry of the porous medium. The hydraulic conductivity depends upon the soil properties of texture (d - average diameter), porosity (n), shape of pores ( S ) , and upon the liquid properties of viscosity q and specific weight y.

where k is called the permeability. The best known porosity function is the Kozeny-Carman formula:

The nondimensional shape factor is highly complex and varies from 1/110 to 11220, often around 1/160. Generally the saturated hydraulic conductivity is high in sandy soils (K = 10-' to 10-2cm/sec) which are pervious or permeable, and is lower in loams (K = 10-3to 10-4 cm/sec). In nonaggregated clay the hydraulic conductivity may be lower than 10-Scm/

Matric potential

, Y,,,

(joules/ kg)

FIGURE 12. Hydraulic conductivity as a function of the matric potential for several soils.

sec. When the hydraulic conductivity of a soil is lower than 10-6cm/sec the soil may be considered impervious or impermeable.

Unsaturated Flow Buckinghamz' indicated that an equation similar to Darcy's Law can be applied to unsaturated flow. However, the hydraulic gradient should be regarded as the matric potential, or suction gradient, and the hydraulic conductivity K , is no longer a constant, but varies with the moisture content, or matric potential. The decrease of the hydraulic conductivity with decreasing water content or increasing suction can be explained by several factors. When the soil is saturated all of the pores can conduct the water. No air-water interfaces exist. When the soil becomes unsaturated the large pores are first emptied, meniscuses are formed, and as the water is held more tightly by the soil the more slowly it is able t o move. As the soil moisture decreases the portion of the soil pore space that is occupied by air (which is a nonconductor of liquid flow) increases. The effective cross section area for conveyance of water becomes smaller, and the hydraulic conductivity decreases. In unsaturated flow the water moves through smaller pores which offer much higher resistance to flow. Comparing fine textured and coarse textured soils it is found that while in the wet range the coarse textured soils are better water conductors, the opposite is true when the soils become drier. The unsaturated hydraulic conductivity is greater in the fine textured, clay soils. In sandy soils flow ceases at a relatively high water potential and they become practically impervious. An example is shown in Figure 12. The hydraulic conductivity is given on a log scale to enable comparison of various soils. It is worthwhile to note that the field capacity is reached when the hydraulic conductivity becomes very small. Hence in clay soil this state is not sharply defined as in the coarser soils. In the higher moisture contents the unsaturated hydraulic conductivity can also be determined with a permeameter as shown in Figure 13. Relations between the unsaturated hydraulic conductivity and the matric potential head v , were suggested by Gardner and others as follows:

34

C R C Handbook of Irrigation Technology

FIGURE 13. Diagram of an experiment to determine the hydraulic conductivity of an unsaturated homogeneous soil.

a,b are experimental constants, m 2 . 2 for clay soils, m 2 . 4 for sandy soils. K = KO exp (-ag)

where K, is the saturated hydraulic conductivity. A relation between the hydraulic conductivity and moisture content was suggested by Childx5

where K, is the saturated hydraulic conductivity, 8 the volumetric water content, n is the porosity, and s is the degree of saturation. Wetting Front, Infiltration Water that moves into unsaturated soil may be supplied by irrigation, rainfall, flooding, or seepage from water channels. Sometimes the entire soil surface is wetted and sometimes only a part of the surface is in contact with water. If the entire soil surface is wetted, movement will be in only one direction, vertically downward. If only part of the surface is wetted, as in furrow or drip irrigation, water will move both downward and laterally. In very dry soil, the lateral movement may be as great as the downward movement for a time. When water is applied by sprinkler, rainfall, or drip irrigation the rate of water entry into the soil is controlled by the water application rate, provided these rates are small. For high rates of water application a thin layer of water forms on the surface and the rate of movement is controlled by the soil. When water infiltrates the soil from the surface water layer, it fills almost all the pores at each successive depth interval, and then moves to the next depth. This gives the visual impression of a sharp wetting front. It has been observed that water advances

Volume I

Time

35

(minutes)

FIGURE 14. Infiltration curves for several soils. (After Free, G. R . , Browning, G . M., and Musgrave, G. S., USDA Tech. Bull. 729, U.S. Department o f Agriculture, Washington, D.C., 1940.)

in soil as a front of moisture. In dry soil the edge of the front is observed to be abrupt. Water behind the wetting front (in the wet soil) flows quite rapidly since the hydraulic conductivity is relatively high. When the water reaches the dry soil at the wetting front, the hydraulic conductivity of the dry soil is so low that it appears that the water accumulates behind the front until the soil is almost saturated and then moves on, as the dry soil absorbs the water. High temperatures may develop at the wetting front due to the heat of wetting. It is observed that the wetting front is more abrupt as the soil is drier. Also, the time required to wet the soil to a given depth is greater as the soil is drier. The shape of the wetting front is dependent on the ratio of the hydraulic conductivities in the moist soil and the soil into which the water is infiltrating. Water moves into homogeneous soils at about the same rate in all directions when the soils are uniformly irrigated. In this case the gravitational potential becomes more important relative t o the matric potential, and the water moves progressively downward more rapidly than laterally. The equations for the transient state flow in the wetting process are difficult to solve because K is not constant. Most of the expressions for infiltration of water into soil, both empirical and analytical, apply only to uniform soils. Two of the more commonly used expressions will be presented. The amount of water that will infiltrate a homogeneous soil in a unit time, under field conditions, decreases as the amount of water that has already entered the soil increases. Thus the curve relating total amount that has infiltrated into soil as a function of time is not linear. Experimental curves are shown in the solid lines of Figure 14. At the beginning the rate of infiltration is high. It

36

CRC Handbook o f Irrigation Technology

0

X) 40 60 80 100 120 140 Time hin)

FIGURE 15. Infiltration rate as a function of time. Aiken clay loam - good structural stability; Houston black clay - low structural stability. (Data of Free, G. R . , Browning, G. M., and Musgrave, G. S . , USDA Tech. Bull. 729, U.S. Department of Agriculture, Washington, D.C., 1940. With permission.)

decreases with time and approaches a constant value, which is known as the infiltration rate, expressed in millimeters of water depth per hour (or inches per hour). The infiltration rate i (i = Qw/A) is empirically described by Kostiakov7"as:

where t is time, and c and a are parameters that depend on the soil and its physical conditions; the curves obtained are shown by the dot-dash lines on Figure 14. Another equation has been introduced by PhilipI4"(dashed line on Figure 14).

in which S, is a soil parameter called sorptivity, and A, is a second soil parameter that depends on the ability of the soil to transmit water. Infiltration rate as a function of time is shown in Figure 15. The rate is high at the beginning, mainly due to some cracks present in dry soils. Then it falls down, and in clay soils may approach nearly zero. In downward flow the wetting front will reach a depth according to:

where D, is the wetting front depth in cm, D, is depth of water applied in cm, O,, is the volumetric moisture at field capacity and Oi is the initial volumetric moisture of the soil. The infiltration rate will give the time required to irrigate the field with a given amount of water. Thus a soil having an infiltration rate of 10 mm/hr (average) will

Dry mass water percentage, P m

0

5

10

20

15

25

30

35

FIGURE 16. Soil water profiles at various times after water was added at the soil surface. (After Staple, W . J . and Lehane, J . J . , 3. Agric. Sci., 34, 329, 1954. With permission.)

absorb a water application of 100 mm in 10 hr. When infiltration ceases, after irrigation is finished the wetting front will have reached a certain depth. Then there is a redistribution of the water (Figure 16), the moisture above the front is reduced, and the front slowly moves down to where moisture increases. However, even after field capacity is achieved the moisture content in the profile is not uniform, and there is, at some depth, an abrupt change from moist soil to a drier one, as shown in Figure 16. Typical infiltration rates for irrigating different soils are:

Sand Sandy loam Silty loam Clay loam Clay

> 30
14) is it recommended to determine the ESP.

WATER QUALITY Introduction All irrigation water contains dissolved or suspended materials which influence the soil structure and, since it is relatively easy and inexpensive, classification systems are usually based on the chemical analysis of water. The use of various types of water for irrigation makes it necessary to look for a classification system which is different from that used for industrial or sanitary purposes. Certain criteria are total concentrations of soluble salts, or salinity hazard (osmotic potential); the concentration of sodium relative to calcium and magnesium, or sodium or alkali hazard; and the concentration of boron, chloride, or other constituents that might be toxic or harmful. The factors to be considered in recommending the classification system, limits, and restrictions depend on local conditions in relation to climate, soils, and plants. Irrigation water quality is determined by its potential to cause problems which will reduce yields unless special management practices are adopted to maintain or restore maximum production capability under given conditions. The evaluation must be done in terms of the specific use and potential hazards. Salinity Hazard Water is classified for salinity hazard according to its electrical conductivity ECi, given in mmho/cm, at 25"C, as follows: 3.0 low quality. In many arid countries most of the water falls in the moderate to low quality groups. With this water it is still possible to practice successful agriculture. Sodium Hazard When a soil is irrigated with waters high in sodium, the structure is adversely aflected and permeability is usually decreased. Sodium also affects plant growth. It is thus considered to be one of the major factors governing water quality. The establishing of criteria for sodium hazard is especially complex because an imbalance of sodium to calcium and magnesium may lead to nutritional as well as structural problems. Even if the nutritional aspects are ignored, the structural problems are far from simple. The sodium hazard is determined by the SAR of the irrigation water. This value does not, however, specifically include the bicarbonate effect, or the possibility of gypsum present in the water. It is evident that the SAR increases as the total concentration increases even though the relative concentration of ions remains the same. The presence of sodium in irrigation water influences the physical properties of the soil, particularly the permeability, by affecting the swelling and dispersion of the clay. Experiments showed that a rather pronounced reduction in hydraulic conductivity occurs

Table 3 CLASSIFICATION O F IRRIGATION WATER BASED ON BORON CONCENTRATION7 Boron index

Concentration

2

4.0

1

Boron toxicity hazard Generally safe for sensitive crops Sensitive crops will generally show slight to moderate injury Semitolerant crops will generally show slight to moderate injury Tolerant crops will generally show slight to moderate injury Hazardous for nearly all crops

Table 4 TENTATIVE CLASSIFICATION O F IRRIGATION WATER BASED ON CHLORIDE CONTENT Chloride index

Concentration (meq/l)

1 2

8

Chloride hazard Generally safe even with sensitive plants Sensitive plants (low tolerance) will generally show slight to moderate injury Medium tolerant plants will generally show slight to moderate injury Slight t o moderate injury for some tolerant plants

when the exchangeable sodium percentage is high and total concentration is low. Thus the evaluation of the sodium hazard should be related to salinity of the water. Water of EC >0.75 mmho/cm and SAR a; and the angle p between the perpendicular plane CD and the vertical CE, which in Figure 5(a) equals a changes in Figure 5(b) to p', such that tan P' = h sin a / Kh cos a = 1/K tan a , or p' < 0 = a . The larger the distortion factor K, the steeper seems the channel bottom in relation to its undistorted presentation, a %- a , and the nearer seems a cross-section perpendicular to the bottom to a vertical section, p' Q p. For example, for a relatively large bottom slope I = 10 O/oo,or sin a = 0.01, a distortion factor K = 10 causes a = 0.573" to change to a' = 5.71 1" = 5'42'39.2'' (from tan a' = 10 tan a), and causes = a to change to p' = 0.057" = 0°03'26.3" (from tan p' = 1/10 tan a). Hence, in distorted presentation the bottom slope is exaggerated, and the perpendicular sections appear almost vertical (in this example less than 3.5 minutes off vertical).

AB

m -=

FLOW REGIMES The flow is said to be uniform in a stretch if a V / a s = 0, or, prismatic channels, = 0. The flow is said to be nonuniform or varied in a stretch if a V / a s # 0, or in prismatic channels, a h/ a s # 0. The nonuniform flow is accelerated if a V/ a s > 0 (or a h/ a s < 0), with V a V/ a s being the convective acceleration; or declerated if a V/ a s < 0 (or a h/ a s > 0). The flow is steady if a V/a t = 0, and unsteady if a V/a t # 0. The unsteady flow is accelerated if the local acceleration a V/ a t > 0; or decelerated if a V/ a t < 0. Open channel flow is laminar if the flow Reynolds Number Rq = VR/u < 500, and turbulent if Re > 1000; it is subcritical, tranquil, or streamingif the flow Froude Number Fr = v/fgZ < 1; it is critical if Fr = 1; and it is supercritical, rapid, or shooting if F r > 1.

a h/a s

Even in perfectly built and meticulously finished artificial canals, of uniform slope and rectilinear alignment, there is almost no chance to find actual steady and uniform flow. Minor disturbances in direction or gradient, lining material or erosion, or even capillary effects may cause changes in flow and velocity, and the flow may no longer be considered steady and uniform. Nevertheless, the basic theory of flow in open channels was developed for the case of steady and uniform flow, and serves as the basis for considerations of all other types of flow, varied in time and/or in form. In steady flow a V / a t = 0 and in uniform flow in a prismatic channel also a V/a s = 0 and a h / a s = 0. Hence V = constant and h = constant, and so the bottom line, the free surface line and, because VZ/2g = constant, also the energy line, are all parallel to each other, J = i = I (Figure 6) The body of liquid in a stretch of channel of length L is isolated by two plane sections, perpendicular to the bottom, and one cylindrical-surface section, eliminating the liquid from the solid channel boundary, and is shown in undistorted presentation in Figure 7. The forces acting on the liquid body, over the section surfaces, are also shown. Since the flow is assumed to be steady and uniform, no accelerations occur, and the system of forces acting on the liquid body must be in equilibrium. The pressure forces

98

CRC Handbook o f Irrigation Technology

FIGURE 6.

FIGURE 7.

Steady uniform flow.

Isolated liquid body in uniform flow.

p,A, and p2Az, being of equal magnitude qnd opposite directions, cancel out: hence, in the direction of + S: W sin a

-

P L T ~= 0

Now, with I = J = th,/L in the flow under consideration, we may transform the last expression to To =

yR

8hf

L

The head- or energy-loss over the stretch of length L was a so-called longitudinal loss only and may be expressed by the well known Darcy-Weisbach formula as:

where h, = longitudinal loss; f = so called friction factor (nondimensional); and V = mean velocity. By comparing the two expressions for head-loss we have:

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99

and substitution of this into the equilibrium equation above gives

This is one of the oldest open-channel-flow formulas for steady uniform flow of water and was arrived at empirically by the French engineer Antoine ~ h & y (1718-1798) as early as 1775. The coefficient C, known today as the ChCzy coefficient, is dimensional, [C] = [\/g] = LU2T-',and its values in metric units vary from about 10 to 80, with 40 being a reasonable mean value.

OTHER UNIFORM FLOW FORMULAS With Ch6zy1s C being dependent exclusively on the engineer's ability to estimate and choose, other engineers and researchers tried to devise expressions for C based upon rational estimates of channel characteristics such as hydraulic radius R, bottom slope I, and some kind of roughness coefficient. The best known - and certainly most cumbersome - among these was a formula published in 1869 by two Swiss engineers, Emile Oscar Ganguillet (1818-1894) and Wilhelm Rudolf Kutter (1818- 1888):

Here n was a roughness coefficient based on several hundred experiments, among others some on the Mississippi River in the U.S., and later adopted for use in connection with Manning's formula. A few years later, in 1897, the French engineer (and assistant to Darcy) Henri Bazin (1829-1917) suggested a simpler formula, without reference to the bottom slope I:

where R is the hydraulic radius and m is a roughness coefficient varying from 0.055 (for channels with smooth cement lining in good condition) to 4.85 for natural watercourses in poor condition, covered by stones, growth of vegetation, etc. (Table 1).

MANNING'S UNIFORM FLOW FORMULA By far the most popular uniform flow formula is connected with the name of the Irish engineer Robert Manning (1816-1897). In 1889 he suggested a formu1a:V = KR2'3 11'2, which he considered to be in good agreement with data then available.

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Table 1 BAZIN'S VALUES O F m FOR VARIOUS CHANNELS Condition Type of channel

Excellent

Good

Fair

Poor

1.05 1.75

1.38 2.40

1.75 3.50

2.10 4.58

0.055 0.50 1.05

0.055 0.22 0.69 1.38

0.14 0.275 1.05 1.60

0.22 0.33 1.38 1.75

Artificial channels Straight, regular earth channel Earth channel with vegetation, stones, etc. Channel excavated in rock Natural channels Channel well maintained Channel with vegetation, stones, etc. Lined channels Concrete lining with smooth cement surface Wooden boards or a smooth stone lining Masonry lining with cement mortar, coarse cutting Masonry lining without cement mortar, coarse cutting

Later, the coefficient K was related to Ganguillet-Kutter's n

and so today's form of Manning's formula has been arrived at: 1 V =-

n

RY3

I1I2

(metric units)

where V = velocity in m/s, R = hydraulic radius in m, and I = slope in m/m.

v = -1.486

I1/1

R Y ~

n

(metric units)

where V = velocity in ft/sec, R = hydraulic radius in ft, and I = slope in ft/ft. Values of n for use in Manning's formula are listed in Table 2. Other values are given in Tables 3 and 4. (See also Figure 8.)

SOLUTION OF PROBLEMS IN STEADY UNIFORM FLOW The solution of problems will at first be tackled in a general, algebraic way, with clear definitions of known and unknown quantities, and schematic outlays of solution procedures. Later, illustrative examples will be given and solved. Listing of Basic Cases Case

Given

Required

Case

I

geometry depth, h roughness, n slope, I

Q

111

I1

geometry h n

I

Q

Given geometry

Required h

Volume I Table 2 MANNING ROUGHNESS COEFFICIENT (n) Channel surface types Glazed coating or enamel Timber

Metal

Masonry

Stonework

Earth

Condition

n

Perfect order Planed boards, carefully laid Planed boards,old or inferior Unplaned boards, carefully laid Unplaned boards, old or inferior Smooth Riveted steel Corrugated metal Cast iron, new Cast iron, tuberculated Neat cement plaster Sand and cement plaster Finished concrete Unfinished concrete Concrete in bad condition Brick, good condition Brick, rough Smooth, dressed ashlar Rubble set in cement Fine, well-packed gravels Dry rubble Regular, good condition Regular, good condition Regular, fair condition Regular, some stones and weeds Regular, poor condition Winding, irregular, but clear Obstructed with debris and weeds

Solution Flow-Charts Case I

and, if requested:

Case I1

Case I11

and, after arithmetic simplifications, equation for h: f(h) = constant from above, by trial and error:

-

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Table 3 VALUES OF R% IF4 MANNING'S EQUATION

Table 4 VALUES OF I !h IN MANNING'S EQUATION

Examples (metric) Similar examples in the English System follow at the end of the chapter.

Case I Example 1 Find the discharge of water flowing at a depth of 1.8 m in a rectangular channel 2 m wide and lined with cement mortar (n = 0.013), and having a (longitudinal) slope of 2°/00.

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FIGURE 8.

Example 2

Nomogram for the solution of Manning's formula.

Case ZI Example 3

Case III Example 4

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Example 5

OPTIMAL CROSS SECTION If a given discharge Q has to be conveyed through a canal built in a certain soil (or lined with a given lining), then the surface of contact limits the velocity to a maximum value V and, hence, the canal has to be of a cross-section A = Q/V. The type of soil, or choice of lining, may also require a certain cross-section geometry; an unlined rectangular channel cannot be excavated in noncohesive soil, and a trapezoidal or trian-

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107

gular cross section there will be possible only with a side slope exceeding a minimum m. With the general geometry of the channel cross section chosen, and the cross-section area prescribed, the section and the channel will be considered optimal when the building expenses will be minimal. This will be the case when the wetted perimeter and therefore, the lining per unit length of channel, will be minimum. A trapezoidal cross section will be chosen for the following analysis, as it implies both a rectangular (with m = 0) and a triangular (with b = 0) cross section, too. With Q and V given, the cross-section area will be A = Q/V. But A, for the trapezoidal cross section considered, may be expressed by

(a) A

-

bh

-

mh2 = 0

and the wetted perimeter by (b) P

=

b +h-J2

= P(b, h , m)

Now, for this channel to be least expensive, and hence, considered optimal, P, as expressed by (b), has to be minimum. However, the three arguments of P - b, h, and m - are interconnected by the limiting equation (a). P,,, may now be calculated according to Lagrange. An auxiliary function is defined:

a@ ab

= l-hh

If m is prescribed, we have from a +/a h = 0: b/h = 2(\J l + m2 - m), and from = bh + mh2 = h2 (b/h + m) = h2 ( 2 f F i i F - m). Hence, from (b):

a+/an = 0: A

and, by definition:

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FIGURE 9.

Optimal trapezoidal cross section.

Let h (Figure 9) be the depth of flow in the trapezoidal cross section shown, and X the two perpendiculars on the side-walls y. Then, if the section is optimal, and R = h/2:

1

or:

-2

and

x = h

1

bh+yx = - bh+yh 2

Hence, in an optimal trapezoidal (rectangular or triangular) cross section with prescribed m, the hydraulic radius is equal to half the depth of flow, and a semicircle may be inscribed into the cross section. If m may be considered variable, too, we have from a +/a m = 0:

or m = $313. With m = cot a we have cot a = \/7/3 and a = 60". Hence, in the most general case of trapezoidal cross section, we have for optimal conditions R = 1/2 h and a = 60°, showing that the optimal cross section is one half of a hexagon. Example 6 Find the bottom width b and the depth of flow h in a trapezoidal canal conveying 6 m3/sec of water at a velocity of 1.5 m/sec at optimal conditions. The side slopes are prescribed to be 1 vertical to 2 horizontal (m = 2).

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FIGURE 10. Special cross sections.

SPECIAL CROSS SECTIONS Figure 10 shows (a) a very wide rectangular cross section and (b) a wide shallow cross section of a natural water course. The hydraulic radius of the special cross section (a) will be, because of h > h it is seen that P R = -A- - A= h

-

B:

-

B

P

For very wide rectangular cross sections the hydraulic radius may be replaced by the depth of flow h; a n d for wide and shallow natural water courses the hydraulic radius may be replaced by its mean d e p t h E

LIMITING VELOCITIES According to the type of soil in which a channel is built, certain limitations are imposed o n the velocity of flow. When velocities excede certain maximum values, particles of soil are dislodged from the sides and the bottom of the channel, and we experience scour o r erosion caused by tractive forces. When velocities fall below certain minimum values, solid particles carried by the stream as sediment load may start to settle, a n d deposition, sedimentation, o r silting occurs. In many types of soil the two limits of the velocity, the maximum, avoiding scour, and the minimum, preventing sedimentation, are rather close to each other and their values must be calculated properly a n d accurately. T h e boundary shear stress T, has been determined previously (See Section o n Steady Uniform Flow):

Limiting values of T, (sometimes called "tractive force" per unit area) a t the incepti:m of scour in various soils were determined empirically by Fortier and Scobey and are shown in Table 5. F o r a given channel the boundary shear stress T, is calculated and compared t o the limiting value of T,. If T, < T, n o scour will be expected.

Example 7 Given a trapezoidal channel, m

=

2, b

=

4.0 m , n = 0.025, and Q

=

10 m3/sec of

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Table 5 TRACTIVE FORCE VALUES A T INCIPIENT SCOUR (7,)

Clean water

Water containing colloids

Type of soil

kg/ml

Ib/ft2

kg/m2

Ib/ft2

Fine sand, sandy loam Silty loam, loam Clay, fine gravel Mixture of silt and gravel Hard clay, gravel

0.15 0.25 0.35 1.20 1.50

0.031 0.051 0.072 0.245 0.301

0.35 0.75 0.75 2.20 3.30

0.072 0.153 0.153 0.450 0.675

clean water at a uniform velocity of 2.0 m/sec. Check whether the tractive force is less than the assumed limiting value of T, = 1.5 kg/m2. Solution:

The tractive force, o r boundary shear stress T,, is larger than the limiting value; hence scour will occur (Table 6). An expression for a "critical velocity, V," was proposed by Robert Gregg Kennedy (1851-1920) in 1895, based on studies of British-Indian irrigation projects in the Punjab (today Pakistan):

where V, . . . is the "critical velocity" in m/sec; h . . . is the depth of flow in m; and C = 0.37 for very fine soils, 0.55 for fine, light, sandy soils, 0.66 for sandy loamy silts, and 0.71 for coarse silt. The critical velocity V, should cause neither scour nor sedimentation. But in engineering practice the minimum, nonsilting, velocity is assumed t o be

Table 6 MEAN VELOCITY VALUES A T INCIPIENT SCOUR Permissible mean velocity V, (m/sec)

Clean Water m/sec

Type of soil

ft/sec

Water containing colloids m/sec

ft/sec

Very fine sand Sandy loam Silty loam Alluvial silt, without colloids Dense clay Hard clay, colloidal Very hard clay Fine gravel Medium and coarse gravel Stones

FIGURE 1 1 .

Specific flow energy.

and the maximum, nonscouring, velocity to be V,,,

=

1.20vc

SPECIFIC FLOW ENERGY RELATIONS As stated earlier, the specific energy related at each cross section to the channel bottom there is termed "specific flow energy" or, after Boris Alexandrovitch Bakhmeteff (1880-195 l), "specific cross-section energy". Often, the terms "flow" or "cross section" are omitted and "specific energy" is used as related to the channel bottom - with a tacit understanding that it will be clear from the context to what kind of specific energy reference is being made. Variation of Specific Flow Energy with Depth at Constant Discharge In Figure 1 1 an irregular cross section is shown, with a steady discharge Q of water

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FIGURE 12.

~ ( h for ) Q

=

constant.

flowing at a mean velocity V , through the cross section of area A, at depth h and top width B. By definition, the specific flow energy there is

where V and A are (in steady flow) both dependent on h (only). At any other depth, the same discharge could pass the cross section, V and A would differ, and the specific , a constant Q, flow energy might assume another value. Let us observe how ~ ( h ) for changes with h (Figure 12). As shown above, the flow energy is expressed by two terms:

where the first is the kinetic energy term

and the second

presents the potential energy. The graphs presenting ~ , ( h and ) ~ ~ ( are h ) shown in Figure 12 by two broken lines, f 2 = h bisecting the right angle a t 0, and E, = Q/(2gA2) being hyperbolic in nature, i.e. approaching asymptotically the two coordinate axes. With the depth h approaching zero, h 0, the area (see Figure l l ) will also approach zero, A 0, and hence +

+

will grow to very large values, E , m; with the depth h growing to very large values, m, the area will grow too, A -* m , hence E I will be nearing zero value, E, 0h all of which is the meaning of ~ , ( h ("approaching ) asymptotically the two coordinate axes"). +

+

+

Now, E is a superposition of the two terms, E, and E,. When h 0, E, grows large while EZ = h grows very small, E Z -, 0. Hence, the value of E "approaches asymptotia,E, -* 0 and EZ -, cally" E, for h -,0. By the same way of reasoning, when h and E approaches asymptotically EZ.If, finally, E grows very large, E for both h -, 0 and h a, and the dependence between E and h is continuous, E must pass through a minimum value, for a value of h somewhere between 0 and a,0 < h < a.The full-line curve in Figure 12 answers to all the conditions imposed and presents graphically (and qualitatively) the relation E = €(h). And now let the value of h for which E = E,, be determined. Mathematical analysis shows that E = €(h) will pass an extreme value (in this case, evidently, a minimum) for that value of h which makes the first derivative of E with respect to h ( d ~ / d h ) disappear, d ~ / d h= 0. +

+

+

+

Inspection of Figure 11 will show that an addition of dh to h will increase the area A by d A = Bdh, and, hence dA/dh = B. Therefore

and this, with B = B(h) and A = A(h), is again a function of h. For a value of h, which we will designate h, (critical depth), we will have B, = B(hJ and A, = A(hc), and

(A ) dh h=h,

= 0. or -

QZ

BC

7 +l = 0 gAc

The equation

enables us to find, sometimes by trial and error, the value of the critical depth, h,. From

we have

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CRC Handbook of Irrigation Technology

whereKCand V, are the "critical mean depth" and the "critical velocity", correspondingly (meaning: "mean depth" and "velocity" at critical conditions, or at depth of flow h = h,). We see also that, at critical conditions

or, remembering that Fr =

v was defined as flow Froude Number,

G

Hence, for h = h, -. Fr = Fr, = 1, and the flow is said to be critical. When h > h,, we have A > A,, usually also >K,,and, with Q = constant, V < V,; hence: for h > h, -, Fr < 1, and the flow is said to be subcritical, tranquil, or streaming. Similarly, for h < h, Fr > 1, and the flow is said to be supercritical, rapid, or shooting. The minimum value of E will be +

or, remembering that

which is also shown in Figure 12. From what was shown above it follows also that

and this may be shown to be the celerity or velocity of propagation of a small disturbance (small surface wave) in a liquid at depth h,. Looking back at Figure 12, it will be seen that a discharge Q may be conveyed through a channel, at a specific flow energy larger than E , ~ , , E > E,;,, at two distinct depths, h, and h*. The first of these depths, being h, < h,, shows the corresponding flow to be supercritical while at h2 > h, the flow is subcritical. The two depths, corresponding at a given Q to a certain E , are called alternate depths.

Examples Example 8 Find the critical depth h, and the minimum specific energy E , ~ , in a rectangular chan-

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115

nel 2.0 m wide, conveying Q = 8.2 m3/sec of water. If Manning's n = 0.030, determine I,, i.e., the longitudinal slope a t which the given Q would pass the channel a t h = h,, a t uniform flow conditions. T o find h,:

Example 9 A flow of water of 14 m3/sec passes through a rectangular channel 2.8 m wide. Find the critical depth h,, the minimum specific energy E,;,, and the alternate depths a t E = 1.2 E,;,. If Manning's n = 0.020 find I,, I, and I,, as well as Fr, and Frz.

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By trial and error: h, = 0.906 m

and from this:

and

h, =

Now, to find 1

1.554 + J 1 . 5 5 4 ~ + 5.632 2

=

=

(S)'

Fr = l = Fr,

2.196m

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1 17

Example 10 In a trapezoidal channel of 2.0 m bottom width and side-slopes 1:l flow 16 m3/sec water. Find the critical depth h,, the minimum energy E,,, and the critical velocity V,.

By trial and error:

And from here:

Example 11 If in the previous example E ing Froude Numbers.

=

2.5 m, find the alternate depths and the correspond-

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CRC Handbook o f Irrigation Technology

By trial and error:

and from here:

V, = 5.65 m/sec; Fr, = 2.13

>1

Again, by trial and error:

and from here:

Variation of Discharge with Depth at Constant Specific Flow Energy From the expression for specific flow energy,

an expression may be derived showing the variation of discharge Q with depth h, at a given constant specific flow energy, r = constant:

For h = E evidently Q = 0 , and h = 0 the area will be A = 0 , and again Q = 0 (Figure 13). For 0 < h < E a maximum value for Q, Q,,,, must be expected. Now, as above, the extreme (maximum) will occur for a value of h making dQ/dh = 0:

Volume I

4

119

I

Q (h)

b

max FIGURE 13.

Q

max

Q(h) for c

=

constant.

Let h' be the value o f h for which dQ/dh = 0: hence B' 2B' (&-h') - A' = 0, o r E. - h' = A'/2B'. The solution of the equation

=

B(h') and A ' = A(h'), and

will provide the requested value h', and the maximum value of Q will be

.2 regrouping of the last expression shows that h

=

h' satisfies the equation

which indicates that if Q,,, in Figure 13 equals Q = const. in Figure 12 the two extremes, Q,,, and E , ~ , will occur a t the same value of h, h' = h,.

HYDRAULIC JUMP Figure 14 presents a stretch of horizontal laboratory flume in which, by aid of a n upstream sluice gate a n d a downstream weir, water isssuing from a reservoir may be forced t o assume a certain set of depths of flow, h, and h, > h,, at which a standing roller wave, known also a s hydraulic jump, will form.

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-v -

7

reservoir

\

4-P

L,t

/ /

U V//\\~VI*/)EIVV\\//\\~/ \\MW\\// \\l/ \V/\\

I =o FIGURE 14.

FlGURE 15.

weir

5

Hydraulic jump.

Isolated body for hydraulic jump calculations.

Such a hydraulic jump occurs occasionally in natural streams, but more often it is artificially induced, because of its ability to extract from the water and dissipate efficiently large quantities of energy. For reasons of simplicity the following analysis of the hydraulic jump will be limited to a relatively wide rectangular channel, and the relation developed for the two depths, called conjugate or sequent depths, will be valid for rectangular channel flow only. The conservation of linear momentum principle, developed in elementary hydraulics, states that the vector-sum of all forces acting over the surface (control surface) of a n isolated body of liquid (control volume) is equal to the difference between the total out-flux of linear momentum and the total in-flux of linear momentum:

In Figure 15 the body of water isolated between the sluice gate and the weir in Figure 14, is shown.

Volume I

1

'i

0

;!

M min FIGURE 16.

M'M minl

M(h) for Q

=

121

-

M (h)

constant.

Substitution into the horizontal components of the vector-equation above leads to:

1

- $h,12 2

-

-1 ?bh2' 2

1 Q2 1 2 bh,, + - = -

gbh,

2

=

rQ2 -

-

gbh,

bh22 +

YQ, gbh,

Q gbh2

It is seen that the expression

assumes the same values for h = h, and h = h2. The function M(h), shown graphically in Figure 16, will, similarly to €(h), approach asymptotically the two curves given by M, = 55 bh2 and Mz = Q2/gbh and will, for a certain value of h, pass through a minimum value, M,,.. The value of h for which M(h) reaches its minimum will now be determined:

It is seen that M reaches its minimum for the same value of critical depth, h,, as developed previously in connection with E , ~ , (at Q = const.) and Q,., (at E = const.). For any value o f M > M,,,, there will be two distinct depths, and if they are maintained a hydraulic jump will occur. The two depths for a given Q and M, h, before

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the jump and h, after it, are called conjugate or sequent depths. The two depths are related by a n expression, which will be developed next. From the basic momentum equation we had: 1

Q2 2 b h 1 2 +- = gbh1

1

- bh 2

2

+

-g

gbh,

and from the continuity equation: Q = bh, V, =bh, V,

Now: 1

- b(hZ2- h,') = 2

b2h2v . gbh,

and, finally:

With h,, and hence Fr, = V,/gh,, known, this expression enables us to determine i n a rectangular channelthe conjugate depth h, causing a hydraulic jump to form. Now, with h,, h,, V,, and V, known, we have

and

The difference E , - E , = h, is the specific energy lost (dissipated) in the jump (per unit weight of flow), and N = yQh, is the energy ( n o t specific) dissipated in the jump per unit time (power).

Example 12 In a rectangular channel 2.4 m wide there is a flow of 9.6 m3/sec of water at a depth of 0.8 m . T o what depth must the water rise downstream for a hydraulic jump t o form? What is the (specific) energy loss along the jump and what the energy dissipation rate?

v

= -Q =p-

bh,

9.6

2.4 X

VIZ Fr,2 = -

gh,

0.8

- 5.0 m/sec

5.0, 9.81 X

0.8

=

3.184

Volume 1

N = -yQhf = 1000 X 9.6 X 0.121 = 1161

kg

sec

123

15.5 HPmet

GRADUALLY VARIED FLOW Definitions If the flow is steady ( a V / a t = 0) and nonuniform ( a V / a s # O), but the change of depth along the channel (dh/ds) is very small - so small, in fact, that everywhere the nonuniform flow can be closely approximated by uniform flow - the flow is called gradually varied flow. T w o basic parameters are used in the analysis of gradually varied flow, (a) the normal depth, h,, a n d (b) the critical depth, h,. The normal depth is the one and only depth a t which a discharge Q would flow in a given channel of roughness n and longitudinal slope I, under uniform flow conditions. T h e critical depth is the depth at which the specific flow energy E for a given discharge Q assumes a minimum value; it depends o n the discharge and the geometry of the channel cross section only, a n d is independent of any roughness coefficient like n. The Theory of Gradually Varied Flow Figure 17 shows a stretch of channel a t gradually varied flow. T h e energy gradient is, by definition (for steady flow):

but

and

dz ds

ds

-

I 1

d

2g

ds

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hence

-dh- --- I - J ds

C)z B

I

- 1 . Q2

/g

Now, the flow shown in Figure 17 is nonuniform and therefore h # h,. Had the discharge Q passed the given channel at uniform conditions, the depth would be the normal depth h, which may be calculated for given Q, n, I, and channel geometry. With h. known we may express: A, = A(h,), P, = P(h.), and R, = A./P, = R(h,). The bottom slope I may now be replaced by

But, as already stated, the actual depth of flow h # h.. Let us now ask what would have been the energy gradient if the discharge Q had passed the channel at the depth h as normal depth (i.e., a t uniform flow conditions). Then we would express A = A(h), P = P(h), and R = R(h). But, in uniform flow the energy gradient and the bottom slope are equal, hence:

The ratio J / I may now be expressed by:

At critical conditions, for h = h,, we have B, = B(h,) and A, = A(h,), and Qz/g = A,3/B, The ratio (QZ/g)/(A3/B) may now be expressed by:

With these expressions we have:

FIGURE 17.

FIGURE 18.

Gradually varied flow profile.

Water surface above both h, and h,.

Let us now investigate the variation of depth h with distance S, dh/ds. (a) h

-'

-

When the water level rises above both normal and critical depth it approaches a horizontal asymptote (Figure 18).

lim h-h,

dh

- -- 1 ds

1-1

. 1

- fc(hn)

=

0

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FIGURE 19.

Water surface approaching h,.

FIGURE 20.

Water surface approaching h,.

When the water level approaches the normal depth, it does so gradually, asymptotically (Figure 19).

lim h-h,

dh

- -- 1

1

.

- fn(hc) = 1-1

ds

m

When the water level approaches the critical depth, it does so abruptly, almost vertically (Figure 20): (d) h

-+

lim h-0

0 dh

-= ds

lim h-0

I-J

-= -Q >

A~/B

f 1A3--. = lim

h+O

'43

lim h+O QZ

-

Q2 -g

a

g

-

.B

fQZ I - 8 g ~ ~- 2 1

Q'B gA3

A

R

= f l i m P- = -f + o h+OB

8

When the water level approaches the bottom it does so at a slope dhlds = f / 8 (Figure 21).

FIGURE 21.

Water surface approaching bottom

FLOW PROFILES Types of Flow Types of flow can be classified: I . According to bottom-slope I I = I, ... critical flow I < I, ... river-type flow I > I, ... torrential flow 11. According to depth of flow h h = h, ... critical regime of flow h > h, ... quiet regime of flow h < h, ... shooting regime of flow 111. According to depth of flow variation dh/ds dh/ds = 0 ... uniform flow dh/ds > 0 ... retarded flow dh/ds < 0 ... accelerated flow Classification of Bottom Slopes Bottom slopes are: (a) descending, normal, or positive i f I = - dz/ds > 0; (b) horizontal or zero if I = - dz/ds = 0; or (c) ascending, rising, or negative if I = - dz/ds < 0. Descending or normal bottom slopes are: @steep, if 0 < I, < I Then there will also be: 0, < h, and V > V,

< h,

Ocritical, if 0 < I, = I Then there will also be: 0 < h, and V = V,

=

@ mild, if 0 < I < I,

Then there will also be: 0 < h, and V < V,

h,

< h.

It should be noted that the critical depth h, depends only upon the geometry of the channel cross section and the discharge, while it is completely independent of any roughness coefficient (n, C). On the other hand, the normal depth h,, depends on all the factors mentioned above, including the roughness coefficient. Hence, two different channels, having the same geometry and conveying the same flow at the same slope may be considered, either hydraulically steep, or hydraulically mild - depending on the roughness coefficient n or C. Not-descending bottom slopes are: @horizontal, if I = 0.

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Here the normal depth escapes to infinity, h, -+ and hence: 0 < h, < h,. A adverse, if I < 0. Here the normal depth has n o meaning, but h, is defined as a flow parameter. Classification of Flow Profiles A flow profile is the longitudinal section through the free water surface and except for the case of uniform flow it is a curved line, rising o r falling, convex o r concave, approaching limits asymptotically o r abruptly. Flow profiles (also called, for example, hydraulic profiles, o r backwater-curves) are classified in accordance with the bottom slope as:

S ... steep profiles, C ... critical profiles, M ... mild profiles, H ... horizontal profiles, o r A ... adverse profiles, a n d in relation t o the two parameters, h, and h, as type 1 curves, when above both h, and h,, type 2 curves, when between h, and h,, and type 3 curves, when below both h, and h,. horizontal 1

FIGURE F.

0Critical h, = h, oc

h=I

Steep orQflow profiles.

I

\ \

FIGURE H .

@

-

H Horizontal. hC< h, I= 0

horizontal

Mild or@flow profiles.

\e

-H W

t FIGURE I.

/

Horizontal or@flow profiles.

horizontal

FIGURE J .

\

Adverse or@flow profiles.

/

I

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CR C Handbook o f Irrigation Technology

Occurrence of Flow Profiles

Steep Slope

FIGURE K.

Examples ofQprofiles.

Critical Slope

FIGURE L.

Examples of Oprofiles.

Mild Slope

FIGURE M .

Examples of@profiles.

Horizontal Slope

FIGURE N.

~ x a m p l e of@rofiles. s

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C R C Handbook of Irrigation Technology Adverse Slope

FIGURE 0. Examples of@rofiles.

Examples (Metric) Example 13 A very wide rectangular channel (R = h) is designed with a bottom slope I = 2O/,,. The discharge flowing in the channel per unit width q ( = Q/b) is 8(m3/sec)/m. Two alternative linings are being considered for the project: (a) very fine, smoothened cement lining (Manning's n = 0.009), or (b) coarse stone lining (n = 0.035). Classify the bottom slopes for the two alternatives. What kind of lining would turn the bottom slope into critical-slope?

(a) (b) (c)

n = 0.009- h, = (178.9x0.009)0.6 = 1.331 m < h, h, < h,, hence the bottom slope is considered steep, S. n = 0.035 h, = (178.9 X 0.035)0.6= 3.006 m > h, h, > h,, hence the bottom slope is considered mild, M. h, = h, = 1.87m 1 .87 = (178.9 n)O n = 0.016. (Such n corresponds, for example, to concrete with clcar signs of formwork.)

-

Example 14 In a rectangular channel with Manning's n = 0.018, 2.2 m wide and having a longitudinal slope of 0.741 O / , , , 4.0 m3/sec of water are flowing. Classify the bottom slope. At a certain point along the channel the depth of flow is 1.80 m. What is the type of flow profile there ? Develop an appropriate expression and Calculate at what distance the depth of flow will be larger by 10 cm. Will that be upstream or downstream from the section at depth 1.80 m? Is the flow there quiet or shooting? Answer the same questions also for starting points at (g), h 0.50 m.

=

1.0 m and (h), h =

Let us first determine the normal and critical depths, h, and h,.

Hence h,

< h, and the bottom slope is considered mild, M.

Hence: h, < h,, < h and the flow profile is of the M1 type, with depth increasing in the direction of flow.

As an approximation: Ae

- e2 - E ,

-

As

-

-

-

I-J

p

As

-

Table 7 TABULAR SOLUTION FOR EXAMPLE 14

where the mean energy gradient J is given by the arithmetic mean of J 1 and J2 at the two ends of the stretch 1 - 2:

Now:

As =

€2 - € 1

I-J

and The calculations are performed in Table No. 7 at two stretches with assumed Ah = 0.05 m for each stretch. The Froude number at depth 1.80 m:

Hence, the flow is subcritical, quiet.

The flow profile is of type M2, depth of flow decreases with distance and depth 1.10 m will be upstream from point of depth 1.00 m. The distance was calculated in the table to be -48.0 m, or 48.0m upstream.

Hence, the flow is subcritical, quiet.

The flow profile is of the type M,, depth of flow increases with distance, and depth 0.60 m will be downstream from point of depth 0.50 m. The distance was calculated in the table to be + 7.98 m, or 7.98m downstream.

Hence, the flow is super-critical (shooting).

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Examples (English System) Example 1 Find the discharge of water flowing at a depth of 6.0 ft in a rectangular channel 6.6 f t wide and lined with cement mortar (n = 0.013) and having a longitudinal bottom slope of I = 2 per thousand.

Example 2 In a circular channel of diameter 6.6 ft flowing half full, at a bottom slope I 2.5 n/oo and n = 0.020, find Q and V.

=

Example 3 In a rectangular channel with depth of 6.0 ft and width of 7.2 ft, n = 0.020, and Q = 350 ft3/sec, find the bottom slope I.

Volume 1 Example 4 In a rectangular channel with a width of 6.6 ft, n = 0.018, Q I = 0.003, find the depth, h.

Let f (h) =

=

137

280 ft3/sec, and

( 6 . 6 h)"3 (6.6

+2

h)Y3

Solving by trial and error

Therefore h is close to 5.73 ft. Example 5 In a trapezoidal section (see drawing in Metric Example 5) the following is given: b = 10.0 ft, m = 2, n = 0.020, I = 0.001, and Q = 350 ft3/sec. Find the depth of flow, h.

Solve by trial and error

h is close t o 4.20 ft.

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Example 6 Given a trapezoidal canal with Q = 210 ft3/sec, V = 5.0 ft/sec, m = 2.0. Find the bottom width b and depth of flow h for optimal conditions.

Example 7 Given a trapezoidal channel, m = 2, b = 13 ft, n = 0.025, Q = 350 ft3/sec of clean water at V = 6.50 ft/sec. Check whether the tractive force is less than the limiting value of T, = 0.30 lb/ft2

The tractive force or boundary shear stress scour will occur.

T.

is larger than the limiting value; hence,

Example 8 Find the critical depth h, and the minimum specific energy rmi, in a rectangular channel 6.6 feet wide conveying 287 ft3/sec. If n = 0.030 determine the I, or the longitudinal slope at which the given Q would pass the channel at h = h, under conditions of uniform flow. Solution: When h = h,;

A' -QZ -

B

l3

Volume 1

R,

=

1.785 ft;

R?

139

= 1.471 ftY3

Example 9 Q = 490 ft3/sec flows in a rectangular channel b = 9 ft wide. Find the critical depth h,, the minimum specific energy E,~,, and the alternate depths at E = 1.2 E , ~ , If n = 0.020 find I,, I , , I,, Fr, and Fr,. Solution: When h = h , ;

A3 --

B

Q' g

By trial and error h, = 3.0 ft h, = 7.23 ft

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CRC Handbook of Irrigation Technology

Now, to find

I =

(

Volume I

141

Example 10 In a trapezoidal channel of 6.6 ft bottom width where m = 1 and Q = 560 ft3/sec, find the critical depth h,, the minimum energy E,(,, and the critical velocity V,. Solution:

A3

-= B

Q Z 6.6h + h Z ,g 6.6 + 2h

-

,

By trial and error

560' 32.2

9739

h, = 4.75 ft v -

Example 11 If in the previous example E Froude Numbers.

=

8.2 ft, find the alternate depths and the corresponding

By trial and error h, = 3.19 f t

And from here:

B,

=

Fr, =

6.6 + 2h, = 12.98 ft;

V, =

h,

=

17.93 4 3 2 . 2 X 2.41

5 B,

= 2.41 f t

= 2.04

-

Again by trial and error

h, = 7.82 ft A, = 112.76 f t 2 ;

Fr, =

4.96

JK5TTEi

B, = 22.24 f t ;

= 0.388

h,

= 5.07 ft

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CRC Handbook o f Irrigation Technology

Example 12 In a rectangular channel 8.0 ft wide, there is a discharge Q of 336 ft3/sec at a depth of 2.60 ft. T o what depth must the water rise downstream for a hydraulic jump to form? What is the (specific) energy loss along the jump and what is the energy dissipation rate?

V' F ~ ; = -2 = gh,

16.15, 32.2 X 2 . 6

- 3.115

v,

= - -Qp - -

N

= -yQhf = 62.4 X 336 X 0.37 = 7747.6

bh,

336

8 X 5.32

- 7.89 ft/sec

Ib - ft sec

Example 13 A very wide rectangular channel (R = h) is designed with a bottom slope I = 0.002. The discharge flowing in the channel per unit width (q = Q/b) is 85 (ft3/sec)/ft. Two alternative linings are being considered for the project: (a) a very fine, smooth concrete lining (n = 0.009), or (b) a coarse stone lining (n = 0.035). Classify the bottom slopes for the two alternatives. What kind of lining would turn the bottom slope into the critical slope? Solution:

(a) n = 0.009 - h n

= (1279 X 0.009)0.6 = 4.33 ft

< h,

Bottom slope is considered steep, S. (b) n = 0.035 + h n = (1279 X 0.035)0'6 = 9.79ft Bottom slope is considcred mild, M. (c) h,

=

h, = 6.08 ft = (1279 n)o.6

> h,

This n corresponds to concrete with clear signs of formwork.

Example 14 In a rectangular channel with n = 0.018, widthb = 7.2 ft, slope I Q = 140 ft3/sec:

=

0.000741, and

Classify the bottom slope At a certain point along the channel the depth of flow was 6.0 ft. What type of flow profile will there be? Develop an appropriate expression, and Calculate at what distance the depth of flow will be larger by 0.33 ft. Will this occur upstream or downstream from the section at depth 6.0 ft? Is the flow there quiet or shooting?

***

First determine h, and h,.

By trial and error:

h,

< h,

and the bottom slope is considered mild, M

h = 6.00 ft; h

> h, > h,

+

h, = 5 . 2 2 ft;

h, = 2.27 ft

The flow profile is M,

Hence: h, < h, < h and the flow profile is of the M, type with depth increasing in the direction of flow. For answers to the remaining questions see Metric Example No. 14.

REFERENCES AND ADDITIONAL READING 1. Kinori, B. Z., Manual of Surface Drainage Engineering, Vol. 1, Elsevier, Amsterdam, 1970. 2. Rouse, H. and S. Ince, History of Hydraulics, Dover, New York, 1963. 3. Morris, H. M., Applied Hydraulics in Engineering, Ronald Press, New York, 1963. 4. Henderson, F. M., Open Channel Flow, Macmillan, New York, 1966. 5. Chow, V. T., Open Channel Hydraulics, McGraw-Hill, New York, 1959. 6. King, H. W. and Brater, E. F., Handbook of Hydraulics, New York, McGraw-Hill, 1963.

Volume 1

145

MEASURING CHANNEL FLOW Herman J .Finkel

INTRODUCTION General In gravity irrigation, where the water is supplied in open channels, it is important to monitor the rate of flow for the following reasons:

1. 2. 3.

4.

Control of amounts of water diverted from a main channel or river Allotment of water quotas to various consumers along the channel Determination of correct discharge at head gate according to the irrigation requirements of the field Determination of flow in furrows for the furrow test and for subsequent irrigation operations

In general, the measurement of open channel flow is more troublesome and less accurate than the measurement of flow in pressure pipes, as it involves the construction of measuring devices, taking of readings, and the calculation of the discharge by means of tables or formulae. For this reason channel flow is measured less frequently and with less accuracy than pipe flow. It has often been thought by irrigators that where the cost of water is very low, there is little justification in bothering with careful measurements. This is a basic misconception since the damage which will result from neglecting to measure irrigation water may far exceed the value of the excess water applied. There are many examples in various parts of the world where water was diverted at low cost from a large river, with little or no measurement and control of the flow. As a result of the consequent over irrigation, the ground water levels rose, and approached the ground surface. This resulted in accumulation of soil salinity and alkalinity, and in the eventual destruction of the irrigated fields. Surface flow control, based upon accurate measurement, is therefore an important measure for sound irrigation practice. In this chapter some of the more commonly used methods of measurement of channel flow will be described briefly. Some tables will be provided, but with the increasingly common use of pocket computers, many of the formulas can easily be solved by direct calculation. Principles The principle common to the many types of channel flow measuring devices is the creation of a constriction along a portion of the channel through which critical flow takes place. This may be accomplished in several ways, such as by a reduction in the channel width, gradual or sudden, a hump in the channel floor, an increase in the bottom slope of the channel, or a combination of several of these methods. A typical, generalized section of a measuring device is shown in Figure 1. The point of measurement is located a distance L, upstream from the constricted throat. The throat is the section through which the flow is critical. Below this is the standing wave which leads to the downstream section. As long as the downstream depth of flow, h,, is not great enough to cause submergence of the flow at the critical section, the flow Q is proportional to the head H at the measuring section. Using the principles demonstrated in the chapter on Hydraulics of Open Channels

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CRC Handbook of Irrigation Technology

P

f i'

/

-7 -

t

Standing wove

Q

H

- h a l l P 7 / ?

1

l

W / ?

BB SECTION

.SECTION

AA

FIGURE 1 .

Typical measuring device.

where Q = discharge in m3/s, A, = area of the constricted section with a depth of H, in m2, H = difference in water elevation between water surface at t 5 e measuring section and the invert or crest of the constricted section, in m, and g = 9.81 m/sec2. The constant K is the product of three factors as follows: C , which is the empirical discharge coefficient or the ratio of measured to theoretical discharge K, which is the velocity of approach factor and depends upon the ratio of Ah/A,, and p, which is a factor of the shape of the constricted cross section. Specific flow measuring devices may also have the flow expressed as an exponential function of the head, or

where H and a are determined experimentally. Where the downstream depth h, is higher than the crest of the weir, the weir is considered to be submerged, or partially submerged. The degree of submergence is S = h,/H, and various measuring devices have calibration curves which are related to the values of S and which have some limiting or critical value for each specific case.

VENTURI FLUMES A Venturi flume is basically a constriction in the channel which creates conditions of critical depth at the throat, and a standing wave just below it. The throat should have a cross-sectional area of not more than 70% of that of the approach channel at maximum flow. It may have various shapes of cross section, such as rectangular, triangular, or trapezoidal, but the section is maintained uniformly throughout the length of the throat. The throat length is usually several times the maximum head, and preceded and followed by suitable transition sections. The rate of convergence on the

Volume 1

147

upsteam side should not be sharper than 1:3, and the divergence on the downstream side at least 1:6. Corners in the structure should be rounded. The approach channel should be colinear with the axis of the flume and of uniform cross section for a distance upstream of approximately 40 h. The Venturi flume is particularly suitable to measure irrigation water, and is preferred to the weir because it causes a minimum of back water in the channel and is less subject to interference by sediments and floating debris. Many standard shapes and sizes of Venturi flumes appear in the technical literature accompanied by discharge tables. In this chapter, however, the flow through the flumes will be calculated from hydraulic principles and empirical coefficients. The designer can then easily prepare a table for the use of the irrigators, by means of the ubiquitous pocket calculator which is rapidly replacing tabulated data in so many fields of technology. Rectangular Venturi Flume This flume has a throat with a rectangular cross section. Three types of rectangular Venturi flumes are shown in Figure 2 in which (a) has a bottom hump only, (b) has side contractions, and (c) has both bottom hump and side contractions. The free flow rating curve is given by the following equation:

is given by the expression where B is the bottom width of the throat, H is the head, /l (2/3)'.= = 0.5442, g = 9.81 m/sec2, and K, is a function of the ratio between the throat and the channel areas, A,/A,. If the approach channel is rectangular, this ratio is equal to

where P is the height of the throat floor above the approach channel floor. Values of K, are given in Table 1. The coefficient of discharge represents frictional and other losses of head and is determined experimentally. Typical values are given in Table 2. When the approach channel is relatively large, so that both K, and C, approach 1.00 the discharge equation for free flow becomes

Values of this equation are given in Table 3 for convenient reference. For more exact results, these values should be multiplied by the true values of K, and C, where these difler materially from unity. The limiting submergence for this type of flume is about 80%, so that values of B and P should be chosen to keep the ratio S = H,/H less than 0.8. Above this limiting submergence it is not advisable to measure flow in the rectangular Venturi flume. Triangular Venturi Flume Flumes with a triangular shaped throat section, and a relatively large approach channel can measure a wider range of flows within the submergence limit, and the head losses through the flume are smaller. Consequently the triangular Venturi flume is suitable for measuring irrigation water in canals with greatly fluctuating discharges. In this type of flume the throat area is

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Table 1 VELOCITY OF APPROACH FACTOR K, FOR RECTANGULAR VENTURI FLUMES

Table 2 VALUES OF THE COEFFICIENT OF DISCHARGE C, FOR RECTANGULAR VENTURI FLUMES

where the side slope of the triangle is 1 vertical to m horizontal.

Hence, Q = 1.268 C,, K, m The values of K, are similar to those in Table 1. The values of C, will generally fall in the range of 0.95 to 0.99. The Colorado State University has developed a small portable triangular Venturi flume for measuring flow in furrows. The length of the throat is from 5 to 7 inches (12.5 to 17.5 cm) and the side slopes form 60" to the horizontal. The approach channel has similar side slopes, and a trapezoidal section of 2 in. bottom width (5 cm). A calibrated rating curve for this measuring device is

Table 3 THEORETICAL DISCHARGE Q (l/sec) FOR RECTANGULAR VENTURI FLUMES IN VERY LARGE APPROACH CHANNEL FOR VARIOUS THROAT WIDTHS B (m) Head H (cm)

B = 0.20

0.30

0.40

0.50

Note: T o convert !/sec to ft3/sec, divide by 28.32. T o convert cm to in. divide by 2.5. T o convert cm to feet divide by 30.5.

0.60

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151

Table 4 RATING CURVES FOR VARIOUS TRAPEZOIDAL FLUMES DEVELOPED AT WSC, CSU, AND U.S. DEPARTMENT O F AGRICULTURE" Discharge in l/sec for flume no. H (cm)

I

I1

I11

IV

V

Triangular

Note: To convert !/sec to ft3/sec divide by 28.32. To convert to in. divide by 2.5. To convert to feet divide by 30.5. a

See Table 5 for dimensions.

Values of discharge in the metric units given by this formula are presented in Table 4. Trapezoidal Venturi Flumes These flumes have a throat cross section of trapezoidal shape, and the approach channel is usually, but not necessarily, also trapezoidal with similar side slopes. Examples of this type of flume are shown in Figures 3 and 4. In Figure 5 a rating curve is presented for a specific set of dimensions related to the flume shown in Figure 3. The submergence for maximum flow in this flume is 80%. For the purpose of conducting furrow irrigation tests (see chapter on Gravity Irrigation: Field Test to Determine the Length of a Furrow) several small trapezoidal Venturi flumes have been designed by the Washington State College (WSC), Colorado State University (CSU), and the U.S. Department of Agriculture (USDA). Typical dimensions are shown in Table 5. These are constructed of lightweight, durable material, plastic or fiberglass, and can easily be installed in the field. They may be equipped with a depth gauge mounted on the side. If they have been calibrated, the gauge may read directly in units of flow. Calibration curves for these flumes are given in Figure 5, and apply to free flow conditions only. The submergence limit is usually around 80 to 85%.

PARSHALL FLUMES The most commonly used device for measuring flow in irrigation channels all over the world is the Parshall flume. It is a form of rectangular Venturi flume which has a

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PLAN

THROAT

PROFILE

END VIEW

t or critical

A

PLAN -

SECTION

SECTION ELEVATION

ELEVATION 8-8 FIGURE 3 .

d@h section

- For

AA

dimensions see Table 5

Trapezoidal Venturi flume.

Volume I

Trapezoidal Venturi flume with a hump.

153

FIGURE 4.

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CRC Handbook o f Irrigation Technology

FIGURE 5 .

Rating curve for a trapezoidal flume.

Table 5 DIMENSIONS (IN CM) OF VARIOUS TRAPEZOIDAL FLUMES DEVELOPED AT WSC, CSU, AND U.S. DEPARTMENT OF AGRICULTURE (FIGURE 3)" Flume no.

"

b,

See Figure 3.

b,

D

C

A

E

F

8

FIGURE 6 .

SECTION FIGURE 7 .

L-L

Isometric view of Parshall flume.

SECTION

N-N

Narrow throat Parshall flume of reinforced concrete.

converging section with a level floor, a throat with a downward sloping floor and a diverging section with an upward sloping floor. Examples of this type of flume are shown in Figures 6 to 8. The Parshall flume has a submergence limit of about 60%. Above this value it is necessary to measure both the upstream and downstream head (H, and H,, respectively), and the degree of submergence is S = H,/H,. For free flow conditions the flow is

CRC Handbook o f Irrigation Technology

156

l

Q

W

l

PLAN

FIGURE 8.

Parshall flume.

Table 6 DIMENSIONS (IN CM) FOR VARIOUS STANDARD DESIGNS OF PARSHALL FLUMESa W

A

B

C

D

E

F

G

K

N

X

Y

See Figure 7 .

and values of K and n are given in Table 7, for the flumes which are dimensioned in Table 6 and Figure 7. A tabular presentation of flows for flumes of various dimensions (Figure 9) is given in Table 8 for the metric system. For the F P S system of units, discharge values are given in Table 9. Graphs showing discharges for Parshall flumes of various widths and degrees o f submergence are shown in Figures 10 t o 14.

BROAD-CRESTED WEIRS Many water distribution structures in a n irrigation system take the form of a broad-

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Table 7 PARAMETERS IN EQUATION FOR FREE FLOW RATING CURVE O F PARSHALL FLUMES

Table 8 PARSHALL FLUMES - DISCHARGE (!/sec) FOR FLUMES O F VARIOUS WIDTHS (W)

H. (cm)

7.6

15.2

30.5

50

75

100

125

150

175

200

Note: T o convert L /sec to ft3/sec divide by 28.32. T o convert to inches divide by 2.5. T o convert to feet divide by 30.5. Recalculated from Irrigation Advisor's Guide, Water and Power Resources Service, U . S Department of the Interior, Washington, D.C., 1951.46.

crested weir. These include diversion works, drop structures, reservoir spillways, and turnout boxes where the walls over which the water flows have a considerable thickness. The weir consists of an obstruction rising from the floor of a rectangular channel over which the water flows. It usually has vertical faces both upstream and downstream, but these may also be sloping. The crest however, must be level across its entire length (Figure 15). The basic flow equation for a broad-crested weir is

where C , is the product of C, and K, as previously defined.

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Table 9 DISCHARGE OF PARSHALL MEASURING FLUMES OPERATING UNDER FREE FLOW CONDITIONS IN FT3/SEC Throat width (ft)

Head (feet)

0.25

0.50

0.75

1.0

1.5

2.0

3.0

4.0

5.0

6.0

7.0

8.0

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Table 9 (continued) DISCHARGE O F PARSHALL MEASURING FLUMES OPERATING UNDER FREE FLOW CONDITIONS IN FT3/SEC Throat width (ft) Head (feet)

0.25

0.50

0.75

1.0

1.5

2.0

3.0

4.0

5.0

6.0

7.0

8.0

From Irrigation Advisor's Guide, Water and Power Resources Service, U.S. Department of the Interior, Washington, D.C., 1951,46.

Values for C, of broad-crested weirs are shown graphically in Figure 16 as a function of H/L where H is the head on the weir crest and L is the breadth of the crest (Figure 15). In the FPS System the discharge formula for the broad-crested weir is

where Q is the flow in ft3/sec, B is the width of the crest in ft, and H is the head on the weir in ft. Values for C are given in Table 10.

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CRC Handbook o f Irrigation Technology

FIGURE 9. Rating curves for Parshall flumes.

SHARP-CRESTED WEIRS The sharp-crested weir is simply a thin, vertical plate with an opening of a defined geometric shape, placed across the stream so that the downstream water level lies 5 to 10 cm below the crest. It is the least expensive and easiest to install of all channel flow measuring devices, but it has the disadvantage of a considerable loss of head. It is used on irrigation channels of relatively large gradient where the head loss can be tolerated. The approach channel cross section should be at least eight times the area of the weir opening, with side walls and bottom floor approaching not closer than 2.5 H,., to the edges of the weir opening. The approach channel should extend with a uniform cross section to a distance of at least 20 H,,, above the weir. The point at which the head is measured should be located 3 to 4 H,,, upstream from the weir. The weir plate should be of metal, about 1.5 mm (1/16 in.) thick with a sharp 90° corner on the upstream

FIGURE 10. Rating curves for Parshall flume. B

=

0.15 m.

FIGURE l l. Rating curves for Parshall flume. B

=

0.30m.

edge of the opening, and beveled to a 45" angle on the downstream edge, as shown in Figure 22. Examples of weir installations are shown in Figures 17 to 21. The three commonly used shapes of weir openings are rectangular, trapezoidal, and triangular. Rectangular Sharp-Crested Weir These are of two principal types. The first is the contracted weir in which the rectangular opening is of narrower width than that of the approach channel, and the crest is raised above the floor, as shown in Figure 17. The second is the so-called "suppressed weir" in which the width of the rectangular opening is the same as that of the rectangular approach channel, as shown in Figure 18. Rating curves have been developed experimentally for both types of weirs according to the equation

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CRC Handbook o f Irrigation Technology

Q ( l i t sec)

FIGURE 12. Rating curves for Parshall flume. B

=

0.50 m.

with B and H expressed in meters and Q in m3/sec. The coefficient C. is dimensionless. It depends upon the ratio of the head on the weir, H, to the height of the crest above the channel bottom, P, as well as the ratio B/B, which is the width of the weir opening over the width of the channel upstream. Values for C, are given graphically in Figure 23. For contracted rectangular weirs an approximate formula for the discharge is

where Q is discharge in m3/sec, and B and H are in meters.

where Q is discharge in ft3/sec, and B and H are in feet. Solutions for these formulas are shown in Tables 11 and 12.

FIGURE 14.

Rating curves for Parshall flume. B = 1.00 m.

FIGURE 15.

Broad-crested weir,

An approximate formula for the discharge of suppressed rectangular weirs in which B/B. = 1.0 is as follows:

This equation is applicable only if the downstream water level is 10 to 15 cm below the crest of the weir and the space below the nappe is well aerated by means of a small

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FIGURE 16. Values of the coefficient for broad-crested weirs. (From Handbook of Hydraulics, 3rd ed., by H. W. King. Copyright@ 1939. Used with the permission of the McGraw-Hill Book Company.)

Table 10 VALUES OF C FOR BROAD-CRESTED WEIRS IN FPS SYSTEM Measured head in feet,

Breadth of crest of weir in feet 0.50 0.75 1.00 1.50 2.00 2.50 3.00 4.00 5.00 10.00 15.00

From King, H. W., Handbook of Hydraulics, 3rd ed., McGraw-Hill, New York, 1939, 164. Used with the permission of the McGraw-Hill Book Company.

Volume 1

FIGURE 17. tracted.

Rectangular sharp-crested weir con-

FIGURE 18.

FIGURE 19.

FIGURE 20.

Suppressed weir.

Trapezoidal sharp-crested weir

Triangular sharp-crested weir.

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CRC Handbook o f Irrigation Technology

FIGURE 21.

Erosion of outlet channel below weir.

FIGURE 22.

Sharp crest of weir.

diameter pipe in each of the side walls. Solutions for the discharge of suppressed weirs are given in Table 13. In the case where there is no free flow because of submergence, the discharge of the weir is a function of the submergence ratio, S = H,/H where H, is the downstream water level above the crest of the weir. The discharge with submergence, Q,, is calculated as follows:

Trapezoidal Weirs A common form of trapezoidal weir has an opening with a horizontal crest and sides sloping at a 4 vertical t o 1 horizontal. This is also known as the Cipolletti weir. (See Figure 19.) The equation of the rating curve in metric units is

This is approximately 2 to 6% higher than the values for the contracted rectangular weir given in Tables l l and 12. (See Figure 24.) Triangular Weirs A common form of triangular weir is that with a 90° angle in the notch. It is sometimes known as the Thompson weir. The rating curve for this weir with a large ap-

FIGURE 23.

Coefficient o f discharge for sharp-crested rectangular weirs.

Table 11 CONTRACTED RECTANGULAR WEIR DISCHARGE (L/SEC) FOR WEIRS OF VARIOUS WIDTHS (B) B.,

5 10 15 20 25 30 35 40 45 50 55

6.1 16.9 30.9 47.5 66.3 87.1 109.6 133.9

60 65 70 75 80

12.1 33.7 61.6 94.5 131.9 173.3 218.2 266.4 318 372 429 489

18.1 50.4 92.2 141.6 197.6 259.5 327 399 476 557 643 732 825 922

24.1 67.2 122.8 188.6 263.2 346 435 532 634 742 856 975 1099 1228 1362 1501

Note: To convert !/sec to ft3/sec divide by 28.32.

To convert to inches divide by 2.5. To convert to feet divide by 30.5.

Table 12 CONTRACTED RECTANGULAR WEIR DISCHARGE (F'T3/SEC) FOR VARIOUS WIDTHS (B) AND HEADS (H)

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CRC Handbook o f Irrigation Technology Table 13 SUPPRESSED RECTANGULAR WEIR - DISCHARGE"

Table 14 DISCHARGE FOR A 90" TRIANGULAR WEIR H (cm)

Q (1 /sec)

Note: To convert I/sec to ft3/sec divide by 28.32. To convert to in. divide by 2.5. To convert to feet divide by 30.5.

In I/sec, for weirs of various heights P and for a width of 1.0 m.

proach channel, a negligible velocity of approach, and free flow conditions (i.e., no submergence) in metric units is as follows:

Values for this function are given in Table 14, and in Figure 25. In FPS units the rating curve is

where Q is in ft3/sec and H in feet. The value of the triangular weir lies in the fact that it gives measurable heads for the small flows as well as the large.

Volume I

Rating curves for Cipolletti weirs. FIGURE 25.

Rating curve for a 90° triangular weir.

169

FIGURE 24.

PIPE FLOW Herman J. Finkel

GENERAL The conveyance of irrigation water in pipes is used under the following circumstances: 1.

2.

3. 4. 5.

6. 7.

T o supply water under pressure for sprinkler and drip systems T o bring water t o fields which are at a higher topographic elevation than the water source, such as from a well, river, o r lake T o irrigate land with sloping and undulating topography T o convey water across hills a n d valleys T o convey water across areas where the soil type makes canal construction difficult o r costly T o convey recycled sewage for irrigation purposes in a safe manner T o convey water with minimum of conveyance losses

Although in general pipe lines are more costly than open canals, they may be economically justified in cases where either method of conveyance is possible, under the following conditions: If the length of the pipe line, being usually straight, is substantially less than that of a winding canal If costly aquaducts and/or inverted siphons are eliminated If the cost of water is s o high that the reduced conveyance losses are economically significant If canal maintenance is exceptionally costly o r difficult because of untrained personnel and inadequate organization If many costly bridges are required over a canal system If land costs are high o r right-of-way for the canal is difficult t o obtain If a n open canal would be subject to sabotage from hostile elements If accurate flow control is desired, including automatic o r remote control operation

HYDRAULICS OF PIPE FLOW T h e flow of water in a pipe line can be represented graphically by Figure 1. It is seen that the total energy, o r total head line represents the energy per unit weight of water (expressed in units of meters, o r feet,). According to Bernoulli's equation, the total energy, o r head, a t any given point is made up of four components, the pressure head = p/y, the head due to topographic elevation = z, a n d the velocity head = vZ/ 2g a n d the friction loss h,, o r

where: p = pressure in kg/m2 (metric) o r lb/ft2 (English), y = weight of a unit volume of water in kg/m3 o r Ib/ft3, z = elevation of the pipe above the datum in meters o r feet, V = mean velocity in m/sec o r ft/sec, g = acceleration due to gravity = 9.81 m/sec2 o r 32.2 ft/sec.'

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1

l 0

N

L 2 --

__

p

-

_

La

_ p _ _ -

FIGURE 1 .

-

DATUM

Flow of water in a pipe.

It will be noted that all of these components are expressed in units of length, either meters or feet. Pressure, p, is normally expressed in the metric system in kg/cm2, where 1 kg/cm2 represents a pressure of one atmosphere. Since y is expressed in kg/m3, in the Bernoulli equation given above, p is expressed in kg/m2, where 10,000 kg/m2 = 1 atmosphere. The difference between the total head a t any two points along a flowing pipe line is h,, o r the head loss due to friction, as shown in Figure 1. The gradient, or slope of the head line is called J and is equal to h,/L where L is the distance between the two points considered, and both h, and L are expressed in meters or feet. J is usually expressed as a percentage (% = m/100 m or ft/100 ft) or in per mil (O/,, = m/1000 m or ft/ 1000 ft). Values of the specific weight y vary with the temperature of the water, but the variation is small enough t o be negligible in hydraulic calculations for irrigation design. The values of y are taken as 1000 kg/m3 or 62.4 Ib/ft3.

HAZEN-WILLIAMS PIPE FLOW FORMULA There are a great many empirical formula for the calculation of pipe flow, based upon tests of various types of pipes under different conditions. Of these one of the most widely used is that of Hazen-Williams, which may take the following forms: English Units J0.54 V = 0.0132 C v = 0.0393 C0.76lQO 239 J0.411 J

=

Q =

D

=

4521.5 (Q/C)' 0.01 c J0.54 5.6678 (Q/C)O." JJ-205

Volume 1

173

Table 1 COEFFICIENT C FOR HAZENWILLIAMS PIPE FLOW FORMULA Coefficient Type of pipe

From

To

Welded steel pipe, untreated-new Untreated - 15 year-old-hard water Untreated - over 15 years high velocities Asphalt lining Cement lining Galvanized iron pipe Concrete pipe (new and clean) Concrete pipe (old) Clay drain tile Asbestos cement Polyethylene and polyvinyl chloride (PVC) Aluminurn

where V

= velocity in ft/sec, C = coefficient (see Table l), J = hydraulic gradient in feet per 1000 ft, Q = discharge in ft3/sec, D = pipe diameter in ft.

Metric Units V = 354 QD-2 = 1.096 X 10-4CJ0.54 - 3.97 10-3 C0.761 Q0.239 J 0 . 4 1 1 D-4.87= 2.16 X 107(V/C)1.852D-1.167 J = 1.131 X 1012(Q/C)'.852 105 C-1.852 V2.436Q-0.584 - 7-02 Q = 2 . 8 3 ~~ O - ~ V = 3.1 D ~x 1 0 - 7 ~ ~ 0 5 4 ~ 2 6 3 = 1.057 X 1010(V/C)4.175 J-'.'14 D = 18.8 Q0.5 V-0.5 = 298 (Q/C)0.38J-0.205 = 1.g3 X 106(V/C)1.S87 J-0.857 whereV

velocity in m/sec, C = coefficient (see Table l), J = hydraulic gradient Q = discharge in m y h r , D = pipe diameter in parts per million (C/'00), in mm.

=

In Table 2 are given values for V and J for various values of D and Q in the metric system. This table is based upon the Hazen-Williams formula with C = 100. For use with values of C other than 100 make transformations as in Table 3. Table 4 gives values of J , Q, and D in FPS units. Local Losses Local head losses occur in a pipe network because of entrances, bends, valves, and changes in diameter. These may amount to from 2 to 20% of the total head losses, and consequently are not always negligible. The local losses are expressed in head, h (ft or m) as a function of the velocity head, as follows:

where h is expressed in ft and V in ft/sec or h is expressed in m and V in m/sec. Values for the velocity head are given in Tables 5 and 6. Values for K are given in Table 7 and apply to either the English or the metric systems.

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CRC Handbook o f Irrigation Technology

Table 2 FLOW CALCULATIONS BY HAZEN-WILLIAMS FORMULA

D=

25

30

50

40

-

-

-

Q

V

J

V

J

V

J

D= Q

V

J

V

J

V

J

V

-

J

V

100

70

-

J

V

J

V

125

p

J

V

J

V

J

V

J

V

J

175

Volume I

Table 2 (continued) FLOW CALCULATIONS BY HAZEN-WILLIAMS FORMULA

150 200 250 300 350 400 450 V

J

V

J

600

500 -

V

-

J

V

V

700

-

V

J

-

J

V

J

V

800

-

J

-

V

J

V

J

V

loo0

900

J

1250

P

J

V

J

V

J

V

J

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CR C Handbook o f Irrigation Technology

Table 2 (continued) FLOW CALCULATIONS BY HAZEN-WILLIAMS FORMULA

600

500 -

V

-

J

V

700

-

J

p

V

Note: C = 100; Q in m3/hr; V in m/sec; J in

J

900

800

1250

loo0

-

V

J

V

J

V

and D in mm.

Table courtesy of S. Irmay, Technion-Israel Institute of Technology, Haifa, Israel.

J

V

J

177

Volume I Table 3 TRANSFORMATIONS FOR PIPES WITH C # 100 Given

Required

Q, D D, J

V, J V, Q

Q. J

V, D

V, D V, Q v, J

Q, J D, J Q, D

Read from the table

Calculation

V (independent of C) Vo, Qo

Q, = 100 Q/C Q = CQ./IOO v = cv,/100 Q. = l00 Q/C

Q (independent of C) D (independent of C)

Read from the table J for D, Q,

D for J, Q, V for Q, D J for D, Q, J for D, Q, D for J, V, Q for V, D

Q, = 100 Q/C Q, = 100 Q/C V, = 100 V/C

Table courtesy of S. lrmay, Technion-Israel lnstitute of Technology, Haifa, Israel.

Table 4 LOSS OF HEAD IN PIPE WITH C = 100 (HAZEN-WILLIAMS FORMULA)

(Loss of head in ft/1000 ft; J in O/oo) Nominal (inside) diameter of pipe (in.) m3/hr

Flow in gal/min

%in.

%in.

lin.

i n .

i n .

2in.

2Viin.

3in.

Nominal (inside) diameter of pipe (in.) Flow in m3/hr gal/min

3 in.

4 in.

6 in.

8 in. 10 in. 12 in. 14 in. 16 in. 18 in. 20 in. 24 in. 30 in. 36 in.

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CRC Handbook o f Irrigation Technology

Table 4 (continued) LOSS OF HEAD IN PIPE WITH C = 100 (HAZEN-WILLIAMS FORMULA) (Loss of head in f t / 1 0 0 0 ft; J in O/,,) Nominal (inside) diameter of pipe (in.) Flow in m3/hr gal/min

m3/hr

3 in.

4 in.

6 in.

8 in. 10 in. 12 in. 14 in. 16 in. 18 in. 20 in. 24 in. 30 in. 36 in.

Nominal (inside) diameter of pipe (in.) Flow in gal/min 8 in. 10 in. 12 in. 14 in. 16 in. 18 in. 20 in. 24 in. 30 in. 36 in. 42 in. 48 in.

Volume 1 Table 5 VELOCITY HEAD (h = V2/2g) IN FEET, FOR VELOCITIES IN ft/sec

Velocity (V)

Velocity head

Velocity (V) (continued)

Velocity head (continued)

179

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CR C Handbook o f Irrigation Technology Table 6 VELOCITY HEAD (h = V2/2g) IN METERS FOR VELOCITIES IN m/sec

EQUIVALENT PIPES Two pipes are said to be equivalent if they produce equal losses of head at the same discharge. Similarly a given section of pipe may be equivalent to a fitting or other local head loss producer if the pipe section causes the same loss of head as the fitting at corresponding values of discharge. The concept of an equivalent pipe is used in the analysis of networks to simplify the computations and avoid going into details at early stages of the analysis. Considering the head losses due to fittings such as valves, pipe bends, reducers, fitters, etc. which are located at various points in a pipe line, they are usually represented by an equation of the type

where k is the local head loss coefficient, Y is the head loss caused by the fitting, and V is the mean velocity in the pipeline. To derive an equation for the equivalent pipe this expression is compared to the Darcy-Weisbach equation for longitudinal head losses

where f is the coefficient of friction, L is the length of pipe, and D is its diameter.

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181

Table 7 VALUES O F K FOR CALCULATION O F LOCAL LOSSES Local condition Entrance losses Inward projecting pipe Sharp-cornered entrance Slightly rounded entrance Bell-mouthed entrance Obstructions in the line For long-radius 90' elbows For long-radius 60' elbows For long-radius 30" elbows For sharp 90° elbows For sharp 60' elbows For sharp 30" elbows For tees or crosses Straight flow Angle flow For gate valves (open) For gate valves (half open) For globe valves (open) For angle valves (open) For sudden contractions (The velocity in the smaller pipe is used in the formula) For sudden enlargements Where d , = diameter of the smaller pipe d, = diameter of the larger pipe (The velocity in the smaller pipe is used in the formula) Venturi meters (The velocity at the throat is used in the formula) Disc meters

Comparing the two equations for head losses at the same discharge or mean velocity (V), leads to

which is an expression for the length of a pipe equivalent to the given fitting. Adopting a mean value of f = 0.025, the last equation may be replaced by the following approximate equation

indicating that the length expressed in pipe diameters of the equivalent pipe for a given fitting is approximately 40 times the local head loss coefficient. A nomogram for obtaining the equivalent length of various fittings is given in Figure 2. If two pipes carrying the same discharge are compared, Darcy-Weisbach's equation should be written in the form y =-

S ~ L Q ' n 2 g D'

Comparing two such equations with f,L,D, representing one pipe and f2L2D,the sec-

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CRC Handbook o f Irrigation Technology

FIGURE 2.

Nornograrn of equivalent length of pipe for various fittings.

ond pipe, and assuming equal discharge Q and equal head losses Y in the two pipes, the following expression is obtained for the equivalent length

This equation gives the length of a pipe of diameter D, and friction coefficient f, which is equivalent to a pipe of diameter D,, length L,, and friction coefficient f , . If the two friction coefficients are equal, the above expression becomes

By a similar procedure based on the Hazen-Williams equation it can be shown that if this equation is adopted the expression for the equivalent length of one pipe which represents another pipe is

where C , and C2 are the Hazen-Williams coefficients for the two pipes. If the two coefficients are equal the last equation becomes

Except for cases where short lengths of pipes of one diameter are included in pipe lines of another diameter, the concept of an equivalent pipe replacing a given pipe is not much used. The other concept of an equivalent pipe to replace a fitting is more common. In the design of pipe lines for the conveyance and distribution of water an allowance is usually made for the effect of fittings in the pipe lines by adding to the actual length of the pipe an equivalent length to represent the fittings. For preliminary designs the added length is taken to be between 5 and 20% of the original length depending on the number of fittings. In Table 8 are presented the friction losses through screw pipe fittings in terms of equivalent lengths of standard pipe of the same diameter. In Table 9 similar data are given for the larger diameter fittings with flanged or welded connections. In Tables 10 and 1 1 are presented head losses of typical fittings for portable aluminum sprinkler pipe connections and valves.

HEAD LOSS WITH VARIABLE FLOW In sprinkler system submains and laterals, as well as in drip irrigation lines the water may be supplied simultaneously to a series of outlets spaced, (usually at uniform distances) along the line. In this case the discharge, Q, is constantly decreasing. A simple method for calculating the head loss along such a supply line is to calculate the head loss over the given section as though the entering discharge remains constant and then multiply by the so-called "F factor" which varies with the number of outlets along the line, and which, for a very large number of outlets, approaches a constant value of %. Values for the F factor are given in Table 12. These values are computed by the following formula developed by Christiansen:'

where N = number of regularly spaced outlets. The exponents 1.85 and 2.85 are based upon the use of the Hazen-Williams formula for pipe flow. The F factor may be used for designing a sprinkler lateral or a line of drip irrigation.

COMPOUND PIPES A compound pipe is a pipe composed of two or more separate pipes connected either in series or in parallel and used for conveyance of water between two given points. A pipe network on the other hand is a combination of a nwnber of pipes which supplies

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CRC Handbook o f Irrigation Technology

Table 8 FRICTION LOSSES THROUGH SCREW PIPE FITTINGS IN TERMS OF EQUIVALENT LENGTHS OF STANDARD PIPE (FEET)" Nominal pipe size (in.)

m

Actual inside diameter (in.)

Gate valve

Longsweep elbow

Mediumsweep elbow

Standard elbow

Angle valve

Close return bend

Tee through side outlet

Globe valve

For lengths in meters divide by 3.28.

From Piping Handbook by Walker and Crocker, Copyright (Q 1930 by McGraw-Hill Book Company, Inc. Used with the permission of McGraw-Hill Book Company.

Table 9 FRICTION LOSSES IN PIPE FITTINGS IN TERMS OF EQUIVALENT LENGTHS OF STRAIGHT PIPE (FEET)= Standard Standard tee tee side Nominal Standard through inlet dipipe size, gate Long rad. Med. sweep Standard Square Standard side outvided. 90"elbow 90' elbow 90" elbow 90" elbow 45" elbow let outlet (in.) valve

"

For lengths in meters divide by 3.28.

Courtesy of Crane Company, 300 Park Avenue, New York.

Table 10 HEAD LOSSES IN METERS THROUGH TYPICAL IRRIGATION PIPE FITTINGS

-$j

valve-coupler

2x2 Cast iron

2x2 Brass

1 Side

2 Sides

1 Side

Flow

Courtesy of Dorot Foundry and Metal Works, Dorot, Israel

2 Sides

1 Side

2 Sides

Table 11 HEAD LOSSES IN FEET THROUGH TYPICAL IRRIGATION PIPE FITTINGS Type

Oblique

--

p

Size (in.)

2x2

3X 3

2x2

2x2

Cast iron

Brass

2x2

2X2X3

3X3x3

3X4X4

1

2

1

2

1

2

side

sides

side

sides

side

sides

Flow

Courtesy of Dorot Foundry and Metal Work, Dorot, Israel (adapted to FBS system).

Table 12 "F" FACTORS FOR A SUPPLY PIPE WITH OUTLETS AT REGULAR INTERVALS Number of outlets

F

water to a number of points distributed over the network. Each compound pipe may be replaced by an equivalent pipe of arbitrary diameter and friction coefficient. Alternatively, the concept of a characteristic curve is found useful in dealing with compound pipes. A characteristic curve of a pipeline is a diagram showing the relationship between the head loss (Y) along the given pipe line and the discharge (Q) flowing in it (Figure 3). The general form of a characteristic curve for a given pipe line may be expressed by an equation of the form

where K is a pipe resistance coefficient which depends on the diameter, length, and type of pipe, and n is an exponent which is determined by the choice of pipe resistance formula adopted. If the Hazen-Williams equation is adopted for describing the head losses the value of the exponent is n = 1.852 and the form of the equation describing the characteristic curve is

where K depends on the pipe for which the equation is written and on the set of units used. The discharge Q in this case is usually expressed in m3/hr and the head loss Y in meters. The characteristic curve for a compound pipe may be derived from the corresponding curves of the individual pipes in the compound pipe by the following procedure. The procedure is illustrated with respect to a compound pipe composed of two pipes. It can be extended to any number of pipes by the simple rules given. If the two pipes are in series (Figure 4), the same discharge flows in both pipes and

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CR C Handbook o f Irrigation Technology

FIGURE 3. Characteristic curve of the function of head loss (Y) in a pipe with the discharge (Q).

the loss of head in the compound pipe at any given discharge (Q) is equal to the sum of heads in the individual pipes.

Summing up vertical ordinates of the individual characteristic curves will produce the characteristic curve of the compound pipe. If the two pipes are in parallel (Figure 5 ) , each pipe will carry its own discharge, but the loss of head along each of the two pipes will be the same. Considering the system of two pipes as a compound pipe it is clear that for a given loss of head, which is equal to the difference in head between the two pipe junctions, the total discharge is equal to the sum of the discharges flowing in the individual pipes.

The characteristic curve for the compound pipe is obtained in this case by summing up, for any given head H, the horizontal intercepts of the two individual curves at the value of the given head. An extension of the idea of a compound pipe and the use of characteristic curves may be made in the case of branching pipe networks. A branching pipe network is a system of pipes which supply water to a number of points but in which the flow path from the main pipe or source to each supply point is uniquely prescribed by the geometry of the pipe network. An example of such a branching network is shown in Figure 6a. The system illustrated is composed of three pipe lines supplied from a main

Volume 1

FIGURE 4.

189

Flow in pipes in series.

at point A, delivering water to three points B, C , D at elevations Z,, Z2, and Z, above and below the elevation of point A adopted as datum. Considering the system beyond the point A as a compound pipe, it is possible to derive a characteristic curve for this compound pipe from the characteristic curves of the individual curves. The curves shown in Figure 6b give the relationship between the total flow Q at point A in the main pipeline and the total head H, measured at the same point. The individual curves marked 1, 2, and 3 give the above relationship for each of the pipes acting alone with the other two pipes shut off. The curve marked 1 + 2 gives the relationship between discharge and head for pipes 2 and 3 operating with pipe number 1 shut off, and finally the curve labeled 1 + 2 + 3 is the characteristic curve for the system composed of the three pipes as shown.

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CRC Handbook o f Jrriga tion Technology

FIGURE 5 .

Flow in pipes in parallel.

FIGURE 6.

Flow in branching pipes.

REFERENCES 1 . Christiansen, J. E., Irrigation by sprinkling, U. Calif. Agric. Expt. Stn. Bull., No. 670, Berkeley, 1942. 2. Crocker, S., Piping Handbook, 5th ed., King, R . C . , Ed., McGraw-Hill, New York, 1969.

SPRINKLER IRRIGATION Amnon Benami

TYPES OF SPRINKLER SYSTEMS Introduction Since the end of World War 11, the development of sprinkler irrigation has been very extensive. One of the factors that helped in the successful development of sprinkler irrigation was the introduction of aluminum pipes. The use of lightweight aluminum pipes reduced the initial investment in equipment, and made it possible to transport the sprinklers from one position to another. Other factors which were important in the development of sprinkler irrigation were the improvement in the construction and water distribution of the sprinklers, improvements in the construction of couplings, and the development of various fittings for use in sprinkling irrigation systems. Every sprinkler system is composed of a pipe network and of sprinklers. The pipes convey the water and supply it to all the operating sprinklers at the correct pressure head. At the nozzles of the sprinklers the pressure head of the water is converted to a velocity head. The water flows out of the nozzle in the form of a jet, and breaks down into drops of water which wet the area within a certain range. The range of the wetted area depends on the magnitude of the velocity head given to the water; it is also influenced by the angle of flow of the jet, the type of sprinkler and its moving mechanism, and by wind conditions during the irrigation period. The provision of the proper pressure head to each sprinkler in the irrigated field, the correct spacing of the sprinklers according to their type and wind conditions, and the design of the sprinkler system according to the nature of soils and crops in the area are the factors which ensure the efficient spreading of water in the correct quantities and at the proper times. The main elements of a sprinkler system are 1.

2.

3.

4.

The source of water. The source of water for sprinkler irrigation can be a regional pipe line, a water reservoir, a well, an irrigation canal, or a natural pond. Water can be obtained from the source by gravitation, but sometimes pumping is required. In some cases it is necessary to have at the source of water screening and settling chambers which are used to free the water of leaves, sand, and silt particles. Main pipe line. The main pipe lines convey the water from the water source to the irrigated fields. The pipe lines are usually steel or asbestos cement. More recently polyvinylchloride (PVC) has also been used. Submains. These pipe lines branch off from the main pipe lines into the irrigated fields and supply water to the sprinkler laterals through risers and valves spaced at regular intervals. The submains are usually of steel, asbestos cement, or PVC. They follow the boundaries of the irrigated plots, but sometimes they are run along the center lines of the fields. Sprinkler laterals. These convey the water, through suitable couplings and risers, spaced at regular intervals, to the sprinklers. The sprinkler laterals are generally aluminum and they can be transported from one irrigation position to another at the end of an irrigation period. PVC or polyethylene pipes are presently also used with stationary (or solid-set) as well as portable laterals that are towed on wheels or skids. In two methods of irrigation to be described later (oscillating rain pipe and perforated pipe), the sprinkler laterals are used for both conveying the water and sprinkling.

194 5.

C R C Handbook of Irrigation Technology

Sprinklers. The most common type of sprinklers in use today is the slow revolving sprinkler. Other types in use are the sprinkler "guns", fixed head (garden) sprinklers, and whirling sprinklers. An example of a simple sprinkler system for one plot, is shown in Figure l . Larger areas can, of course, be designed for a greater number of mains and submains.

Classification According t o Portability Sprinkler irrigation systems are classified according to their portability. Three main types of systems are distinguished. Stationary (Permanent) Sprinkler System In a stationary (permanent) system all elements, starting with the water source and including the sprinklers, are fixed in place. Such a system is generally very expensive. Another disadvantage of such a system is that the pipes and risers may interfere with field operations. Its main advantage is that the expenses involved in operating the laterals and sprinklers are smaller. The stationary sprinkler system is found mostly in dense orchards, such as banana plantations, where the moving of pipes is very difficult and in some cases entirely impossible. At present stationary (or solid-set) systems mainly with plastic pipes are used with many other crops. This is done to save water and labor. Such systems are now often partially, or fully automated. The sprinkler laterals in banana plantations are steel or plastic pipes, 1 to 2 in., depending on the number of sprinklers. The pipes are placed on the ground along the centerlines between adjacent rows of trees, or more commonly along the rows of trees. The risers are made of galvanized steel or aluminum pipes. They should be 3 m, or more, high so that sprinkling is above the trees. To ensure the stability and verticality of the risers they are supported by suitable brackets. In order to reduce the number of submains, relatively long sprinkler laterals of small diameter are sometimes used in dense plantations. The small diameters are made possible by operating only every second or third sprinkler at any one application, thus decreasing both discharge and head losses. The above scheme of alternate sprinkling requires the installation of stop valves on each riser. In some plantations the risers are made of two sections. The lower section of the riser is fixed in place and the upper section, including the sprinkler, is portable. The portable section is screwed (by hand) into the valve at the top of the fixed section at those stations where it is desired to irrigate. At the end of the application the portable sections are moved over to their next positions along the sprinkler laterals. Another possibility of reducing the number of stopvalves is by a screwed coupling at the bottom of the portable section of the riser. This coupling is then attached, with the help of a handle welded to it, t o the threaded top of the fixed section of the riser. The fixed sections of the risers that are not in use are closed off by caps. It is clear that the cost of irrigation increases in this type of arrangement. Semiporta ble Sprinkler System This system is composed of fixed mains and submains, made of steel, asbestos cement or PVC and of light portable aluminum or plastic sprinkler laterals. The sprinkler laterals are moved at the end of an application from one station to another along the submains. The semiportable sprinkler system is the most widely used at present. It is used for irrigating field and industrial crops, fruit plantations, and vegetable gardens. The use of light portable pipes reduces the initial investment and makes possible field operations without interference. The annual expenditure for irrigation operations increases, however, because of the frequent moving of the pipes. In order to decrease the labor involved, laterals are sometirnes fitted with skids or

Volume I

The main elements of a sprinkler system.

195

FIGURE 1.

196

CRC Handbook of Irrigation Technology

FIGURE 2 .

Sprinkler system with laterals towed across the submain.

with carriages on wheels. This makes it possible to tow the laterals by hand, animal, or tractor across the submain or dry land, with minimum interference from plants. Special paths have to be prepared for the taller plants. Flexible-polyethylene and PVC pipes are also used. They are very adaptable for use as towed laterals. Black polyethylene pipes are flexible and easily dragged or pulled and they are quite light. They are relatively cheap and withstand acids and other corrosive materials. Also, these pipes do not heat up easily and are very smooth inside. They are made in the smaller diameters only and can be used for relatively short lengths. Polyvinyl chloride pipes are also relatively smooth and light and they can withstand inside or outside corrosion. These pipes have certain flexibility, so that strict alignment is not necessary. They are made in larger diameters and can, therefore, be used when longer laterals are required. All couplers and other fittings required for plastic laterals are available and are of good standard. In a proper installation the joints should be tight and no water leakage should be noted. Several forms of sprinkler systems with towed laterals are common. Figure 2 describes such a system for an orchard, with tree spacings of 8 m X 4 m and sprinkler spacings of 8 m X 8 m. The submain is 3 in. aluminum, perpendicular to the tree rows, which feeds 25 mm plastic. The laterals are on wheels and are towed across the submain to new positions at the end of an irrigation shift. The number of submains in the field and laterals operating simultaneously depends on local design conditions. Another type of system is described in Figure 3 . In this case the trees are spaced 4.5 m X 5 m, and sprinkler spacings are 4.5 m X 10 m. Laterals are 25 mm in diameter and are towed on wheels. Three sprinklers are installed on each lateral. At the end of application in position (1) each lateral is towed three tree spacings to position (2), and so on to position (6) on the other side of the submain. (The number of laterals operating simultaneously again depends on local design conditions. This system employs flexible polyethylene pipes. The small number of sprinklers on the lateral facilitates the use of smaller diameter pipes. Portable Sprinkler System In a portable sprinkler system all parts, including mains, submains, and sprinkler

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FIGURE 3.

197

Sprinkler system with gradual towing of laterals.

laterals are portable and moveable. Portability of the main and submain lines is important in regions where only supplemental irrigation is practiced. Supplemental irrigation, meaning a small number of applications during the growing season, is used for winter crops in dry regions, or in some temperate regions of irregular rainfall pattern. Some summer crops, such as sorghum, are sometimes given three or four irrigations during the growing season, so as to increase yields. The need for a pumping station depends, of course, on the nature of the source of water. If water is obtained, for example, from a regional water main, the pressure may be sufficient to operate the sprinkler irrigation system. If the pressure available is insufficient a stationary pumping system is usually designed. If the water source is an open channel, running through the irrigated areas, a portable pumping unit, operated by a diesel engine or a tractor is preferred. In some regions portable sprinkler systems are used to irrigate corn and cotton for the first few applications only. When the plants reach a height which makes the moving of the pipes difficult, water is applied by furrows. The supply mains make it possible to use both sprinkler and furrow irrigation. The supply mains are made up of concrete or asbestos cement pipes, buried along the boundaries of the fields, with concrete risers at regular intervals. When the outlet side of the riser is closed the water begins to rise. For sprinkler irrigation, the suction pipe of the portable pump is then submerged in the riser. The portable pumping unit may be designed to supply water to one or two sides, as required. After completion of all the irrigation possible from one riser, the pumping unit and the laterals are shifted to the next riser. Classification According to Over-Under Foliage Basically, sprinkler irrigation is a method in which water is applied above the foliage. The risers should, therefore, be high enough to clear the plants, so that the water will

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be distributed freely and without interference. Part of it is intercepted by the foliage and reaches the ground after some delay, during which evaporation may occur. In fruit orchards both undertree and overtree sprinkling is practiced. The system selected in any case depends on local conditions. Undertree Sprinkling The basic requirement for undertree sprinkling is to have spacings of trees which permit moving of the sprinkler laterals. An undertree sprinkler irrigation system, as a rule, is a semiportable system with stationary main and submain lines and portable aluminum o r plastic laterals. The laterals are placed midway between the lines of trees, so that sprinklers operate at the centers of squares formed by each four adjacent trees. After an application, the sprinkler laterals are moved to the next sprinkling position, unless a stationary or solid-set system is used. The risers are short, usually not more than 15 to 20 cm high. The sprinklers used are of the low exit-angle type. The angles are 4 or 7", so that drops from the issuing jet do not hit the foliage and fruit. The low trajectory of the jet is especially important in those cases where there is danger of damage t o the leaves or to the fruit by the falling water, and in cases where the water may wash away chemicals sprayed on the trees. In some regions it is suspected that overtree sprinkling causes rotting of oranges, bananas, and vines. In the U.S. and Canada signs of fruit rotting or cracking were noticed in apricots, peaches, and pear orchards. It is evident that in all cases of possible damage to trees or fruits, a system of undertree sprinkling should be designed. If this type of sprinkling is not possible, because of the high density of trees, the solution may be to use border or furrow irrigation. It should be noted that many farmers, although using short risers, d o not use low trajectory sprinklers. The low riser in itself is not very helpful if the angle of exit of the jet is high, and cannot prevent water from hitting the foliage. The sprinkler chosen should distribute the water efficiently when laterals are spaced every row or two rows of trees, and sprinklers along laterals are spaced every tree row. The maximum spacings used in undertree sprinkling are 6 m X 12 m, the larger value being the spacing between sprinkler laterals (20 X 40 ft). Sprinklers used for undertree sprinkling operate at low pressure heads. This is an advantage where water sources are inadequate to supply high pressures without additional pumping. The disadvantage is that the close spacings require a larger number of laterals, thus increasing pipe and labor costs. However, because of the small discharges of undertree sprinklers, laterals can have small diameters even when they are relatively long. This partially offsets the disadvantages mentioned above. Undertree sprinkling has another advantage in that it decreases evaporation losses and reduces wind effect. Both factors tend to give better efficiencies. The portability of the system enables the removal of the pipes when cultivation operations are needed. Overtree Sprinkling This method of sprinkling is used mostly in orchards where the close spacing of trees makes it difficult, or impossible, to transport laterals. In this case, the sprinkler system is stationary. The sprinkler laterals are usually steel or plastic pipes, laid along the rows of trees or at the center between two rows. The risers are high, up to 3 m and in some cases higher, and are fixed. They are preferably 1 in. diameter pipes, with supports, to give extra stability. This type of sprinkler system is expensive, but irrigation operations are very simple, consisting only of the opening and closing of valves. Even this operation may be automated. Because of the intial high cost, medium and high pressure sprinklers are generally used in overtree sprinkler systems. These enable larger spacings to be used. The source of water should, of course, be such that it can supply

FIGURE 4. BERMAD automatic metering valve. (Courtesy of Kibbutz Evron, Post Ashrat, Israel.)

the necessary pressure. The maximum spacings used are 15 m X 18 m. The larger spacing is between sprinkler laterals where there is no wind, or where the prevailing wind is perpendicular to the laterals (50 X 60 ft). In some cases, where spacings between trees are reasonably large, partly or fully portable sprinkler risers are used. Thus initial costs may be reduced. However, the amount of work involved in transporting the tall risers after each application increases the annual irrigation costs. Sometimes, although not very frequently, semiportable overtree sprinkler systems are used in orchards, having wide tree spacings. In these cases, both laterals and tall risers are portable. With a water source that supplies medium or high pressures, thus enabling larger lateral spacings to be used, the system described above may be relatively cheap, even though labor costs are increased. Overtree sprinkling during the day, when strong variable winds are blowing, is accompanied by considerable water losses by evaporation and spray drift. The winds also distort the water distribution. If the system is intended for use during the day, an effort should be made to design for sprinkling in hours of light winds. It is also important to select the proper type of sprinkler for the prevailing wind conditions. There is no doubt that low-intensity night sprinkling is preferable where overtree sprinkler systems are practiced. Night irrigation reduces losses because of lighter winds, lower temperatures, and higher relative humidities. Compared with daytime irrigation, it is possible to save 10% or more of the water by night sprinkling. Special Systems

Automatic Hydraulic Control The systems so far discussed are of the conventional type. As mentioned above, labor has become both scarce and expensive. To this end automation of sprinkler systems has become quite popular in recent years. Although automation may increase the initial cosis of the equipment, it reduces the need for labor and may, with full automation, dispense with it almost entirely. Automation also saves water and facilitates night irrigation, resulting in higher application efficiencies. In Israel automation generally means the introduction of control facilities in conjunction with stationary or solid-set systems of the conventional type. The simplest way of automating a system is through the use of automatic metering valves (Figure 4), each controlling one plot. The water application required (in m3) is set with a dial on the meter, and the valve will shut automatically at the end of the application, which is uninfluenced by pressure variations or duration of irrigation. The valve is controlled hydraylically.

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I st Set of laterals

Last set of ktemls

1

Main supply vake

-&t -

m

-

BERMAD

hydraulic

BERMAD

I"-

valve

1 15'' automatic

metering valve

FIGURE 5 . BERMAD follow-thru system. (Courtesy of Berrnad Automatic Metering Valves, Kibbutz Evron, Post Ashrat, Israel.)

Further and more advanced automation for irrigation control is achieved by use of "Follow-Thru" irrigation systems. Several arrangements are available and one of them is described in Figure 5. Small ( l in. or 1 '/z in.) automatic metering valves are installed at the inlet of each set of laterals. Pressure-actuated hydraulic valves are installed in the submain, downstream from each of the inlets to the lateral sets. The metering valves and the hydraulic valves are connected by thin tubes of copper or plastic. At the beginning of an irrigation cycle (interval), the metering valves are manually preset to the quantities of water required for delivery. All hydraulic valves in the submain are open. Irrigation is carried out in sequences. Water flows from the submain to the first set of laterals through the metering valve at its inlet. A pressure build-up shuts the hydraulic valve situated downstream in the submain. At the end of delivery of the preset quantity t o the first set of laterals, the metering valve closes automatically, and the pressure drop in the laterals increases as a result of the pressure in the submain so that the hydraulic valve now opens. As a result the water flows to the second set of laterals, while the hydraulic valve downstream is now closed. This sequence of operation is repeated until the last set of laterals has applied the preset-required water application. In this manner irrigation is automated and continuous and the amount of labor required is minimized. Attention is required only at the beginning of each new irrigation cycle when all automatic metering valves have to be preset for the required quantities of water. Further advances in automation have been made to minimize labor and save water when large, and often distant areas are irrigated. As an example, a number of "FollowThru" systems, as described above, can be controlled electronically by a single controlmechanism, and a number of the latter can further be controlled by a master panel at the center of the farm. Ultimate automation is achieved by the use of sensors, such as tensionmeters, which are preset to activate the irrigation system at a required moisture level in the soil profile.

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Self-Propulsion In the U.S. and Europe automation is generally achieved by mechanical means. One example is the self-propelled lateral system, with wheels, which is activated by a power unit. The wheels are propelled by transmitting the power through a driveshaft, running alongside the tubing, to a number of "movers" installed along the lateral. The lateral moves the desired distance and will then stop. Power units are commercially available to move laterals along the selected spacings, normally employed in systems with revolving sprinklers. Systems are often provided with automatic drainage of the lines, activated as soon as the lines are turned off. Laterals are moved across submains, or from field t o field, by turning the wheels through 90" or by separating them from the lateral and transporting them on a pipe trailer to another location. Some degree of labor is thus employed to operate the system, although no special skill is required. In order to reduce the initial investment the power units are sometimes provided as separate units. They may be attached only when moving the system and are then detached and used to operate another lateral. In this case some additional labor is required. Another example of mechanized sprinkling is a self-propelled giant rotary irrigator, which is tractor mounted. Spanning over 40 m for the smallest model and over 70 m for the largest model, the rotating boom applies 1 in. in 3 to 4 hr on approximately 1 acre, and is capable of irrigating up to 50 acres or 20 ha in a 10-day cycle. Nozzles along the boom are graduated to ensure even precipitation within the radius of the boom. A range nozzle operates at the tip of the boom. The smaller model can be fed from 3 or 4 in. portable (generally aluminum) pipe lines, and requires a supply of about 30 m3/hr. Pipe racks are provided to carry the portable pipe lines. For easy movement the boom arms can be raised and lowered, as desired, by a hydraulic jack fed from the tractor hydraulic system. Irrigation is started in the furthest operating position of the field from the submain, so that the total portable line is laid on the ground. At the completion of application of the desired amount of water, the water supply is turned off and the unit is driven to its new operating position. For the smallest model the new position is 72 m and for larger models it is 108 m closer to the submain. As the unit advances to the new position the disconnected light weight tubings are collected and stacked on the pipe rack. The process of moving one spacing takes two men about 10 to 15 min with one driving and the other uncoupling, collecting, and loading the portable line. When the length of the field is completed the unit is driven laterally the required spacing and then forward towards the extreme new operating position. While the unit is driven the portable pipe is relaid in its new location. For a field about 360 m long it is claimed by the manufacturer that the procedure should take about 30 min. Some self-propelled machines available commercially are designed to move (on wheels) continuously across the field at desired speeds, normally between 0.15 and 1.20 m/min. The machine is supplied with a pump, a winch with a steel guide cable, and a propulsion unit with a water-driven turbine, a sprinkler gun with discharges of up to about 60 m3/hr at pressures of up to about 7 atm, wetted diameters up to 125 m. Irrigation starts at one end of the field. An anchor is firmly staked at the other end o f the field and the winch guide cable is laid on the ground between the machine and the anchor. A flexible water-supply hose, coupled to a takeoff at the field center, is also laid on the ground and attached to the machine-pump inlet. The machine is started and moves steadily forward, guided by the winding cable, towards the anchor at the other end of the field. As it moves, the supply hose bends and follows. The unit stops automatically at the end of run. The machine is then moved laterally to its new position, ready to start a new run across the field. A windup reel is used to quickly and conveniently reel up the hose, to allow it to be moved to the next area of watering. Due to the large areas sprinkled in single runs the amount of labor involved is minimized.

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The strip covered in one run is often up to 100 m wide and 420 m long (4.2 ha). Depending on the speed of travel one run (strip of field) can be completed in daily shifts of between 6 and 22 hr long. Thus two or even three runs per day are possible if soil conditions permit. In the choice of sprinkle discharge and speed of travel special consideration should be given to the proper application rate (in mm/hr) and the required depth of application (in.) over the field. Recently, the Center-Pivot method of irrigation has become very widely used. A pipeline of aluminum, up to 400 m in length, on which the sprinklers are installed, has mobile supports or towers on wheels at regular intervals. This pipeline is anchored to a center-pivot structure at one end and rotates around it with a selected speed. The wetted area is obviously circular, but recent developments make it possible to irrigate a more or less square shape. As more experience has been gained, this method of irrigation has become quite dependable, requiring minimum labor for operation, maintenance, and repairs. In some cases the method has allowed the successful irrigation of land previously considered impossible for growing crops, and often very high yields have been achieved. Generally the system is designed so that a full revolution is completed in 1 to 3 days. This means that the moisture content in the soil is constantly kept at a high level and water is easily available to plants at all times. Manufacturers often claim that the systems are highly successful and work well on varying types of soils. However, high application rates that may cause runoff on some of the heavier soils, have been observed along the periphery of the wetted area. Center-pivot systems are adaptable to rough ground and rolling fields with slopes of over 20%. Elements of the system are generally corrosion-free. Systems allow the application of fertilizers through injection. Center-pivot systems are designed for an electric drive, or a water mechanical-hydraulic propulsion system drive. The systems are often capable of being towed from one pivot location to another, thus reducing initial costs. The light-weight pipes may be 6 in., or more, in diameter depending on length and sprinkler discharges. Standard spacings between sprinklers are generally 10 m.

SPRINKLER TYPES AND THEIR CHARACTERISTICS The various sprinklers may be divided into two main groups: Group B

Group A 1. 2. 3. 4.

Revolving sprinklers Whirling sprinklers Fixed-head (garden) sprinklers Sprinkler guns

1.

2.

Perforated pipe Oscillating rain pipe

General Description of Group A The sprinklers are connected at the top of risers equally spaced along the sprinkler lateral. The function of the sprinkler lateral is to convey the water under the desired pressure head and divide it efficiently among the risers. Sprinklers of this group distribute the water over a circular rectangular area under light wind conditions. Water distribution may be greatly distorted under heavy wind conditions. Each sprinkler has one or more nozzles through which the water is ejected. The water jet coming out of the nozzle breaks up into drops which spread over the sprinkled area. The manner in which the water is distributed along the jet path, i.e., the water distribution pattern, and the range over which the water is sprayed, are determined for a particular sprinkler by the pressure head in the riser just below the sprinkler, and the nozzle diameters. At the nozzles, the pressure head is converted into velocity head,

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giving the water jet its initial velocity. The combination of pressure head and nozzle diameter determines the intensity of drop formation and the distribution over the wetted area. For a fixed nozzle diameter an increase of pressure head causes a finer drop formation. Similarly, with a fixed pressure head, smaller nozzles produce a finer spray. The larger drops fall farther away from the sprinkler. The finer drops, possessing a larger specific surface area, and thus having larger resistance to air, fall nearer the sprinkler. The spray range and water distribution pattern are also influenced by the ejection angle of the nozzle and the sprinkler rotation velocity. Under conditions of no air resistance, maximum spray range would be achieved with a nozzle ejection angle of 45". Experiments show that under normal field operation conditions, the maximum range is achieved with a 30 to 35' ejection angle. Rotation velocity influences the water distribution pattern by affecting the spray range. A low rotation velocity, as with revolving sprinklers, decreases the spray range only to a small degree. Increasing rotation velocities as with whirling sprinklers, shows a fast decrease in wetted area. For each sprinkler with a fixed nozzle (or nozzles) an optimal range of operating pressure heads exists. Within this range the initial velocity of the water jet and the breaking up and distribution of the drops over the irrigated area, produce an efficient water distribution pattern. An efficient distribution pattern of the individual sprinkler, and proper sprinkler spacings combine to achieve an efficient water distribution over the entire irrigated area. Poor water distribution may result when operating pressure heads or sprinkler spacings are not chosen properly. The optimal range of pressure heads, for which the water distribution pattern is considered efficient, is different for various types of existing sprinklers. This range is also affected by nozzle diameters. It is lower for small nozzle diameters, and it increases as nozzle diameters get larger. With small nozzle diameters, operating pressure heads that are too high may break up the water jet into drops that are much too fine. Similarly, with larger nozzle diameters operating pressure heads that are too low may result with a too high percentage of the larger drops. The water distribution pattern of most sprinklers of group A (within the optimal range of pressure heads for each sprinkler and under light or no wind conditions) is characteristically triangular (Figure 6 ) . For this pattern the maximum depth of water falls near the sprinkler, while no water falls at the perimeter of the wetted area. The depth of water decreases gradually from maximum to minimum. Normally, distribution patterns of existing sprinklers do not achieve the ideal triangular form, especially when sprinklers are operated under windy conditions. With proper overlapping of individual sprinkler patterns an efficient wetting of the area may be achieved (Figure 6 ) . Points in the field that receive too little water from one sprinkler may get the balance of the needed water from adjacent sprinklers. The magnitude of overlapping depends, of course, on the deviations of the individual distribution patterns from a true triangular pattern, and on the minimum acceptable requirements for water distribution uniformity. Normally, a good water distribution uniformity is reached with an overlapping of about 50 to 60% of the wetted diameter. Sprinkler spacings between and on laterals, need not be equal. Frequently, larger spaci n g ~are preferred between laterals, while shorter spacings are assigned to the sprinklers on the lateral. The larger spacings between laterals may save in the initial cost of the pipes, and also reduce time and cost of pipe hauling. Sprinkler operation under windy conditions normally necessitates adjustment in overlapping and spacing. Usually, efficient sprinkling under windy conditions may be achieved by spacing the sprinklers closer together. It is more economical to decrease spacings between the sprinklers on the lateral. To this end, sprinkler laterals should be designed to operate at right angles to the prevailing wind direction. Operating the

204 CRC Handbook of Irrigation Technology

FIGURE 6.

Distribution patterns of individual sprinklers and groups of sprinklers operating with proper overlapping, without wind.

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system with sprinklers of higher pressure heads and larger diameter nozzles also helps. If the direction and intensity of the wind change constantly during sprinkling, water distribution efficiency may be decreased for all spacings. Variable wind conditions usually exist during the daytime. Therefore, under variable wind conditions, consideration should be given to night sprinkling. It should be noticed that a few group A sprinklers produce a distribution pattern that in section approaches a trapezoid or a rectangle. For a trapezoidal distribution pattern the depth of sprinkled water is more or less constant for part of the wetted diameter. Towards the periphery of the wetted area the depth of water tapers off towards zero. For a rectangular distribution pattern the depth of falling spray is approximately constant for most of the wetted diameter, with a sudden decrease towards zero close to the limits of the wetted area. It is evident that wider spacings may be used as the distribution pattern approaches a rectangular shape. Operating the sprinklers at pressure heads above the optimal range results in the formation of very fine drops. Consequently the wetted area increases only to a small degree. At the same time, the distribution pattern is distorted due to changes in drop size distribution. Further increase of pressure head can eventually result in such a fine spray that the wetted area is reduced. The distribution pattern can become completely ineffective since a high concentration of water forms in the vicinity of the sprinkler, while an inadequate amount of water falls at the periphery of the wetted area (Figure 6). Thus it may be seen that operating sprinklers with pressure heads above their optimal range results in nonuniform water distribution for any chosen spacings. Also, water losses through evaporation and winddrift are increased. The water distribution pattern is also distorted by operation at suboptimal pressure heads. These reduce the spray range. The water jet disintegrates mainly into larger drops. In this case, the amount of water falling at the periphery of the wetted area is too large, while that falling near the sprinkler is too small (Figure 6). Large drops also create a hazard in that they can damage plants and soil structure, especially in the case of heavy soils with poor plant cover. These soils may seal, causing reduced infiltration rates, increased surface runoff, erosion, and ponding. Sprinkler risers should be at right angles to the soil surface, in order to maintain a uniform distribution pattern. Also, tall risers, as in corn or orchards, should be provided with ample support. Maintaining a constant rotation velocity is also important for efficient irrigation; otherwise some sectors of the wetted area receive more water then others. The water used in sprinkling should be clean, especially when small diameter nozzles are used. Water containing leaves, and sand or silt particles may hinder the proper operation of sprinklers by clogging nozzles and wearing out of moving parts. Such water should be screened. Special chambers for settling of particles may also be used. In addition, pipes should always be flushed after hauling and before regular operation. As previously mentioned, a uniform distribution of the water is a prerequisite of any sprinkling system. However, an efficient system should also supply water in the quantities needed by the plants. These quantities are determined by the duration of sprinkling, the spacings, and the discharge of the sprinklers. The discharge of a sprinkler depends on the combination of inlet pressure-head and nozzle cross-sectional area, as follows:

where Q = discharge, in m3/hr; C, = discharge coefficient, describing the ratio of actual t o theoretical discharge capacities; A = total cross-sectional area of sprinkler nozzles, in m'; h = inlet pressure head, in m and g = gravity constant, 9.80 m/sec2.

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In F P S units Q = C, A -h, with Q in ft3/sec, A in ft3, h in ft and g = 32.2 ft/ sec2. The discharge of a sprinkler increases with increase of the inlet pressure head. For a fixed pressure head the discharge increases for larger diameter nozzles. It is possible t o get with small nozzles, operating a t high pressure heads, the same discharge as with large nozzles, operating a t lower pressure heads. This relationship is important in the solution of problems encountered in sprinkling irrigation and will be discussed later in greater detail. Equation 1 shows that the discharge varies with the square root of the pressure head. Letting Q , a n d Q, be the discharges at pressure heads h, and h,, respectively, then:

Dividing the equations, we get:

Efficient sprinkling irrigation requires that fluctuations in discharges of all sprinklers in the irrigated area be limited to 10% of the design discharge. This requirement is arbitrary, a n d is based o n experience alone. Equation 2 shows that in order to fulfil1 the requirements mentioned above, the irrigation system should be designed in such a way as t o limit pressure-head variations in the field to not more than 20% of the design pressure head. T h e depth of water applied (in mm) per unit time (hours) over the irrigated area is determined, as already mentioned, by sprinkler discharges and spacings, and is defined as the application rate. For fixed sprinkler spacings, the application rate, i, is calculated as follows:

where i = application rate, in mm/hr; Q = sprinkler discharge, in m3/hr; S, = spacing between laterals, in m; and S, = spacing between sprinklers o n the lateral, in m. In F P S units i = Q / A where i is in in./hr, Q is in ft3/sec, and A is the wetted area in acres. T h e application rate is very important in the design of sprinkling systems. This rate determines the time required t o apply the desired amounts of water. Also, it determines the suitability of the chosen sprinkler to the type of soil in question. The application rate of the sprinkler should always be lower than the basic infiltration rate of the soil. Excessive application rates can lead t o soil-surface sealing and t o erosion o r ponding. When the pressure head varies, and sprinkler spacings are fixed, the application rate varies linearly with the discharge. If differences in the pressure heads of the operating sprinklers are greater than 20% of the design pressure head, the application rate changes over a range that is larger than 10%. This change of the application rate in relation t o the design rate adversely affects the irrigation efficiency and the application of the desired irrigation requirements. A n efficient sprinkler system is designed s o that sufficient pressure heads are available a t all parts of the irrigated field, n o matter how remote o r high they may be. In

- STAINLESS

STEEL

TENSION

PIVOT R N

SPRING RANGE

DRIVING SPRAY

NOZZLE

HEAD NOZZLE SPRINKLER

BODY

SEAUNG WASHER

FIGURE 7.

The main elements of a revolving sprinkler of the regular hammer type.

Sprinkler nozzle

FIGURE 8. Operation of wedge hammer - top view. (a) Hammer in initial position at the start of operation; (b) Returning hammer just before striking the sprinkler body.

this way the proper application rates are guaranteed and the required amounts of water may be supplied within the desired number of hours. In some parts of the field the pressure heads, available for operation, may be too high. Unless these pressure heads are regulated with the aid of manometers, resulting application rates may become excessive, causing water wastes and possible damage to the soil. Detailed Description of Group A Sprinklers Revolving Sprinklers These sprinklers are operated by a hammer which acts horizontally around a vertical pivot and is regulated by a spring. Two types of hammers are commonly used: the regular hammer (Figure 7) and the wedge hammer (Figure 8). Rotation of the sprinkler with the regular hammer is effected when the jet, leaving the nozzle, strikes the driving head of the hammer. The striking jet produces a hori-

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zontal force component, perpendicular to the driving head. Thus the hammer is forced to rotate in this direction, as far as the spring would allow it. A counter moment then returns the hammer to its initial position. At this stage the returning hammer strikes the body of the sprinkler, causing it to rotate. The above procedure is repeated time after time. Rotation is slow, generally one to a few revolutions per minute. Because of the slow rotation the spray range is affected to a small degree only, and larger spacings can be used. Also, slow rotation reduces wear of moving parts. Most revolving sprinklers today operate with the wedge-type hammer. Figure 8 illustrates its operation. Position (a) shows the wedge at the start of operation. The jet strikes diagonally the face of the wedge and produces two force components, H, and V,. Component H, is tangent t o the face and, therefore, has no influence. Component V,, perpendicular to the wedge, operates the hammer to the left. While the hammer rotates, the wedge turns around its vertical axis and point B moves to point A. The hammer rotates as far to the left as the spring would allow, and then returns due to a counter moment. The hammer returns, with the wedge at position (b). When the wedge is just opposite the nozzle, the jet hits it again and produces force component V2 acting to the right, perpendicular to the face of the wedge. The hammer then strikes the body of the sprinkler with an increased force, due to both returning moment and the component V,. As a result the wedge returns to position (a) and the procedure is repeated. The sprinkler rotates t o the right with slow regular motions. Operation with the wedge hammer generally improves the distribution patterns of the sprinklers, especially when pressure heads are low (10 m or 15 lb/in.2). At these pressure heads sprinklers with regular type hammers stop functioning properly. The reason is that when the jet strikes the returning driving head of the hammer, it produces a force component that acts in an opposite direction to the movement of the hammer, thus weakening its action considerably. Certain revolving sprinklers operate without a spring. The jet, striking the driving head, produces two force components. One component acts horizontally at right angles to the driving head and operates the sprinkler. The second component acts vertically downward, thus driving the end of the hammer in that direction. A weight at the other end pushes the driving head back to its initial position, opposite the nozzle. The procedure is then repeated. Revolving sprinklers are manufactured with either one or two nozzles. With two nozzles, one is the range nozzle - wetting mainly the outer rings of the wetted area - and the other is the spray nozzle, which is opposite the driving head, or the wedge. The range nozzle is normally the larger. Some of the better known two-nozzle sprinklers are Naan 323/90-91, 333 and 344, and Lego S33A, S33/22 and B7.* These sprinklers operate at either low or high pressures, and have a wide range of spacings and application rates. Spacings vary, according t o nozzle diameters, pressure heads, and wind conditions, generally from 12 X 6 m to 18 X 18 m. Common spacings are 12 X 12 m, 18 X 12 m and 18 X 15 m. Application rates usually vary between 5 and 20 mm/hr (0.4 to 0.8 in./hr). The angle of water ejection for these sprinklers is generally 30". At this angle the spray range approaches the maximum range for the sprinkler. Some revolving sprinklers are manufactured with only one nozzle. The one nozzle combines the effects of both range and spray nozzles. Generally, these sprinklers operate at low pressure heads, and are used for either undertree or low-application irrigation. Nozzles for undertree sprinklers are constructed to operate at either 4 or 7" ejection angles. These low angles necessitate the reduction of sprinkler spacings. Maximum spacings normally used are, therefore, 12 X 6 m. Naan 223/94 and Lego S33/66 are examples of undertree sprinklers (Figure 9). Sprinklers with low application rates are * Manufactured in Israel.

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FIGURE 9. Low-angle undertree sprinkler. (Courtesy of Naan Mechanical Works, Post Naan, Israel.)

FIGURE 10. Part-circle sprinkler. (Courtesy of N a a n Mechanical Works, Post Naan, Israel.)

used to irrigate either heavy soils or areas with strong varying daily winds. Where heavy soils are encountered, low application rates keep the soil from sealing up and prevent reduction of infiltration rates. In areas of strong daily winds these low application rates enable night operation, thus reducing hazardous wind effects. Care should be exercised in the selection of the sprinklers. With the larger diameter nozzles, high application rates result for the smaller spacings and the higher pressure heads. These high application rates may be damaging. The part-circle sprinkler is another example of the one-nozzle sprinklers. This sprinkler is used to irrigate the boundaries of irrigated fields. A special mechanism attached to the body of the sprinkler enables the irrigation of any sector desired. Naan 223/31 and Lego L55 are two examples of part-circle sprinklers (Figure 10). In choosing the proper nozzle, consideration should be given to the size of wetted sector. For example, if the area t o be irrigated is half a circle the nozzle selected should discharge half the capacity of the other sprinklers on the lateral. In this manner, water wastes and possi-

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ble damage at the end of the lateral can be prevented. Assume a lateral with Naan 323191 (nozzles 4.8 X 3.2 mm) sprinklers operating at an average pressure head of 15 m (22.5 Ib/in.l). The average discharge per sprinkler on the lateral is then 1.40 m3/hr (6.2 gal/min). If the last sprinkler on the lateral is Naan 223/31 (part-circle), a 4-mm nozzle should be selected for proper operation. At a pressure head of 15 m this nozzle discharges 0.71 m3/hr, (3.1 gal/min), which is half the normal discharge of a sprinkler on the lateral. Revolving sprinklers may also be distinguished according to their operating pressure heads. A sprinkler belongs to one of three classes of pressure heads: low, medium, or high. Low pressure head sprinklers normally operate between 10 and 25 m (15 to 37.5 1bhn.l); (examples: Naan 323/90-91, Lego S 33 A). Medium pressure-head sprinklers operate at 25 to 35 m, (37.5 to 50 lb/in.2; examples: Naan 333, Lego B7). High pressure-head sprinklers operate above 35 m (50 lb/in.2; example: Naan 344). The above definitions are, of course, arbitrary. Generally, sprinkler systems are designed for low or medium pressure-head revolving sprinklers. Occasionally, when the pressure at the water source is high, or when a pump is required in any case, systems are designed for high pressure revolving sprinklers, or even for sprinkler guns. Revolving sprinklers are used with all types of sprinkler systems, but mainly with semiportable systems. These types of systems are usually the cheapest and most efficient. The advantage of revolving sprinklers is that they can be adapted to all soils and crops. The large number of these sprinklers available today enables the designer to choose from a wide range of pressure heads, spacings, and application rates. The range of pressure heads of a revolving sprinkler and the choice of nozzles sometimes enable the designer to make simple and economical changes, if needed, in existing systems. One example is the reduction of pressure supplied by the water source, after the system has been operating for some time. The reduction in pressure head brings about reduction of sprinkler discharges and application rates. This in turn forces the irrigator to increase the number of hours needed for supplying the required amounts of water. Such a solution is not always possible. The most efficient approach is to replace the nozzles with larger ones. This approach is valid if the larger nozzles apply at the lower pressure head the original rate of water, with no change required in the existing spacings. As an example, let us consider a system designed for Lego B7 sprinklers, operating under average wind conditions with a pressure head of 30 m (45 lb/in.l). The sprinklers have 5.0 X 3.5-mm nozzles, and discharge 2.17 m3/hr/sprinkler (9.5 gal/min). Spacings are 18 X 12 m, and the application rate is 10 mm/hr (0.4 in./hr). An amount of 12 m3/ha is required for irrigation. The duration of application is, therefore, 12 hr. The system had been operating satisfactorily for a time, when the available pressure head dropped from 30 to 20 m (45 to 30 lb/in.2). The proposed solution is to replace the original nozzles with new ones, having diameters of 5.5 X 4.0 mm. These new nozzles apply 2.15 m3/hr (9.5 gal/min) at a pressure-head of 20 m (30 Ib/in.2). The new application rate is 9.9 mm/hr (0.4 in./hr). The operating time for applying the desired amount of water is 12 hr, as before. Another example is the reduction in infiltration rate of the soil. This may result in ponds and erosion. To prevent possible damage, lower application rates - associated with a greater number of hours - should be used. In this case the solution involves replacing the original nozzles with smaller ones, thus reducing the application rate of the sprinklers. The new nozzles should be able to sprinkle efficiently without necessitating any changes in the existing spacings of the system. Let us now consider a system with Lego B7 sprinklers, operating under average wind conditions. At the time of design the infiltration rate of the soil was rather high, about 25 mm/hr (1.0 in./hr) at 30 m pressure head. With 18 x 12 m spacings the application rate is 14.9 mm/hr

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FIGURE 1 1 . Whirling sprinkler. (Courtesy Naan Mechanical Works, Post Naan, Israel.)

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(0.6 in./hr). Thus 5 hours are needed to apply 7.5 m3/ha (3 in 1 application). After one season of irrigation the infiltration rate of the soil dropped to about 12 mm/hr (0.5 in./hr). T o solve the problem, smaller nozzles are selected. These nozzles are 5.0 X 3.5 mm. They apply 2.17 m3/hr (9.5 gal/min) at a head of 30 m (45 lb/in.2). Since the original spacings may also be used with the new nozzles, the resulting application rate is 10 mm/hr (0.4 in./hr). This rate is safe. Seven and a half hours of sprinkling are now necessary to apply the desired amount of water.

Whirling Sprinklers These sprinklers are simply and sturdily constructed. They have either two or three long arms at the ends of which are the nozzles (Figure 11). Rotation is effected by a reaction force, resulting from the ejecting jet. A whirling sprinkler wets a circular area when operating without wind. It whirls at about 60 or more r/min. It normally operates at a limited range of pressure heads, the optimal pressure head being, generally, 10 m (15 lb/in.2). It discharges generally up to 1 m3/hr or 4.4 gal/min. Maximum spacings are 9 X 6 m under light wind conditions. These spacings should be reduced to 6 X 6 m under average wind conditions. With strong varying winds, these sprinklers should not be used at all, since the fine spray is carried away and the efficiency of irrigation is impaired. Application rates are high and generally vary between 15 and 30 mm/hr (0.6 to 1.2 in./hr) or more. Whirling sprinklers are used at the present time to a small degree only. They are found mainly in lawns and small garden tracts. The main disadvantages of these sprinklers are (1) the range of pressure heads is very narrow, thus limiting the choice o f spacings, (2) the high application rates limit the use to light soils, and crops that completely cover the ground, and (3) the close spacings necessitate a larger number of pipes and sprinklers and investment for large areas may run high. Fixed-Head (Garden) Sprinklers These sprinklers operate without any moving parts (Figure 12). They are simple and cheap. They sprinkle a fine spray and should preferably operate without wind. They are mainly used for irrigating lawns and gardens with permanent systems. Fixed-head sprinklers are manufactured to wet full circles, half-circles, or strips. They operate at low pressure heads and close spacings. Generally, these sprinklers operate at pressure heads of 10 m (15 1bAn.l) and discharge up to 0.75 m3/hr (3.3 gal/min), with spacings up to 5 m in each direction. However, some of the larger sprinklers can operate at pressure heads of 20 m or 30 lb/in.2 with discharges up to 2 m3/hr (8.8 gal/min) and spacings of 6 X 6 m, or more. Fixed-head sprinklers have high application rates that vary normally between 20 and 50 mm/hr (0.8 to 2.0 in./hr). These application rates are too high for most soils and crops, and are mainly adapted to lawns. In fixing the time required for irrigation of lawns, the high application rates of fixed-head sprinklers should be considered. Since the roots of lawns are shallow the amount of water re-

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FIGURE 12. Fixed-head sprinkler. (Courtesy of Naan Mechanical Works, Post Naan, Israel.)

FIGURE 13. Sprinkler-gun. (Courtesy of Naan Mechanical Works, Post Naan, Israel.)

quired per irrigation is rather small. Therefore, sprinklers should be operated for a short period only. If we consider, for example, a medium soil, the amount of water per irrigation is about 450 m3/ha. With an average application rate of 30 mm/hr (1.2 in./hr) the irrigation time should not exceed an hour and a half. Nevertheless, sprinklers are often left to operate for several hours, which causes a large waste of water. Care should also be taken to operate the sprinklers at the proper pressure head. Too high a pressure head results in a very fine spray that may be carried away even with a light wind. Sprinkler Guns (Figure 13) These sprinklers operate at high pressure heads, varying in general between 40 and 75 m (60 to 110 lb/in.2). They discharge from about 20 to 100 m3/hr (90 to 440 gal/ min). Some of the larger sprinkler guns may discharge up to 150 m3/hr and more (660 gal/min). The high pressure heads quite often necessitate the use of pumps, which increases the initial investment and the annual costs. On the other hand, sprinkler guns can be spaced farther apart. Spacings vary generally, according to the type of guns and pressure head, between 30 X 30 m and 70 X 70 m. Because of these wide spacings, the area irrigated by one sprinkler is rather large. This causes a reduction in the number of laterals, and in the time and labor required for moving aluminum pipes. Sprinkler guns are manufactured with connector bases of 2 or 3 in., and they may

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weigh several kilograms. They normally have from one to three nozzles. The range nozzle is usually at the end of a long arm, and may have a diameter of 30 mm or more. The other nozzles have much smaller diameters. Sprinkler guns may be used to irrigate pastures, forage crops, orchards, cocoa, etc. They are mainly used in large, rectangular areas. The sprinkler systems are generally semiportable or portable, with aluminum pipes and quick couplers. Moving the gun from one position to another is not easy, and frequently more than one man is needed for the job. To facilitate movements the gun riser may be connected to wheels. The gun riser and quick coupler are then moved separately from the pipes. Application rates are usually higher than 10 mm/hr (0.4 in./hr). The spray consists of relatively large drops, in order to achieve the long range of sprinkling. Consequently guns are not adapted to a large number of soils and crops. Care should especially be taken with heavy, sloping soils that are not fully covered. The use of guns in wind regions should be carefully considered. Under windy conditions the water distribution tends to become poorer. Also, water losses due to evaporation and drift may be rather high. Frequently, sprinkler guns are operated at insufficient pressure heads. As a result, the spray may contain large drops that can harm both crops and soils. At the same time the water distribution may become unsatisfactory, leaving large areas of the field dry. General Description of Group B In this group of sprinklers the water jets out through nozzles spaced at regular intervals along the tubing (oscillating rain pipe), or through holes that are drilled along the upper side of the tubing (perforated pipe). The lateral, thus, has two functions. It conveys the water at the desired pressure head and sprinkles the water at the same time. The wetted area is a strip along both sides of the lateral. The width of the wetted strip depends mainly on the size of nozzles or holes, their arrangement, the pressure head available, and the wind conditions. With no (or light) wind the water spreads more or less equally on both sides of the lateral. When operating under windy conditions the laterals should be placed at right angles to the prevailing wind. The laterals should also be moved closer to the field boundary from which the prevailing wind is blowing. Under variable wind conditions efficient sprinkling is practically impossible. Both types of sprinkling operate with low pressure heads. This is because the nozzles, or holes, are of small diameter. In the optimal range of pressure heads the distribution pattern is more or less rectangular. This necessitates only a small amount of overlapping (Figure 6). Choice of pipe diameters is governed by the same rules as for group A sprinklers, i.e., the pressure head variations between the lateral ends should be limited to 20% of the design pressure head. Detailed Description of Group B Sprinklers Perforated Pipe In this type of sprinkler system the water jets out through a great number of holes (0.8 to 1.2 mm in diameter) which are bored in the upper half of the tubing surface. The number of holes, their arrangement, and their diameter combine to fix the characteristics of a particular perforated pipe. Unclean water may wear out or plug the holes, thus disturbing the characteristics of sprinkling. Perforated pipes are used mainly in the irrigation of orchards and small vegetable fields. Systems are generally of the semiportable type. An advantage is the lack of risers which reduces the labor needed for pipe hauling. The jet trajectory is quite steep. Therefore, in orchard irrigation the water spray wets the foliage. The spray, at the optimal range of pressure heads, is fine. Consequently, sprinkling under varying wind conditions results in poor water distribution. In the event that the wind during operation is more or less fixed in direction and magnitude and is not

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excessively strong, the resulting distribution can be satisfactory if the pipes are placed perpendicular to the wind direction. This is not possible in the case of row crops, laid along the contours, and winds that blow across the slope. Perforated pipes operate at low pressure heads and high application rates. Pressure heads vary between 5 and 15 m (7.5 to 22.5 lb/in.l), the optimal pressure head being generally 12.5 m (19 lb/in.2). Spacings vary, according to the pressure head, between 6 and 15 m. The spacing recommended for a pressure head, of 12.5 m, is 12 m. Perforated pipes are manufactured for sprinkling rates of 19, 25, 38, and 50 mm/hr (0.75, 1.0, 1.5, and 2.0 in./hr). The discharge flowing at the head of the pipe depends on the application rate, the spacing between laterals and the length of the pipe. This discharge is known when the application rate is multiplied by the area wetted by the pipe. For example, when the pressure head is 12.5 m, the wetted area of a lateral, 100 m long, is 100 X 12 = 1200 mZ (13,000 ft2 or 0.3 acre). For an application rate of 25 mm/hr (in./hr) the discharge at the head of the perforated pipe is

Q

= Ai =

13,000ft2 X 0.083 ft/sec 3600

=

0.3 ft3 /sec or 132 gpm

The high application rates of perforated pipe limit this method of sprinkling to light, permeable soils. At the same time, once a system has been put into operation no changes are possible. For example, if the infiltration rate of the soil is reduced after a time, there is nothing to prevent ponding and erosion. This is due to the constant application rate of the perforated pipe. Sprinkling with high application rates on light soils enables application of water in a relatively short time. As a result, pipes may be moved several times a day and their total number may be relatively small. However, because of the frequent movements, regular and constant care is needed in the field, which increases labor costs. Another disadvantage of this method is that night operation is impossible due to the short periods of sprinkling. Perforated pipe is not adaptable to long fields because of the large discharges per unit length of pipe. In order to avoid large diameters, the laterals have to be quite short. In large fields, then, a large number of submains may be needed. This can increase the cost of the system considerably.

Oscillating Rain Pipe In this method of sprinkling a pipe, supported on stationary or portable posts, turns back and forth around its horizontal axis. Operation is effected by an oscillator. The water flows out through nozzles, inserted at regular intervals along the top of the pipe. While the oscillator is turning, the water covers a strip of land on each side of the pipe. The oscillator is operated by the pressure of the water, passing through it into the lateral. It can turn the pipe through an 85 to 90" angle, starting at a desired elevation from the horizon. Under no, or light, wind conditions, the pipe is turned 90°, from 45" above the horizon, to 135". The spacing between nozzles is generally 0.8 m (32 in.). The supports are from 0.8 to 0.9 m high. At this height, the lateral turns freely and the spray has no chance of hitting the foliage as it comes out. Oscillating rain pipe is used mainly in small vegetable fields. The irrigation system is generally semiportable, with a buried submain laid in the direction of the main slope. The laterals operate in the direction of the contours, which is also the direction of the crop rows. Galvanized pipe (1 in.) or aluminum (1 in., 2 in., or a combination) may be used for laterals. The laterals and oscillator are moved from one position to an-

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other. The supporting posts can be either stationary or portable. The disadvantage of stationary supports is that they interfere with field work. Also, grass usually grows all around them. The portable supports are transported while hanging on the pipes. The cost of labor is thus increased. However, they can be moved with the pipes out of the field, thus facilitating farm operations without any interference. Nozzles are either 0.8, 1.0, or 1.2 mm. The 1.0 mm nozzle is the most widely used. Oscillating rain pipe operates at low pressure heads. The recommended optimal pressure head is 25 m (37.5 lblin.'). Spacings at this pressure head are 15 m. Discharge-capacities for the three nozzles are 0.8 mm nozzle (q = 0.023 m3/hr; 0.10 gal/min); 1.0 mm nozzle (q = 0.040 m3/hr; 0.176 gal/min); 1.2 mm nozzle (q = 0.064 m3/hr; 0.28 gal/min). Application rates are low. For a 25-m pressure head the application rate of the l .O-mm nozzle (nozzles spaced at regular intervals of 0.8 m) is

Application rates for the other two nozzles (same pressure head as before) are 2 mm/ hr (0.08 in./hr) for the 0.8 mm nozzle, and 5.5 mm/hr (0.2 in./hr) for the 1.2 mm nozzle. Discharges in the laterals are rather small. For 1.0 mm nozzles, spaced at 0.8 m intervals, the discharge at the head of a lateral, 100 m long is

Because of the low application rates, this method is adaptable to all soils. It can be used for night operation. The small discharges enable the planner to design rather long laterals with relatively small diameters. Level laterals generally can be l-in. galvanized pipe for a length of 60 m, l-in. aluminum for a length of 75 m, and 2-in. aluminum for a length of 240 m. These lengths are governed by the 20% pressure-head-difference rule. Actually, the length of a lateral is determined by both hydraulic considerations and the capacity of the oscillator to turn the pipe without causing torsion. Thus the length of a lateral is also influenced by the type of oscillator selected. The oscillator can operate one lateral at a time, or two laterals on both sides of the submain simultaneously. At a pressure head of 25 m (37.5 lb/in.') the regular size oscillator can operate efficiently 2 X 60 m of l-in. galvanized pipe, 2 X 75 m of l-in. aluminum pipe, or 2 X 60 m or 1 X 100 m of 2-in. aluminum pipe. At the same pressure head the large size oscillator can operate efficiently 1 X 200 m of 2-in. aluminum pipe, or 2 X 120 m of a combined 2-in.-l-in. aluminum pipe. Sometimes, if a higher application rate is desired, the nozzles can be spaced at intervals of 0.4 m (16 in.). However, this has the disadvantage of doubling both the number of nozzles and the discharge of the lateral. This in turn requires shorter laterals than previously recommended, thus necessitating a larger number of submains and increasing the cost of the system.

SPRINKLER LATERALS Types of Laterals and Fittings Stationary or semiportable sprinkler systems in which the sprinkler laterals are made of steel or iron are quite rare nowadays. The majority of sprinkler systems are portable or semiportable, with polyvinyl chloride or aluminum sprinkler laterals. The sprinklers are usually of the revolving type.

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FIGURE 14.

Various types of quick couplers. (Courtesy of Ravit Irrigation Systems, Tel-Aviv, Israel.)

Aluminum pipes generally range from -'/4 to 6 in. in diameter. Pipes of -'/4 and of 1 in. diameter are used mostly for sprinkler risers, while the larger diameter pipes are used for the sprinkler laterals. The pipes are supplied in standard lengths of 6 m or 20 ft, but on special order other lengths, such as 9 or 12 m can be obtained. Some makes of pipes are supplied with double wall reinforcements, near the ends of the pipe, as a protection against accidental damage. The assembly of the aluminum pipes is facilitated by quick couplers (Figure 14). The couplers are provided with suitable gaskets for prevention of leakage during operation. They also allow for rapid draining of the pipe lines at the end of the application. Couplers used for the connection of risers are provided with threaded openings, suitable for -'/4 or 1 in. pipes. One type of quick coupler, commonly used in conjunction with low risers of less than 1 m height, is permanently attached to the upstream section of pipe. It can be quickly coupled to the downstream section of pipe by means of the latch that hooks onto a band, fastened around the pipe. This arrangement enables the transfer of the section o f pipe, coupler, and riser as one unit. It is suitable when the risers are low and d o not interfere with moving of the pipes. The same type of coupler may also be used with tall risers, for sprinkling of corn, vinyards, or orchards. In this case, a special fitting is added in order to enable quick and easy coupling and uncoupling of the tall riser. After uncoupling, the upstream section of pipe and the quick coupler are moved as one unit, while the tall riser is moved separately. Another type of quick coupler, used for tall risers, is the double-latch coupler. This double-latch coupler can be easily uncoupled from the two pipes connected to it, and is transported together with the high riser. The sprinkler laterals operate under pressure and their ends should, therefore, be

properly plugged to ensure proper action. Several types of plugs for closing off the ends of the laterals are on the market. Another fitting, available for cases where pipes of different diameters are used, is the reducer. The sprinkler laterals should be flushed after they are transported and reassembled in their new location. This operation is very important as it prevents the accumulation of soil and debris and the clogging of the sprinklers. Design of Laterals The choice of the proper size of lateral is of vital importance to the proper operation of sprinkler systems. The determination of the pipe diameter depends directly on the allowable differences in discharge and pressure between the upstream and downstream ends of the lateral. The allowable differences are usually expressed as a percentage of the discharge and pressure of the selected sprinkler, located midway along the lateral. Sprinkling is considered t o be efficient when the difference between the values of the discharge, obtained from sprinklers at the extreme ends of the lateral, are not more than 10% of the selected sprinkler. For example: if the discharge of the selected sprinkler is 2.0 m3/hr (8.8 gal/min) the lateral should be so designed that the difference in discharge of any two sprinklers along the lateral is not more than 0.2 m3/hr (0.88 gal/ min). Sprinkler discharges can be kept within the required range if the difference in the values of the pressure head at the ends of the pipe is not larger than 20% of the operating pressure head of the selected sprinkler. For example, if the operating head of the selected sprinkler is 20 m (30 1 b / h 2 ) the pipe should be of such a diameter that the difference in head along the pipe is not more than 4 m (6 lb/in.2). The difference in pressure head along the sprinkler laterals is equal to the sum of the longitudinal head losses and elevation differences along the pipe. For example, given that the head losses in the sprinkler lateral are 3 m, the pipe is laid on a downward slope of 2 % , and its length is 100 m. The difference in elevation between the two ends of the lateral is, therefore, 2 m. Thus the difference in pressure head is 3 - 2 = l m. In this example, if the pressure head at the entrance to the first sprinkler is 20 m, then the pressure head at the last sprinkler on the lateral is 19 m. If the same pipe is laid along the contour line, the pressure head at the last sprinkler will be 17 m. In the computation of head losses along sprinkler laterals it is customary to neglect local head losses at the multiple-outlet couplers. These losses are caused by the fact that some of the water flows out to the risers, thus causing an extra disturbance. Experiments have shown that the magnitude of the local head losses is very small, even in such cases where a large number of sprinklers operate along the lateral. Computations of head losses in a lateral are carried out after the sprinkler and its discharge have been selected, and after the number of sprinklers on a lateral and the length of the lateral have been fixed. The first step is to compute the required discharge at the head of the lateral pipe, This discharge is equal to the product of the selected sprinkler discharge and the number of sprinklers along the lateral. This computation is only approximate, but the error involved is not large if the difference between discharges of extreme sprinklers is within 10% of the selected discharge. The value of the head loss is determined by the diameter of the pipe used, its coefficient of friction, and its length. It is also assumed as a first estimate that the discharge, computed for the head of the pipe, flows along the full length of the lateral. The head loss is usually computed with the aid of Hazen-Williams tables, taking a value of C = 140 for aluminum or PVC pipes. The actual discharge in the lateral is not constant but diminishes along the pipe. It follows then that the head losses will also be smaller than the values obtained from the tables, since the latter are based on the assumption of constant discharge. T o obtain the actual head loss in a lateral, the head loss for constant discharge is multiplied by a coefficient F (see chapter on Pipe Flow: Head Loss with Variable Flow, and Table 12, page 187).

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After computing the head loss along the lateral, for the selected diameter, the changes in the pressure head are checked, taking into account the differences in elevation. If the differences in the pressure head are larger than 20% of the pressure head for the selected sprinkler, a larger pipe should be considered. When these differences are less than the allowable 20070, the diameter used in the computation may be adopted as final, or a smaller diameter may be used for at least part of the length of the sprinkler lateral. Example 1: Design of a sprinkler lateral Data: Sprinklers used are of the slow revolving type, Lego B7, having 4.0 X 5.5 mm nozzles. The selected discharge is 2.61 m3/hr, obtained at a pressure head of 30 m. Spacing of the sprinklers along the lateral is 12 m, except for the first sprinkler which is spaced 6 m from the head of the lateral. The length of the field is 120 m. The number of sprinklers is 10, and the length of lateral is 120 - 6 = 114 m. The lateral operates along the contour line. Aluminum pipes are used. Solution: The value of the coefficient F obtained from Table 12 (page 187) is 0.353. Values of J, for constant discharges, are taken from the Hazen-Williams tables for C = 100 and are multiplied by the coefficient K = 0.536, corresponding to a value of C = 140 for aluminum pipes. The total discharge at the head of the lateral is Q = 10 X 2.61 = 26.1 m3/hr. The computation of head losses for sprinkler laterals of three diameters is shown below: D (in.)

J for C = 100

J for C = 140per thousand

Y, for 0.114 Km pipe

The allowable difference in the pressure head is 0.20 X 30 = 6 m. As the lateral is operating along a contour line, the difference in pressure head is due solely to the head loss YL.It can be seen that the 2 in. lateral is too small, since the head loss is larger than the allowable loss of 6 m. The pipe chosen should, therefore, be 3 in. An alternative solution is to use a lateral composed of two sections of different diameters. The first section will be 3 in. diameter, and the second section 2 in. diameter. The proper choice of the lengths used of each diameter, will enable the full use of the allowable head losses. In the above example, the lengths chosen are 30 m of 3 in. diameter pipe, and 84 m of 2 in. diameter pipe. The computation of the head losses in the combined lateral is as follows: 1.

2.

3.

The head loss for the sprinkler lateral is computed for the discharge of 26.1 m3/ hr, assuming it t o be 3 in. in diameter. This loss was already found to be 2.2 m. The discharge is computed for the upstream end of the 2 in. lateral section, considering the number of sprinklers along this section. For the 84-m section, the number of sprinklers is 7, and the discharge is:

The head loss is computed for the latter section, the discharge, Q, being 18.2 m3/hr, and the diameter being 3 in. The value of the coefficient F, according to Table 12, page 187 (all spacings are equal), is F = 0.425. The head loss is computed below:

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D = 3 in.

4.

The head loss computed in (3) is subtracted from the head loss in (1):

5.

The head loss is computed for the 84-m section of 2 in. diameter:

D = 2 in.

Y,,

6.

= 256 X 0.084 X 0.536 X 0.425 = 5.2 m

The head loss computed in (5)is added to that computed in (4)to give the total loss of head:

The total loss of head obtained for the combined sprinkler lateral is slightly larger than the allowable loss, which is 6 m. It should be remembered, however, that the allowable loss was chosen arbitrarily. The head loss is 21% of the selected pressure head, and the above solution is satisfactory. Another possible solution is to shorten the length of the 2-in. pipe to only 72 m, thus decreasing the head loss below the allowable 6 m. Computing the head loss for the latter alternative, according to the procedure given above, leads to a value of head loss of 4.9 m which is 16% of the pressure head of the chosen sprinkler. The pressure head required for the selected sprinkler should be available at the entrance to the sprinkler located at the center of the sprinkler lateral. The pressure head at the head of the lateral should, therefore, be also computed. Factors to consider in addition to the head loss are the change in elevation along the lateral, the height of the riser, and the head loss in the riser. The shape of the energy line along a sprinkler lateral, with a number of sprinklers, is approximately a second order parabola. The head loss along the first half of the lateral is between 65 and 85% of the total loss along the lateral, depending on the number of sprinklers. A value of 75% may be taken as a mean value for the ratio of loss along the first half of the sprinkler lateral, to the loss along the full length of the lateral. The computations for the required pressure head at the entrance to the sprinkler lateral are as follows: 1. 2.

The head loss along the lateral is computed, and 75% of the value obtained is added t o the pressure head required at the selected sprinkler. The change in elevation between the head of the lateral and its midpoint is added to the value computed in (l)if the pipe is on an upgrade. The change in elevation is subtracted if the pipe is laid on a downgrade.

220

3.

CR C Handbook o f Irrigation Technology The height of the sprinkler riser and the head loss in the riser are added to the value obtained in (2).

In Example No. 1, given above, the sprinkler lateral (3 in.) was operating along a contour line and the loss of head was 2.2 m. It is assumed that the riser is 2.5 m long, 1 in. in diameter and is made of galvanized iron (C = 120). The computed head loss in the riser is 0.4 m, and the pressure-head needed at the entrance to the sprinkler lateral is

The above computation is approximate but it is sufficient for practical purposes. The result indicates that the submain should be designed to provide a minimum pressure head of 35 m at the entrance to each sprinkler lateral. Despite the fact that the design of the sprinkler laterals is approximate, an efficient irrigation can be expected if the sprinklers are operated at the correct pressure heads for which they are designed. In many cases the main and submain lines convey the water over long distances. When these lines are on small slopes, large differences in pressure heads can be developed. The values of the pressure head at the parts of the system nearer to the water source can be much larger than those available at the end of the lines. Efficient irrigation can be obtained if the high pressure heads are regulated. The regulation is effected by valves, located in the risers from the submains to the sprinkler laterals, and simple pressure gauges. Proper regulation ensures the equal distribution of irrigation water, according to needs, to all laterals in the field. The investment in the pressure gauges is small in comparison to the cost of the pipes and sprinklers. Present equipment makes possible easy and cheap installation of pressure gauges at the head of laterals. For sprinkler laterals on a slope, the difference in elevation between the ends of the sprinkler lateral has a direct bearing on the choice of the diameter of the lateral. For a downward slope the allowable energy loss, for a given discharge, is increased by the difference in elevation. Increasing the allowable head loss makes it possible to choose a pipe of smaller diameter. If in Example 1Jo. 1 the pipe is on a uniform downward slope so that the difference in elevation is 6 m, the allowable head loss will be increased from 6 to 12 m. The sprinkler lateral can be in this case of 2 in. diameter, giving a head loss of only 11.5 m. The pressure head required at the entrance to the sprinkler lateral is

If in the same example the sprinkler lateral is on an upward uniform slope, with a difference in elevation of 5.5 m between the first and last sprinkler, the allowable head loss will decrease from 6 m to 0.5 m. Having the lateral on an upward slope will make it necessary to choose a 4-in. diameter pipe, giving a head loss of 0.4 m at the given discharge. A pipe of this size is expensive and also involves a great deal of work in the moving of laterals. The pressure head required at the upstream end of the sprinkler lateral in this case is

Spacing of Sprinklers The spacing best suited for each type of sprinkler is determined by field tests. For a

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given sprinkler, tests are carried out at various pressures in the optimal range of pressure heads for the sprinkler. For a given pressure the recommended spacings are determined for various wind velocities. The wind velocity referred to is the mean wind velocity during the test. Sprinkling is usually not recommended during the time of the day when the wind intensity varies greatly. For a given pressure head the wind velocity has a most pronounced effect on the required spacings of the sprinkler. Usually, closer spacings are required for efficient irrigation during high velocity winds. Using spacings recommended for low velocity winds a t times when winds are strong can cause poor application of water. The change in spacings depends on the type of sprinkler, its pattern of distribution, and the wind intensity. Some sprinklers d o not require a change in spacings when the wind intensity varies within a limited range. Spacing the sprinklers closer together along the lateral is economically more desirable than decreasing spacings of the laterals. Sprinkler tests are carried out, for this reason, with the prevailing winds (approximately) at right angles to the sprinkler late r a l ~ .It is not recommended, as a rule, to operate the sprinklers at times when the direction of the wind shifts constantly during application. In the design of sprinkler systems based on rectangular spacings, the direction of the sprinkler laterals should be at right angles to the prevailing winds in cases where the larger spacings are between laterals. Field crops on sloping fields are usually planted and cultivated along contour lines. The sprinkler laterals are usually also installed along the contour lines. If the prevailing wind, during the irrigation period, is also in the direction of the contours, the spacing between the sprinkler laterals should be equal to the smaller side of the rectangle. The number of laterals required in this case is, of course, larger and the cost of the system is increased. The work involved in moving the pipes is also increased. The method of determining sprinkler spacings for a given pressure head and for a given wind velocity is as follows: certain values of the spacings are selected, and the water distribution obtained for the selected spacings is determined experimentally. The water distribution is expressed by a uniformity coefficient, defined below. The spacings are considered suitable if the computed coefficient is above some minimum value. If the coefficient is higher than the desired minimum, larger spacings may be tried. The field test is usually carried out with a single sprinkler lateral (Figure 15a). The tested sprinklers, I1 and 111, are placed at the desired spacings (S,) along the lateral. In case the spacing between two sprinklers is smaller than the sprinkler spray range, a t the selected pressure head, two more sprinklers, I and IV, are placed on the lateral and the test is carried out with all four sprinklers operating. The sprinklers are usually mounted on risers 0.3 m high. These risers are supported in a vertical position. Special tests are sometimes carried out with tall risers. The discharge of the individual sprinkler, at the selected pressure, is predetermined in a separate installation. The discharge for the sprinkler lateral is determined by the number of sprinklers on it. This discharge and the diameter of the lateral are used to compute the head losses. Due allowance is made for sloping laterals. The pressure head needed a t the head of the lateral is computed. The required pressure is maintained by means of a valve and a pressure gauge. It is preferable to use a sprinkler lateral of a somewhat larger diameter, so that differences in the pressure head for the various sprinklers will be small. The accuracy obtained in this case is greater. Cans, for catching the sprinkled water, are arranged in a regular pattern on both sides of the sprinkler lateral. The cans should be of regular shape, with a sharp upper edge, and they should be elevated on bricks to avoid splashes and to insure that the upper edges are in a horizontal plane. The cans are usually arranged in a square pattern, with spacings of between 1 m for low pressure sprinklers, and 5 m for sprinkler

CRC Handbook o f Irrigation Technology

222

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9' 8' 7' 6' 5' 4' 3' 2' COLLECTING CAN

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61 5 ' 4 ' 31 21 1'

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11'

FIGURE 15. Field test with one lateral for sprinkler spacing recommendations. (a) Field test with predetermined spacing S,; (b) superposition in the area between 4 sprinklers for a selected lateral spacing S , .

guns. The spacings used for the ordinary revolving sprinklers are 2 m. The area covered by the cans should be larger than the spray range of the sprinklers tested. The accuracy of the results depends on the number of cans. A better accuracy is obtained if a larger number of cans is used. On the other hand, this necessitates a longer period of time for measuring the sprinkled quantities of water. The mean wind velocity during the test is determined by an anemometer, which is read at regular intervals. Readings of the relative humidity and the temperature are

usually also taken at the time of the test. The rotational speeds of sprinklers are also measured. The duration of each test depends on the intensity of sprinkling, and should be sufficient to enable accurate measurements of water collected in the cans. The duration of the field tests is usually 60 to 120 min. After sprinkling for the desired duration the quantity of water in each can is measured with a graduated flask, and the results are recorded in cubic centimeters. The analysis of the results is as follows: the sprinkler lateral is drawn to scale, with the two sprinklers, I1 and 111, shown in their correct positions. A second lateral is drawn at a distance equal to the desired spacing (S1) between the laterals, and the two sprinklers 11' and 111' are marked, thus forming a rectangle with the sprinklers I1 and 111. It is assumed for analysis purposes that the distribution of water to the left of sprinklers 11' and 111' is identical to that actually obtained in the field by sprinklers I1 and 111. The cans within the rectangle, defined by the four sprinklers (11, 111, 11', and 111') are plotted in their corresponding positions and the quantities collected in each can are noted near the plotted points. For each point, the quantities applied by sprinklers 11, 111, 11', and 111' are summed up. For example (Figure 15b) the total quantity sprinkled into the can next to sprinkler 111 is A 0 (from sprinklers I1 and 111) + A' 6 (from sprinklers 11' and 111'). The uniformity coefficient is computed from the values noted for the cans. The coefficient generally adopted in the U.S. and in other countries, is that proposed by Christiansen:

In this equation C, is the uniformity coefficient expressed in percent, n is the number of cans in the rectangle, and m is the mean quantity of water (cm3) collected in the n cans (equal to the total quantity of water collected, divided by the number of cans, n) 11x1 is the sum of absolute deviations of the individual values from the mean value m. If the mean of the water quantities for the area is 100 cm3, the absolute deviation, 1x1, is 5 cm3 both for a reading of 105 cm3 and for a reading of 95 cm3. The practice in many countries is to recommend tested spacings for a minimum value of C, = 84%. If the value of C,, obtained by the above procedure, is less than 84% the computation can be repeated with a different value of the spacing S, between late r a l ~ .If it is desired to check the water distribution for a new spacing S2, between sprinklers along the lateral, a new test should be carried out in the field.

SUBMAINS AND MAINS General Layout The function of the submain is to convey the water and distribute it through risers, spaced at regular intervals, to the sprinkler laterals. Submains can run either through the centers or along the boundaries of the irrigated fields. In contrast, the function of the main is to convey the water from the water source and distribute it to the submains. When fields are wide, two or more submains may be needed. Where the fields are scattered over the irrigated area, it may be necessary to use secondary mains that branch off from the main lines and convey the water to the individual fields. The layout and the design of the mains and secondary mains depend on the location of the water source and the irrigated fields. The layout and the design of submains in each field are dependent on the shape of fields, topography, types of crops grown, necessary

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CRC Handbook o f Irrigation Technology

farm operations, and the intensity of winds during sprinkling. In planning submain layouts the direction of the sprinkler laterals should be taken into consideration. Often, the direction in which the laterals are run is predetermined by the type of crop. For example, row crops on steep sloping land should be planted and cultivated along the contour lines. The laterals are run in the same direction. Thus the submain would run in the direction of the main slope. If the prevailing wind is parallel to the contour lines, and if rectangular sprinkler spacings are selected, the shorter of the two spacings should be used between the laterals. Generally, however, the desirable system layout is the one which is most economical. For example, given a sloping land surface, the water source is located at the highest point in the field. The crop is pasture, or orchard designed for overtree sprinkling. The prevailing wind is parallel to the contour lines. If the laterals are run along the contour, shorter lateral spacings are required. The number of laterals is increased and the initial costs rise. However, the submains can be placed down the slope, with smaller pipe diameters. A second possible solution is to run the laterals at right angles to the prevailing wind (i.e., down the slope). In this case the number of laterals required is reduced. Smaller lateral diameters may be chosen due to the gain in elevation head. However, the submains have to be placed along the contour lines, thus necessitating larger pipe diameters. After cost calculations are made, the more economical of the two solutions should be adopted. Materials Submains and main lines are generally of asbestos cement, steel, or PVC. Aluminum pipes are often used where supplemental irrigation is practiced. Steel main lines can be placed either under or on the ground surface. Where main lines are placed on the ground the initial cost is lower and repairs can be made easily. However, some interference with farm operations can be anticipated. Also, damage by farm machinery and implements is possible. Asbestos cement main lines are always buried. Submains (except aluminum) that are run through irrigated fields are mostly buried. However, steel pipes that are run along the boundaries of narrow fields can be placed over the ground surface. Steel pipes are strong, elastic, and unbreakable. They are usually manufactured in lengths of up to 12 m and require few connections. Pipe sections can be welded together, thus giving additional flexibility. Steel pipes permit repair work while water is flowing in the system. Steel pipes that are buried in heavy soils can be severely damaged by corrosion even during short periods of time. A double outer coating of asphalt and a special asbestos paper covering are often inadequate, where outside corrosion due to galvanic currents occurs. Cathodic protection can be very effective. However, this increases the initial and annual maintenance costs of the system. Steel pipes that are not coated inside may also be damaged by corrosion, due to the flowing water. Where inside corrosion occurs the result is an increase in the head losses. The effect of corrosion can be best expressed by changes in the Hazen-Williams coefficients. Water of low corrosiveness can reduce the value of C from 135 (new pipe) to 110 in 8 years, and to 105 in 10 to 15 years. Water of medium corrosiveness can reduce the value of C from 135 (new pipe) to 80 in 8 years, and to 70 in 10 to 15 years. Where the water is of high corrosiveness, pipes that are not coated inside should not be used. Commonly used inner coatings are cement or asphalt. This inside coating is very smooth and increases the carrying capacity of the pipelines. Asbestos cement pipes are usually manufactured in lengths of up to 4 m. Therefore, a large number of connections are required. Pipe sections are connected by mechanical couplings. These pipes are always buried and should be aligned carefully. Often, asbestos cement pipes develop cracks when they are buried in heavy soils. These cracks

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can usually be prevented if the pipes are laid over a gravel bed. Two noticeable advantages of asbestos cement pipes are their long life span and their resistance to corrosion. The Hazen-Williams C coefficient has a high value of 135 to 140. This value is constant for a rather long period of time. Fittings and Technical Details General 1. Air valves should be installed at all high points of the mains. Also, drainage valves should be installed at all low points to facilitate emptying of the system. Pipes should be anchored at regular intervals to prevent movement. This is espe2. cially important where steep sloping lands, turns, and junctions are encountered. 3. Submains should not end with the last lateral-riser outlet, but should continue several meters downstream. The additional pipe section reduces losses at the last outlet, and also serves to collect sand and other material. 4. Underground pipelines should be buried at least 0.6 m (2 ft) below the soil surface. This is important especially where heavy farm implements are used. 5. Fast opening or closing off of valves in sprinkler systems should be avoided, in order to prevent water hammer (i.e., the formation of very high pressure heads) which may damage pipes severely. Riser- Valve Turnouts These are used to convey water from the submains to the sprinkler laterals. The risers are usually installed along the submains at regular intervals corresponding to the selected lateral spacings. Sometimes, the risers are installed at spacings that are three times the lateral spacings. This is done to save in equipment costs and prevent possible damage by farm implements. Each riser then serves to irrigate three sprinkling positions. The intermediate positions between risers require the use of extra pipe sections, whose lengths are equal to the lateral spacings and one elbow. Riser-Submain Connections Where steel submain sections are connected by welding, holes are bored for the riser outlets. Each hole has a diameter equal to the inside diameter of the riser pipe. A threaded nipple is then welded around the hole, and the riser is screwed into it. Where pipe sections are connected by couplings multiple outlet T couplers are used at the required spacings. The T couplers are either threaded (usually up to 3 in.) or provided with flanges. On asbestos cement submains multiple outlet T couplers are used for riser connections. Riser outlets are either threaded (up to 3 in.) or provided with flanges. On portable aluminum submains aluminum multiple outlet couplers (6 in. and more) with 2 in.- or 3 in.-threaded openings are used for riser connections. Risers that are installed in buried submains, especially where close lateral spacings are used, can be damaged by farm implements. When risers are damaged, the submains (especially of asbestos cement) may be broken. To prevent this, grooves are often turned in the risers, about 10 cm (4 in.) above the submain. These grooves weaken the risers, s o that when they are hit they are broken without causing damage to the pipes. The risers can then be exchanged for new ones with minimum trouble and cost. Another method is to use special couplers that provide flexibility of movement to the riser around its lower end. A large variety of equipment is available for riser-lateral connections. Some of these are shown in Figure 14. They include the following: 1.

Single or double outlet valve is connected to the top of the riser. The valve outlet, o r outlets are in the direction of the submain. An elbow is used to turn the water

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CRC Handbook of Irrigation Technology

into the lateral. This elbow also facilitates easy and convenient uncoupling of the lateral. A riser-valve is permanently screwed onto the riser. A portable valve opener elbow, coupled by means of latches, is used to regulate the water flow into the lateral. By unhooking the latches the opener elbow can be easily uncoupled and transported to a new position. The elbow outlet can be turned in the direction of the submain to facilitate alternate sprinkling. A 45" valve, screwed onto the riser, and a portable starting elbow are used for turning the water into the lateral. The elbow outlet can be turned to any desired direction.

Pressure-gauges or Pitot tubes are used for pressure regulation purposes. The latter are cheaper but less convenient and less accurate. Alternate Sprinkling In this method of sprinkling, laterals are placed at the center of the previous sprinkling positions every second irrigation interval. Sometimes sprinklers are also moved half a spacing along the lateral. Field observations indicate that alternate sprinkling generally improves water distribution efficiencies, especially when sprinklers operate under windy conditions. Equipment is available to facilitate alternate sprinkling. Figure 16 describes an arrangement for 12 X 12 m spacings, using single or double outlet valves. The first sprinkler on the lateral is a part-circle sprinkler. This sprinkler is set for full-circle operation in irrigation interval A, and for half-circle operation in irrigation interval B. Discharge, during irrigation interval B, is regulated with a valve installed in the sprinkler riser. Head Losses in Riser- Valve Turnout These losses should be included in the design of sprinkler systems. The losses depend on submain and riser diameters, and the type of riser-valve turnout used for turning the water into the laterals. If small diameters are used the initial cost of equipment becomes lower. However, head losses can increase appreciably. Generally, 3 in. riservalve turnouts should be used. Two inch turnouts may be sufficient when low intensity sprinklers and short laterals are used. Approximate head losses in a riser-valve turnout, of the type described in Figure 14a with a 4-in. submain, 3-in. riser of 80 cm length, and a 3 in.-3 in.-3 in. Dorot valve, are 0.7 m at a discharge of 20 m3/hr and 1.2 m at a discharge of 30 m3/hr. If a 2-in. riser and a 2 in.-3 in.-3 in. Dorot valve are used instead, the head losses increase t o 1.9 m at a discharge of 20 m3/hr and 3.6 m at a discharge of 30 m3/hr.

Design of Submains and Mains Submains and mains should have ample diameters so as to assure proper pressure heads at the upstream ends of all laterals in the field. In the selection of pipe diameters the planner should aim at the most economical system, for which the annual cost is at a minimum. The design of pipe diameters is directly influenced by the type of water source. Generally, two types of water sources can be distinguished: (1) water sources that need pumping, or additional pumping, to develop the pressure for sprinkling; and (2) water sources that necessitate no pumping. When the water source is of the first type (for example, a well), the electricity or fuel expenditure should be considered. This expenditure can be rather high if pipe diameters are small and energy losses are large. On the other hand, pumping expenditure can be low if large diameter pipes are selected and energy losses are decreased. The best solution is that for which the annual depreciation and interest costs of the

FIGURE 16.

Alternate sprinkling with 12 x 12 m spacings.

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C R C Handbook of Irrigation Technology

pipe system and the pumping expenditure are at a minimum. This solution is reached by a proper balance of pipe diameters and the selected pump, and is different for each system according t o specific local conditions. Factors that affect the choice of pipe diameters and size of the pump are the size and the shape of the irrigated area, topography, system discharges, cost of equipment, number of pumping hours per season, prices of electricity (or fuel), and the efficiency of the pumping unit. When the water source is of the second type (for example, regional pressure line) both the pressure head available and the pressure head needed at laterals should be considered. The most economical combination of pipes is then selected in view of the computed head losses and elevation differences. This combination of pipes should be able to supply the desired pressure head to each lateral in the field. Before the submains and mains are designed the flows in the sprinkler system should be determined. The pipe lines are designed for the maximum flows expected during the irrigation season. The Submain The maximum discharge, Q1, is computed from the maximum number, N,, of laterals operating simultaneously in the field and the discharge, Q, of the individual lateral. The maximum number of laterals is determined according to the different crops grown and their irrigation intervals, the length of submain, the lateral spacings, and the number of daily irrigation shifts (see examples). The design discharge of the submain depends on the arrangement and manner of advance of laterals that operate simultaneously. Normally, laterals that are designed to operate simultaneously at two neighboring positions result in overdesign of pipes, due to the fact that the whole length of the submain has to be designed for the full discharge, Q1. If however, the laterals are spread equally along both sides of the submain, there will be a gradual decrease of discharges. This permits the use of smaller pipe diameters. One typical arrangement of laterals is shown in Figure 17 (Example No. 2). In this arrangement four laterals each irrigate 10 irrigation positions, thus completing a total of 40 positions in one irrigation interval. Example 2: Submain design Basically, the design of submains and main lines is very similar. Therefore, the following example is limited to the selection of submain diameters. Data and assumptions: 1. 2. 3.

4. 5.

6.

The field is 360 m long and 240 m wide; the submain runs along the center of the field, at a uniform downward slope of 2.2% (Figure 17) The selected sprinkler is "Lego" B7 (5.5 X 4.0 mm nozzles); selected pressure head and sprinkler discharge are 30 m and 2.61 m3/hr, respectively; spacings are 18 X 12 m; sprinkler riser height is 0.8 m Laterals are portable and operate along the contour lines; the number of sprinklers along each lateral is ten; the discharge at the head of each lateral is 26.1 m3/hr; each lateral is 3 in.; required operating pressure head at the upstream end of laterals is 33 m (3.3 atm) All riser-valve turnouts are 3 in.; local head losses are 0.6 m Submain is of asbestos cement; the value of C (Hazen-Williams) is 140 (k = 0.536); the submain is buried 0.6 m below the ground surface; energy loss at the main-submain junction is l .O m Maximum available pressure head at the main-submain junction is 37.5 m (3 % atm)

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4"-Wm.

I

SOLUTION B

ASBESTOS CE

FIGURE 17.

7.

Example of submain design.

Design irrigation interval is 10 days. One daily irrigation shift is used.

Solution: The total number of sprinkling positions along the submain is (360/18) X 2 = 40. Considering one daily irrigation shift the required number of laterals is: 40/ 10 = 4. The arrangement of laterals and manner of advance along the submain is shown in Figure 17a (laterals 1, 2, 3, 4). The discharge distribution along the submain, at maximum flow is shown in Figure 17B. The minimum required pressure head a t any submain-riser outlet is

As a first step it is assumed that this pressure head is zvailable a t the furthest lateral

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CRC Handbook o f Irrigation Technology

(No. 4) along the submain. Submain diameters are then computed upstream from point 4, step by step. Each submain-riser outlet is checked for the required pressure head of 34.2 m. Also, in the selection of pipe diameters consideration is given to the pressure head (37.5 m) available at the main line. The partial discharges along the corresponding submain sections are computed and recorded. For each discharge head, losses are then computed for several selected pipe diameters, and are recorded in a table. This table of head losses is helpful in the design of the submain (J values in the table are for C = 100). D = 3in.; D = 4in.; D D D D D

D D

J

4 in.; 6 in.;

J

4 in.; 6in.; = 8 in.;

J J J

6in.; 8 in.;

J J

= = =

=

= =

Discharge: 26.1 m3/hr, length: 90 m Y, = 9 8 ~ 0 . 0 9 0 x 0 . 5 3 6 2 . 4 . 7 m = 17°/,, Y, = 17X0.090x0.536%0.8m Discharge: 52.2 m3/hr, length: 90 m Y, = 62 X 0.090 X 0.536 3.0 m = 62 O/, Y, = 9 X 0.090 X 0.536 2 . 0 . 4 m = 9 O/, Discharge: 78.3 mVhr, length: 90 m Y, = 131 x0.090x 0.536% 6.3 m = 131 "/,, = 18°/o, Y, = 1 8 ~ 0 . 0 9 0 x 0 . 5 3 6 2l.. 0 m Y, = 5 x 0.090 X 0.536 2 . 0 . 3 m = 5 O/W Discharge: 104.4 m3/hr, length: l00 m = 31°/,, Y, = 31xO.lOOx0.5362.1.7m Y, = 8 X 0.100 X 0.536 2. 0.4 m = 8 o/W

J = 9S0/,,

J

Selection of pipe diameters (Figure 17 C): 1.

2.

3.

4.

Section 4-3 (Q = 26.1 m3/hr). The required pressure head at point 4 is 34.2 m. Initial observation indicates that a 3-in. pipe is too small. A 4-in. pipe is selected. Head losses in section 4-3 are 0.8 m. Elevation difference is 92 - 94 = -2 m. The computed pressure head for point 3 is 34.2 + 0.8 - 2.0 = 33.0 m. This computed pressure head is not sufficient, due to the fact than the elevation difference along section 4-3 is smaller than the head loss. Therefore, the hydraulic grade line is raised by 1.2 m, thus assuring a pressure head of 34.2 m at point 3. The pressure head at point 4 will be 34.2 + 1.2 = 35.4 m, which is above the required pressure head at that point. Section 3-2 (Q = 52.2 m3/hr). A 4-in. pipe seems suitable. Required pressure head at point 3 is 34.2 m. Computed pressure head at point 2 is 34.2 + 3.0 2.0 = 35.2 m. This pressure head is higher than the required pressure head. Section 2-1 (Q = 78.3 m3/hr). A 4-in. pipe seems too small. A 6-in. pipe is selected. Required pressure head at point 2 is 35.2 m. Computed pressure head at point 1 is 35.2 + 1.0 - 2.0 = 34.2 m. This is just the required pressure head, and no adjustments are necessary. Section l-A (Q = 104.4 m3/hr). A 6-in. pipe seems suitable. Required pressure head at point 1 is 34.2 m. Computed pressure head at point A (including local head losses of 1.0 m) is 34.2 + 1.7 + 1.0 - 2.0 = 34.9 m. Available pressure head a t the main line is 37.5 m.

In view of the selected pipe diameters an extra pressure head of 37.5 - 34.9 = 2.6 m is left over. Changes can now be made. For example, a short length (about 25 m) of a 6-in. pipe, a t the end of section 2-1, can be replaced by a 4-in. pipe. However, the advantage of this change is rather doubtful. Because of inaccuracies in the computations and assumptions the extra pressure head of 2.6 m may be regarded as a safety factor against any possible lack of sufficient pressure. The proposed solution is, therefore: 190 m of a 6-in. pipe and 180 m of a 4-in. pipe. Normally, results of computations are set u p in tables. The detailed computations in the above example were given merely for demonstration purposes.

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Additional remarks: 1.

2.

3.

4.

An instruction plan, showing the arrangement and the manner of advance of the laterals, should be prepared for the benefit of the farmer. This plan should also include lateral operating pressure heads and daily sprinkling hours. A plan of this kind is very helpful in the efficient operation of sprinkler systems. Submains and main lines are designed in steps. First, pipe diameters are selected in accordance with the water source. Then, pipe diameters are checked and if necessary changes are proposed. Finally, an economical and efficient solution is chosen. Sometimes the soil surface along the submain is not uniform. In the event that high spots exist along the submain, care should be taken to assure sufficient pressure heads at these spots. Where long, downward, steep sloping submains are used very high pressure heads can result in the distant, downstream parts of the irrigated areas. These high pressure heads are not desirable. Generally, the solution involves the installation of valves at regular intervals along the submain. These valves are used to regulate pressure heads along different sections of the submain. In addition, pressure heads required a t each lateral along individual sections of the submain are regulated with the usual manometers, mounted on the riser-valve turnouts. Long main lines, laid along steep downward slopes, are also divided into pressure zones, in the manner explained above.

Summary: Submains and mains should be designed on the basis of local conditions. In each case consideration should be given to the required pressure heads, the discharges, the types of pipes used, the surface topography, and the water source. The sprinkler pipe system has to be both efficient and economical.

DESIGN OF A SPRINKLER SYSTEM The complete design of a sprinkler irrigation system makes use of the principles presented in the previous sections of this handbook for the determination of the specific irrigation requirements and design factors. These will, for the most part, not be repeated here, but references will be made to the appropriate chapters. A few additional factors must be considered. Sprinkler System Efficiency The efficiency of water distribution uniformity and water losses, occurring prior to infiltration, combine to give the system efficiency. T o get the gross water requirement the net water requirement is divided by the system efficiency: Gross water requirement

=

net water requirement sprinkling efficiency (percent)

X

100

The efficiency of water distribution (which is the ratio of minimal depth to average depth of wetting over the entire irrigated area) depends largely on the type of sprinklers used, the sprinkler spacings, and the winds that blow during operation. This efficiency may change even for the same area, since winds are seldom constant in magnitude and direction, and therefore the accuracy with which it can be determined is questionable. Under proper design and operation conditions for daytime irrigation, the distribution efficiency is generally assumed to vary between 75 to 85%. These figures may be increased somewhat for night sprinkling. Sprinkling water losses result from evaporation and drift of drops while in the air,

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and from evaporation of wetted foliage and soil. Evaporation losses depend on several factors, such as temperature, relative humidity, wind, sprinkling rate, and size of drops. Both evaporation and drift losses can change greatly during the irrigation season. This makes it rather difficult to reach an accurate estimate for design purposes. Generally, evaporation and drift losses are estimated on the basis of experience. We may assume that such losses may reach 30% (of the sprinkled water) and more under extreme climatic conditions, or 15 to 20% under average climatic conditions. These figures apply to daytime irrigation. For night irrigation losses may be perhaps 5 to 10% of the sprinkled water. If we consider these figures as a fair estimate of losses, then the efficiency for daytime irrigation may be estimated to vary from 70% or less, under extreme conditions to 80 to 85% under average conditions. For night irrigation the efficiency would be 85 to 90%. The overall sprinkler system efficiency is computed by multiplying the estimated uniformity efficiency by the efficiency resulting from evaporation and drift losses. Thus, for average daytime conditions, the uniformity efficiency is estimated at 80% and the losses estimated at 20%. The estimated design system efficiency would be 64%. For night irrigation, under the same average conditions, the estimated design system efficiency would be 0.85 X 0.90 = 0.76. T o help the planner, following are recommendations for the Pacific Coast of the U.S. 1. 2. 3. 4. 5.

6.

The design basic efficiency is 70% under temperate climatic conditions. The basic efficiency may be increased to 80% in coastal areas. The basic efficiency is 50 to 60% under very arid conditions. The efficiencies, mentioned in the above sections, should be decreased by 5% for each additional 7 k/hr. These efficiencies should also be decreased when sprinklers operate on slopes above 12%. The rate of decrease is 5% for each additional 5% slope above the first 12%. The basic efficiency should be decreased, according to the planner's judgement, when sprinklers operate at low rates during the daytime. Other recommendations are presented in Table 1 as a general guideline.

Design Procedure When the necessary basic information has been gathered, the sprinkler system is designed step-by-step, until a final solution is reached. The procedure described below would serve best the design of semiportable systems with revolving sprinklers. However, with a few changes the procedure may be used successfully to solve design problems of fully portable or permanent systems, with other types of sprinklers.

Step 1: Determination o f the irrigation requirements The readily available moisture content on volume basis, i.e. the range between the average critical point and field capacity, is first determined. (See Soil-Water Relationships: Soil Moisture Contents in Irrigation Calculations.) The net moisture requirement is then computed in consideration of the main root-zone of the crop (see chapters on Plant-Water Relationships and Water Requirements of Crops and Irrigation Rates). The net moisture requirement is divided by the estimated system efficiency to give the gross moisture requirement, and by the average daily peak consumptive use to give the peak irrigation interval. A sprinkler system is generally designed for the average daily peak consumptive use. Thus, when we divide the maximum net irrigation requirement by the average daily

Table 1 RECOMMENDATIONS FOR SPRINKLER SYSTEMS EFFICIENCIES System efficiency Irrigation interval Net water requirement 50 mm or 2 in. Net water requirement 100 mm or 4 in.

AVwind - up to 6 k/hr (%)

AVwind - 6 to 12 k/hr (%)

10 days 7- l 0 days 5-6 days 20 days 12-20 days 10 days

peak consumptive use (generally between 3 to 7 mm/day), we get the peak irrigation interval, i.e., the minimal period of time needed to complete the irrigation of the field. This irrigation interval requires the maximum number of sprinkler laterals, and thus is used in determining the discharge-capacities of the system submain and main pipes. Actually, the computed peak irrigation interval should be reduced by a certain magnitude, so as to allow for any needed farm operations. This gives the effective peak irrigation interval used for design purposes. For example, the computed peak interval for cotton at a certain locality is 14 days. The selected effective peak interval is about 7 days (allowing for spraying, etc.). This means that the sprinkler system should have ample capacity to complete irrigation of the field in about 7 days, instead of the computed 14 days. Example 3: Determination of net and gross water requirements, and design irrigation interval A new area is to be designed for sprinkling irrigation. The design will be based on soil data received from soil samples. Following is the accumulated information, needed for design: 1. 2.

3. 4. 5.

6.

7.

The soil is homogeneous to the full depth of the main root-zone. Field capacity is 22% and wilting point is 12% (dry-weight basis). Bulk density is 1.2. The crop is cotton with a main root-zone of 1.20 m. The average critical moisture content for the main root-zone is 16% by weight. In other words, irrigation would follow as soon as 60% of the available moisture content in the main root-zone has been used up. The average daily peak consumptive use is 5.0 mm/day (0.2 in.). The cotton is sprinkled at night, and system efficiency is estimated at 80%. The sprinkling rate is 10 mm/hr (0.4 in./hr). Total number of lateral irrigation positions, along the submains, is 48.

Solution: Step 1 . The readily available moisture content (volume basis) is

The net moisture requirement (volume basis) is 7.2% X 1.20 m = 86 mm (3.4 in. or 860 m y h a )

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The calculated peak irrigation interval of the irrigated field is 8615.0

- 17 days

(or 3.4 in.10.2 in./day = 17 days)

The effective peak irrigation interval is estimated at 12 days. The gross irrigation requirement is 86 mm p

0.80

100 mm or 4 in.

"

Sprinkling time for one lateral setting is 100 mm 10 mm/hr

or

4 in.

--

0.4 in./hr

10 hrs

The number of laterals needed per day is 48/12 = 4.

Step 2: Determination o f system layout The locations and directions of mains, submains, and laterals are chosen. Factors that influence the system layout are the water source, crops (directions of rows and cultivations), and prevailing wind directions. Consideration should be given in wide fields to a balance between the number of submains and the lengths of laterals. A saving in the number of submains does not necessarily reduce system costs, since larger or longer laterals may be needed. Since the laterals will generally be laid out close to the direction of the contour in order to be parallel to the crop rows, the submains will generally flow down the slope. On somewhat rolling topography the submains should, as much as possible, be located on the ridges, and supply to laterals on either side. The lower ends of the laterals will meet in the valleys or draws where grassed waterways may also be located for drainage. If this pattern is not followed, sharp bends may be required in the laterals if they follow the contour crop rows. Step 3: Selection o f sprinklers Sprinklers are selected according to pressure head, discharge, sprinkling rate, and spacings. The pressure at the source of water affects the selection of sprinklers. Where this pressure is high the planner can choose sprinklers that operate at higher pressure heads, thus making larger spacings possible. Sometimes high pressure-head sprinklers can be used even where the pressure at the water source is low. A booster pump is then used. Alternatively, low pressure head sprinklers can be used. The calculated annual costs of the alternatives would show which solution is optimal. The magnitude and direction of the prevailing wind also affect the choice of sprinklers. Perhaps the most important factor to consider in the selection of a sprinkler is its sprinkling rate in relation to the soil infiltration rate. Soil water-infiltration is measured in mm/hr or in./hr. When sprinkling rates are higher than infiltration rates ponds form over the soil surface. On sloping land the water flows, causing erosion and soil puddling. Experiments show that infiltration rates of different soils vary with time. At the start of irrigation the infiltration drops at a fast rate, then at a slower rate until it becomes more or less constant. The rate of infiltration drop, the time elapsing until it becomes constant, and the final (constant) value depend on the type of soil, its slope, its physical condition, water drop sizes, soil cover, and soil moisture at the start of irrigation. The final, constant infiltration rate is defined as the basic infiltration rate of the soil. In choosing sprinklers make sure that sprinkling rates are sufficiently lower than the basic infiltration rate of the soil. Methods for determining the infiltration

235

Volume 1 Table 2 RECOMMENDED MAXIMUM ALLOWABLE SPRINKLING RATES Maximum allowable sprinkling rate (in./hr)

0-5%

5-8%

Over 12%

8-12%

Description of soil and profile conditions

With cover

Bare

With cover

Bare

With cover

Bare

With cover

Bare

Sandy soil; homogeneous profile to depth of 1.8m Sandy soil over heavier soil Light sandy-loam soil; homogeneous profile to 1.8m Sandy-loam soil over heavier soil Silty-loam soil; hom. profile to 1.8m Silty-loam soil over heavier soil Clay soil; silty clay loam soil

2.00

2.00

2.00

1.50

1.50

1.00

1.00

0.50

1.75

1.50

1.25

1.00

1.00

0.75

0.75

0.40

1.75

1.00

1.25

0.80

1.00

0.60

0.75

0.40

1.25

0.75

1.00

0.50

0.75

0.40

0.50

0.30

1.00

0.50

0.80

0.40

0.60

0.30

0.40

0.20

0.60

0.30

0.50

0.25

0.40

0.15

0.30

0.10

0.20

0.15

0.15

0.10

0.12

0.08

0.10

0.06

From Handbook of Engineering Practices for Region 7, Planning Sprinkler Irrigation Systems, Pacific Region, Soil Conservation Service, U.S. Department of Agriculture, Washington, D.C., 1949, p. V1-l1 (1-6).

time curve for a soil are described on pages 34 to 37. Table 2 presents recommendations for maximum allowable sprinkling rates to be used in the selection of sprinklers. The sprinkling rate is also important in determining the time required for irrigation. Sprinkling at low rates may require more laterals, because discharges are smaller. On the other hand, sprinkling at higher rates enables a larger number of irrigation shifts per day, because the discharges increase. These factors should be weighed by the planner before a final selection of sprinklers is made.

Step 4: Determination o f the number o f laterals per day, the lateral length and discharge Based on the selected sprinkler spacings the total number of lateral operating positions is determined for each field. For example, if the submain is 360 m long and spacings between laterals are 18 m, the number of lateral operating positions along one side of the submain is 20. The total number of lateral operating positions is 40. The number of laterals per day (for each field) is then computed on the basis of the effective irrigation intervals already determined. If, in the above example of the crop irrigation interval is 10 days, then the number of laterals needed per day is four. The lateral length is determined next. It is usually some even fraction of the width of the field, such as 1/2, 114, 1/6, etc. This enables each submain to feed laterals on both sides. Since the spacings between sprinklers along the lateral are known, the number o f sprinklers can now be fixed. The lateral discharge is computed, using the selected sprinkler discharge. For example, assume that the selected sprinkler discharge is 2 m3/hr, (8.8 gal/min) and the lateral length is 120 m (400 ft). If sprinklers are spaced every 12 m (40 ft) along the lateral, then the discharge at the head of the lateral is: (120/12) X 2 = 20 m3/hr (88 gal/min). Step 5: Determination o f lateral diameters Lateral diameters are determined on the basis of their calculated discharges, selected

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CRC Handbook of Irrigation Technology

pressure heads, and number of sprinklers. The operating pressure at the head of each lateral is also determined (see page 217, Design of Laterals).

Step 6: Determination o f sprinkling operating time, number o f irrigation shifts per day, number o f laterals per irrigation shift, and the total number o f laterals per field For each crop the sprinkling operation time at each operating position (i.e., the duration of one irrigation shift) is determined. The peak gross moisture requirement, and the sprinkling rate of the selected sprinkler are used in the computation. For example assume the selected sprinkling rate is 9.2 mm/hr, (0.36 in/hr). The gross moisture requirement is 100 mm or 4 in. (see Step 1). Therefore, the lateral operating time at any one position is 100/9.2 = l 1 hr. With this information the number of shifts per day for one lateral can be determined. Accordingly, the number of laterals needed per shift, for each field, is determined. In planning the irrigation shifts the system discharge, at any one shift, should be checked against the discharge available at the water source. The system discharge at any time is computed by multiplying the number of laterals, operating in the different fields, by lateral discharge. The need for extra laterals is also checked. Once this has been done, the total number of laterals per field, and for the whole system, can be determined. Extra laterals are used where two or more irrigation shifts are planned, and night moving o f pipes is to be avoided. They are also used where daytime shifts immediately follow each other, or where heavy, muddy soils have no chance to dry up in the time interval between two consecutive irrigation shifts. For example, assume a field is irrigated in two 6 hr shifts per day. These are 6 a.m. to 12 a.m. and 16 p.m. to 22 p.m. Two laterals are needed per shift. A total of four lateral positions have to be irrigated in 24 hr. However, two extra laterals are needed to avoid night hauling of pipes. These laterals are placed in position during the daytime and would be ready for operation the next morning. The total number of laterals needed for the field is six. Step 7: Determination o f submain diameters For each field the critical arrangement of laterals, operating simultaneously along the submain, is checked to determine the design discharges of the submain along different sections of its length. The design is made for the crop which requires the maximum number of laterals. For example, a field is planned for a 3-year crop rotation. The effective irrigation intervals for the three crops are 6, 8, and 10 days. The total number of lateral operating positions along the submain is 48. Thus the number of positions to be operated daily is 8, 6, and 5, respectively. Assuming two daily irrigation shifts for the first and second years, and one daily irrigation shift for the third year, it becomes obvious that the maximum number of laterals that operate simultaneously is five because of the single shift. Step 8: Determination o f main diameters The discharges of the main lines for each irrigation shift are used to determine pipe diameters. For each section of the main line the maximum flow is considered. Several alternatives are checked, so that the final plan will be the most economical. At this stage changes may be in the previous steps. For example, it may be necessary to go back and select other sprinklers, or plan new irrigation shifts, etc. Step 9: Preparation o f instruction plans for the farmer Instructions are prepared for the use of the farmer. This is done for each field, and should include the operating pressures at the head of laterals, the arrangement of laterals along submains, and the pattern irrigation shifts. All other pertinent information should also be included.

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237

Step 10: Specifications, selection o f equipment and bill o f materials Specifications should be prepared for all equipment and installation procedures. Quality of materials and methods of construction should be fully detailed. If more than one brand of equipment, such as sprinklers or fittings are available, the catalogue numbers of the acceptable alternatives should be indicated to avoid incorrect substitutions. I f the project is to be let out to contractors for competitive bids, precise methods of measurement for each item should be indicated. This is especially important in the laying of the mains and submains, as it involves excavation, backfill, etc. After the specifications are written a complete bill of materials should be prepared which includes the quantities of every item of equipment and work. It is customary for the design engineer to add his estimate of the unit prices for every item to serve as a guide for the client, but these estimates are not revealed to the bidding contractors. The total investment cost of the project is then calculated. Step 11: Calculation o f annual costs The annual fixed and operating costs per hectare or acre are computed. Items to be considered are depreciation of equipment and structures, interest, insurance, annual fixed costs for water and electricity connections, maintenance and repairs, labor, electricity, and water bills, etc. The following figures for estimated life of equipment may be used to compute depreciation. 1. 2.

3. 4. 5. 6.

Steel pipe, laid over ground: 20 to 25 years, or 4 to 5% annually Aluminum pipe: 8 to 10 years, or 10 to 12.5% annually Asbestos cement pipe: 25 to 33 years, or 3 to 4% annually Centrifugal pumps and electric motors: 10 to 15 years, or 7 to 10% annually Sprinklers: 5 to 6 years, or 17 to 20% annually Valves: 15 to 20 years, or 5 to 7% annually

Annual interest on capital investment depends upon the current bank rate. A commonly used figure for insurance can be 2% of the initial investment. Estimated annual repairs and maintenance costs, in percent of the initial investment, are given below for some characteristic items: l. 2. 3. 4. 5.

Steel pipes: 2 to 3% ~ l u m i n u mpipes: 4 to 6% Pumps:4to5% Electric motors: 2% Valves: 2%

Annual irrigation labor costs depend on several factors, such as current wage rates, number of irrigations per season, lateral spacings, type of equipment and height of sprinkler risers, number and diameters of laterals, topography and soil type, crop density and height, and experience and physical condition of the farmer, etc. Example 4: Design of alfalfa field and orchard for sprinkling irrigation The following example is given to demonstrate the step-by-step procedure for design of sprinkling irrigation. Only one alternative plan will be checked. Also, cost computations will be excluded.

Data: Map of area. Fields, elevations, water source, and direction of prevailing winds 1. during the daytime are shown in Figure 18.

FIGURE 18.

Example of sprinkler system design.

Volume1

239

2.

Water source. A regional canal west of the irrigated area supplies water for irrigation. Water elevation in the canal during the main season is + 10.0 m. Maximum allowable discharge to be pumped is 175 m3/hr (770 gal/min). The canal is deep and wide. The irrigation water is clean and no special screening is needed. Water is of low corrosiveness. Electrical conductivity of the water is very low. Chlorine concentration is 75 mg/l, which is low.

3.

Soil. A l f a l f a field: The soil profile is a homogeneous silt loam to a depth of 3 m, (10 ft) over the whole field. Drainage is good. Water table is deep. No clay or hard pan is present. Field capacity is 33% and wilting point is 26% (dry-weight basis). Bulk density is 1.25. The maximum design infiltration rate is 12 mm/hr (0.5 in./hr) (considering row crops in the future). Orchard: The soil profile, drainage and water table are same as in the alfalfa field. Soil is sandy loam. Field capacity is 18% and wilting point is 13% (dryweight basis). Bulk density is 1.3. Design infiltration rate is 18 mm/hr (0.7 in./hr). Crop. Alfalfa: The peak consumptive use occurs in July. Effective root-zone depth is 1.2 m (4 ft). Average daily consumptive use, at the peak irrigation interval, is estimated at 5 mm/day (0.2 in./day). Average critical moisture content (for the effective root-zone) is 40% above wilting point (i.e., the next irrigation is required when 60% of the available moisture in the effective root-zone has been used). Field is designed for night sprinkling. Orchard: The peak consumptive use occurs in July. Effective root-zone depth is 1.2 m. Average daily consumptive use, at the peak irrigation interval is estimated at 3.5 mm/day (0.14 in./day). Average critical moisture content (for the effective root-zone) is 30% above wilting point. Orchard is designed for daytime undertree sprinkling. Miscellaneous. The design system efficiency is 75% (for both orchard and alfalfa field). Prevailing wind during the day time has a west-east direction; magnitude is 2.0 m/sec (4.5 mi/hr). Wind at night is very light.

4.

5.

Solution: 1.

Gross irrigation requirements and design irrigation intervals. Alfalfa: Available moisture content (weight basis): 33 - 26 = 7% Readily available moisture content (weight basis): 7 X 0.6 = 4.2% Readily available moisture content (volume basis): 4.2 X 1.25 = 5.25% Net irrigation requirement: 5.25 X 1.20 m = 63 mm (630 m3/ha) or 2.5 in. Gross irrigation requirement (night sprinkling): 63/0.75 = 840 m3/ha or 3.33 acre-in. Calculated irrigation interval: 63/5.0 2. 12 days (2.5 in./0.5 in.). Effective irrigation interval (considering the local practices of two irrigations between consecutive harvests, and spraying demands): 5 days.

Orchard: Available moisture content (weight basis): 18 - 13 = 5% Readily available moisture content (weight basis): 5 X 0.7 = 3.5% Readily available moisture content (volume basis): 3.5 X 1.3 = 4.55% Net irrigation requirement: 4.55 X 1.20 m = 55 mm (550 m3/ha) or 2.2 in.

CRC Handbook o f Irrigation Technology Gross irrigation requirement (daytime undertree sprinkling): 55/0.75 or 2.9 in. Calculated irrigation interval: 55/3.5 2. 16 days (2.2/0.14 = 16) Effective irrigation interval: 12 days

S

73 m

System layout. The system layout, including fields, water source, pump location, main and submain pipes and laterals is shown in Figure 18. The pressure is supplied by a centrifugal pump, operated by an electric motor. The main and submain pipes are asbestos cement (c = 140; k = 0.536). These pipes are buried 0.6 m (2 ft) under the soil surface. The sprinkling system (in both alfalfa field and orchard) is semiportable. Riservalve turnouts are 3 in. in diameter, of the type described previously. Adapters (3 in. X 2 in.) are to be used in orchard for 2 in. laterals. Submain risers in the alfalfa field are to be constructed at the selected lateral spacings. However, the risers in the orchard are to be constructed at intervals three times larger than the selected lateral spacings. Lateral operating positions between risers will be irrigated by using extra sections of tubing. Sprinklers. Alfalfa: Selected sprinkler is Naan 333 (?A in.), 4.6 X 3.8 mm nozzles Selected sprinkler pressure head: 25 m (2.5 atm), or 37.5 lb/in.' Spacings: 18 X 12 m (60 X 40 ft) Selected sprinkler discharge: 1.98 m3/hr (8.7 gpm) Calculated sprinkling rate: 9.2 mm/hr (0.36 in./hr)

Orchard: Selected sprinkler is Naan 223 (?A in.), 4.0 mm nozzle (7') Selected sprinkler pressure head: 20 m (2.0 atm), or 30 lb/in.2 Spacings: 10 X 6 m (33 X 20 ft) Selected sprinkler discharge: 0.69 m3/hr (3.0 gal/min) Calculated sprinkling rate: 11.5 mm/hr (0.45 in./hr) Laterals needed per day. Lateral discharge. Alfalfa: Total number of lateral operating positions in submain DC and EC: (360/18) x 2 = 40 Number of laterals needed per day: 40/5 = 8 Number of laterals needed per day for each submain (i.e., DC and EC): 812 =4 Lateral discharge: number of sprinklers along each lateral is N = 10; therefore, Q = 10 X 1.98 2.20 m3/hr, (88 gal/min)

Orchard: Total number of lateral operating positions in submains JH and KI: (360/10) X2 = 144 Number of laterals needed per day: 144/12 = 12 Number of laterals needed per day for each submain (i.e., J H and KI): 12/2 = 6 Lateral discharge: number of sprinklers along each lateral is N = 21; therefore, Q = 21 X 0.69 = 14.5 m3/hr (64 gal/min)

Volume I 5.

241

Sprinkling operating time, number of irrigation shifts per day, number of laterals per irrigation shift and total number of laterals for each field. Alfalfa: 'Sprinkling time at .each operating position (length of irrigation shift): 85/9.2 =9?Ahr Number of shifts per day: 1 (night shift) Hours of sprinkling: 20:45 p.m. to 06:OO a.m. Extra (spare) laterals: not needed (laterals will be moved each afternoon) Number of laterals per irrigation shift: 8 (4 laterals operating simultaneously on submain DC and submain EC) Total number of laterals needed: 8 System discharge at night: 8 X 20 = 160 < 175 m3/hr (770 gal/min)

Orchard: Sprinkling time at each operating lateral position: 73/11.5 = 6.25 hr Number of shifts per day: 2 (daytime shifts) Hours of sprinkling: 06:OO a.m. to 12:15 p.m., 12:15 p.m. to 18:30 p.m. Extra laterals: 6 Number of laterals per irrigation shift: 6 (3 laterals operating simultaneously on submain JH and submain KI) Total number of laterals needed: 12 System discharge per irrigation shift: 6 X 14.5 = 87 175 m3/hr (770 gal/min) Regulation: with 2 valves at point B 6.

Laterals. Alfalfa: Laterals are laid along the contours Lateral length: 144 m (475 ft) Number of sprinklers along lateral: N = 10; F = 0.371 Lateral discharge: 20 m3/hr (880 gal/min) Selected pressure head: 25 m (37.5 lb/in.=) Allowable pressure head loss along lateral: 5 m (7.5 lb/in.'); c = 140; k 0.536 Riser height: 80 cm; riser diameter: % in. Riser energy loss: 0.4 m Computation of energy losses for two diameters, with Q = 20 m3/hr D = 2 in.

D = 3 in.

=

242

CRC Handbook o f irrigation Technology Selected lateral diameter: 3 in. Lateral operating pressure head:

Orchard: Laterals are laid along the contours Lateral length: 123 m (400 ft) Number of sprinklers along lateral: N = 21 ; F = 0.360 Lateral discharge: 14.5 m3/hr (64 gal/min) Selected pressure head: 20 m (30 lb/in.2) Allowable pressure head loss along lateral: 4 m (6 lb/in.*); c = 140; k = 0.536 Riser height: 20 cm; riser diameter: 3/4 in. Riser energy loss: 0.2 m Computation of energy losses for two diameters, with Q = 14.5 m3/hr: D

=

2 in.

D = 3 in.

Selected lateral diameter: 2 in. Lateral operating pressure head:

Diameters of submains and main pipes; capacity of pump. All discharges were marked on the map for design purposes. Submain DC only is calculated for the alfalfa field, and submain K1 only for the orchard. Local equivalent energy losses (for submains and main pipes) are assumed to be of the order of 0.3 m/100 m (these include losses in elbows, valves, etc.). Energy losses in riser-valve turnouts are 0.5 m. Total energy losses i1-r suction side of the pump are assumed to be 1.5 m. Minimal diameter for submains is 4 in. Alfalfa: Data of J values (according to Hazen-Williams tables, with C = loo), for design discharges and for several diameters, are given below (all J values are in meters per kilometer; selected values are marked).

Volume 1

243

Discharge (Q) in m3/hr'

"

40

20

D(in.)

60

100

80

Multiply by 4.4 for gpm.

Submain DC (4 in., 6 in. selected diameters) Pressure-head needed at the head of last lateral: 27.5 m Energy losses in riser-valve turnout: 0.5 m Energy losses along DC (according to selected diameters):

Elevation of C is + 19 m Elevation difference in DC: 20 - 19 = + 1 m Local equivalent energy losses: 0.3 X 1.7 = 0.5 Computed pressure head at point C: 27.5 + 0.5

+ 2.0 +

1.0

+ 0.5

=

31 .S m

Main CB (8 in. selected diameter) Computed pressure head at point B (no elevation difference along CB) :

Main BA (8 in. selected diameter) Computed pressure head at point A:

Total pressure head for pump: 42.7 160 m3/hr (700 gpm)

+

1.5

+ 4.0

=

48.2 m. Pump discharge:

Orchard: Main BA is 8 in., determined in the previous sections. J values are given below for design discharges and several diameters (all values in meters per kilometer, and for C = 100; selected values are marked). Discharge (Q) in m3/hra D(in.)

14.5

2 3 4 6

168

33 6*

29

44

119

256

21* 3

45*

6

8 "

87

159

22* 5

Multiply by 4.4 for gpm

Remarks

Along section BFGH Along section AB

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CRC Handbook o f Irrigation Technology

0

50

100

150

200

DISCHARGE, IN M~/HR

FIGURE 19. Characteristic curves for the centrifugal pump selected in example (points A and B are for the alfalfa field and the orchard, respectively).

Submain K1 (4 in. selected diameter) Pressure head needed at the head of last lateral: 24.0 m Energy losses in riser-valve turnout: 0.5 m Energy losses along K1 (according to selected diameter):

Field is level Local equivalent energy losses: 0.3 X 3.6 = l . l m Computed pressure-head at point I: 24.0 + 0.5 + 4.6 + 1. l = 30.2 m Main IH (4 in. selected diameter) Computed pressure head at point H (no elevation difference):

Main HB (6 in. selected diameter) Computed pressure head at point B:

Main BA (8 in. selected diameter) Computed pressure head at point A:

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Total pressure head for pump: 53.9 + 1.5 + 4.0 = 59.4 m. Pump discharge: 87 m3/hr (383 gpm). The selected pump should supply the demands of both alfalfa field (night sprinkling) and orchard (daytime sprinkling). Of the several centrifugal pumps considered, the one whose characteristic curves are described in Figure 19 has been selected. It has a speed of 2900 r/min, an impeller diameter of 7 in., and a 40-hp motor. P u m p efficiency varies between 82% (alfalfa field) and 68% (orchard).

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DRIP IRRIGATION Dov Nir

INTRODUCTION General* Irrigation consists of the practice of providing water to the plant's roots, in such a way that it can readily absorb it, and with it also absorb mineral nutrients from the soil. Efficient irrigation, that is to say irrigation that utilizes at a maximum efficiency the water, the soil, the plant, and all other resources involved, will thus be the application of the exact amount of water required by the plant for optimal use, at the best time, and exactly at the right place where the active roots are to be found. To achieve this we must know what these amounts, times and places are, and devise the equipment and technology to make such an application possible. Irrigation science provides us with the data necessary for the achievement of efficient irrigation. Calculations and estimates of potential evapotranspiration show US how much water the crop can use, according to climatic, soil, and growth conditions. Theories of water availability to the plant indicate to us to what extent is it advisable and economical to supply the water at a rate similar to the consumption rate of the plant, or else to store water temporarily in the soil. Soil physics shows us what is the possible water storage within the crop's root zone. Biological, soil, and technical aspects and relationships join in determining the best location for water application. Irrigation engineering (or irrigation technology) provides us with the instruments, equipment, and instructions for operation and maintenance, with the aid of which we try to achieve maximum irrigation efficiency by applying the water according to the above requirements. Water meters, controlled irrigation, and uniformity of application enable us to supply to the crop the correct water amount. Various irrigation methods which provide water at a very low rate (such as pulse irrigation, which provides water only during a certain fraction of the time, intermittently) enable us to keep the soil moisture at a high level of availability (or low water tension), supply the water at the right time, and to the root zone only. Conventional irrigation practicesachieve these conditions only partially, at best: Border irrigation can provide, if optimally designed and operated, a rather uniform application; however, this requires high flow rates and large discharges, and therefore infrequent irrigations. Thus water is not continuously readily available to the plant; moreover, all the field area is wetted, even where no plants grow, wasting water and encouraging weed growth. Furrow irrigation can apply water just where the crop is planted, and more frequently, but the uniformity of application is not always satisfactory, and decreases as irrigation intervals get shorter. Sprinkling irrigation, when properly designed, can apply water in much more precise amounts than the previously mentioned methods; also, by means of pulse irrigation, it can achieve a rate of supply fairly similar to the plant's rate of consumption; still, it must wet all-or most-of the soil area, whether covered by crops or not. Subirrigation is wasteful in water, provides water to large soil volumes, and generally cannot be used in very short intervals. * For definition of units and notations, see end of chapter.

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Drip Irrigation Drip irrigation is termed "drip," or "trickle," irrigation in English ("daily flow" in Australia); "irrigation en goutte goutte," or "igoutte," in French; "irrigacion por goteo" in Spanish; "irriga550 por gotejo" or "gotejamento" in Portuguese; "irrigazione a goccia" or "diuturnal" in Italian; and "Tropfelbewasserung" in German. This method is supposed to provide water most efficiently by applying it at the right rate and practically only to the plant's root area. This is actually not a single method but a set of solutions to the above problems based on a common principle of very low application rates (few liters per hour or cm3 per second), at zero ( = atmospheric) pressure, at specific points of the soil. There is no movement of water over the surface of the soil, and lateral and vertical spread of water occurs inside the soil, and only to a limited extent. This form of application is attained with the help of a special piece of equipment - the emitter - designed to produce low discharges at atmospheric pressure heads (in spite of possible high line pressures) at specific points; only a fraction of the soil surface is wetted, generally between 10% and 50%. The drip irrigation system may be located at a certain depth under the surface, on the surface, or even at a certain height above the surface. In general it is a solid, or nonportable system, but portable and semiportable systems are being used now in many parts of the world, cheaply and efficiently. Drip irrigation systems (or, in short, drip systems) are classified according to: Emitter type System location (on or under the surface) Operation pressure ("low", about 5 m or less; or "high", around 1 atm [ l 0 m] or more) Portability (nonportable, semiportable, or portable) In general, the present trend is in the direction of a solid system placed on the ground surface, operating at a pressure of about 1 atm and using orifice- or long-path emitters. In most of what follows, a system of that type will be assumed. Originally, drip irrigation was called subsurface irrigation, since the principle started as an attempt to bring the water directly to the root zone. Since then the system has been mostly moved to the top of the soil surface, and the term also created confusion with the method of subirrigation, which really consists of the manipulation of the ground water level by means of a ditch or buried pipe system ("reverse drainage"), and has nothing in common with drip irrigation. Another name, used by the Italians (and mainly by the Italian pioneer of drip irrigation, Dr. Pietro Celestra of Pisa, who has been experimenting with the method, developing it and publicizing it since 1951), is diuturnal irrigation, which means longlasting, or persistent irrigation.'* As a matter of fact, this name fits many methods based on slow, low-rate application, of which drip irrigation is only one. In order to prevent misunderstandings, we shall use the name Drip (or Trickle) irrigation, and leave the name of subsurface irrigation to the method of supplying water to the rootzone continuously from buried pipes.

A Brief History Drip irrigation in principle evolved from subirrigation when, in 1920, the drainage tubes (with open joints) of subirrigation were replaced experimentally by porous pipes. The supply of water to the soil was due to the soil suction and not to the pressure inside the pipe. During the next decades, subirrigation and subsurface irrigation were developed in parallel, with work on the latter method concentrating on the development of suitable porous materials for the pipe. Another version of this approach was

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the perforated pipe. This was a pipe which allowed the exit of water through holes or slits in its wall - but here the flow was caused by the pressure inside the pipes. This type of pipe developed slowly due to difficulties in its manufacture, until the appearance of the plastic pipe - cheap, versatile, easy to perforate, and with different variations to suit many conditions - which solved many of its problems. Still, the perforations were not uniform, and they changed with time (enlarged due to the flexibility of the material or reduced in diameter due to clogging or chemical precipitation; and though larger perforations were less subject to these problems, they allowed a higher than the maximum allowable rate of flow). These problems have been finding their solutions in the last decades through the development of new approaches: in 1948 Cameron Irrigation Ltd. (England) introduced a screw-threaded metal nozzle which had the water passing a helical path around the "screw" and supplied about 1 Iph at 1.3 m pressure; in 1967 it was replaced by a plastic nozzle with twice the output (2.3 jph). In 1956 the Volmatic system was invented in Denmark; this system had the water passing through a long (usually 85 cm) 0.8-mm diameter capillary tube. This supplied water at the rate of about 2 lph at a pressure of about 2 m. In 1962 S. Blass in Israel developed the "high" -pressure long-path emitter, where 3 m long fine tubes, of 1.2 1.4-mm inner diameter, stuck into the wall of a distribution pipe, dissipated the 1 atm pressure in that pipe and created in each an outflow of 2 l / h r . For convenience the tubes were wound around the distributing pipe. Later this was improved and changed into the long-path emitter used at present. Bringing the drip system to the ground surface solved a great many of the clogging problems of the system. Improved manufacturing methods resulted in precisely-sized, uniform emitters, more dependable, cheaper, and longer-lasting. The availability of a wide range of emitters and auxiliary equipment and fittings brought about the great increase in the use of drip irrigation in many countries in the world, mainly the U.S., Australia, Israel, Mexico, South Africa, and others. And in addition to the increase in drip-irrigated areas all over the world, there has been a parallel increase in types of crops irrigated, from deciduous fruits and vegetables to include now almost all crops (field crops, citrus, subtropical fruits, and decorative plants, in fields and in greenhouses). There have also been similar increases in the range of soils used and in the range of water qualities. Reports on the extent of drip irrigation in the world7 mention 290,000 da drip-irrigated in the U.S., 250,000 da in Australia, about 65,000 each in Israel and Mexico, and 35,000 in South Africa, with a world total of about 600,000 da, or 60,000 ha. These values are changing from year to year, at an ever-increasing rate, with the supply o f better, more dependable and cheaper systems, together with an increasing amount of information and know-how. Advantages and Disadvantages of Drip Irrigation Advantages Soil moisture - Drip irrigation keeps soil moisture at a constant, optimal level by renewing the water supply to the root zone at the same rate it is used up. This results in low soil suction, facilitating water and nutrient intake by the plant, and high soil hydraulic conductivity, letting the stored moisture be more readily available to the roots, while the soil, on the other hand, is never saturated, and good aeration is maintained at all times. Moreover, the low irrigation rate makes the method suitable even for low-infiltration soils. Water saving - Water is applied most efficiently, exactly as much as required, when required and where required, so there are minimum losses due to deep percolation, wetting of areas not under crop, or evaporation from land surface, from foliage, or

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in the air. In comparison to sprinkling irrigation where losses due to overirrigating and out-irrigating at plot margins may amount to 20070, this type of loss is almost completely eliminated in drip irrigation. This is even more important in the case of irregular plots. Also, no water is lost through the transpiration of weeds because water is supplied directly and exclusively to the crop. Hydraulics - Water control is easy and more complete. The large number of irrigating points (200 to 2000 per dekare, compared with 5 to 30 in sprinkling) provides better uniformity of application. Low discharges and low pressure heads in the distribution network permit the use of smaller pipes of lower pressure rating which reduces costs. Since irrigations are slow and spread over a long time, peak discharges are reduced, thus requiring smaller pipes, pumps, and fittings, and causing less wear and longer life of network elements. Irrigation operation - Work is comparatively easy and requires less manpower. Irrigation can be continued day and night, regardless of wind, daylight, or other cultivation activities. Automation is easily incorporated into the system. Irrigation of covered crops (in greenhouses or under plastic) is easily carried out, with no wetting of the walls or of the cover (which would have caused a cooling of the microclimate within). Agricultural considerations - Crops often show higher yields, better quality and earlier maturity than under "conventional" irrigation. Fruit yields (including citrus fruit) were found to be higher, and of better quality, and the same was true in the case of flowers; vegetables also showed an increase in yield, while maturing early and out of season. Plant diseases and pests are rarer, there are no leaf burns due to wetting, and sprays and dusting materials are not washed away from the foliage. Weeds are greatly reduced in extent, thus saving the water they do not use, and eliminating the need of control activities. There is no formation of soil crusts and much less mud. All other field operations can be carried out in parallel with the irrigation, since a part of the area remains always dry. Irrigation of saline soils and/or using saline water is possible with no reduction in yield value. Fertilizing - Application of fertilizers can-and should-be done in a dissolved form through the irrigation water, thus making possible a constant nutrient supply, regulated in rate and in composition according to the plant's age and requirements, with reduced fluctuations in availability and less losses. The same goes also for soil sterilization through the irrigation water. Economics - Drip irrigation equipment is not cheap, but compares well with the cost of solid systems of other methods. Labor and operating costs are low. In many cases the increased value of the crop (due to quantity, quality, and time of supply) pays for the whole system in one or two seasons. Disadvantages, Problems, and Some Solutions Agricultural - The localized water application causes the development of a dense, but limited in volume, root mass. This works well as long as there is no change in conditions; but there is no provision or defense against any lack of water due to interruption of supply or system failure, a considerable volume of soil remains unused, effectivity of rainfall is reduced, and there may be poor tree anchorage to withstand strong winds. Continuously high soil moisture conditions may cause root diseases or ,points of low aeration in the soil, while dust problems may arise in that part of the area which remains always dry. Use of the irrigation system for microclimatic control (similar to the use of sprinkling for climatic conditioning in cases of extreme dryness or frosts) is not possible, except for conveyance of hot air or hot (80°C) water to the root zone. Some crop-soil combinations are not suitable for drip irrigation (for example, citrus in sandy soils).

Technical - The main problem in drip irrigation is clogging of the emitters by suspended materials (sand and silt), precipitated dissolved salts (mainly carbonates), rust and other iron oxides, and organic material (including plant roots, live organisms such as algae and minute animals - and inert matter). Cleaning is difficult, costly, and not always successful; filtering, if properly designed and carefully carried out, can solve that part of the problem caused by suspended material (sand and silt), but cannot cope with dissolved salts and oxides, and only in some cases with organic matter. Dissolving carbonates by means of dilute acids (mostly HNO, or HCl) is effective, but it involves an interruption in the system's operation, and does not provide a permanent cure, but must be repeated again and again. Mechanical flushing of the system by water or air under pressure is feasible if the pipes and jointscan withstand the pressure, but its effect is only partly successful generally. Irrigation at higher pressures (10 to 15 m or 1.0 t o 1.5 atm) will make the system less sensitive to this problem and more self-cleaning. Pulse-irrigation (irrigating at a higher rate during a fraction of the time) is even better in such a case, because discharges are higher, while the overall irrigation rate still remains low. Other technical problems include the need for a constant water supply and the high sensitivity of discharge to topographical variations (especially at low pressures of 1 to 3 m). The difficulty of control and maintenance of a system with so many components (the number of emitters per unit area is about 50 times the number of sprinklers) may result in a lower standard of operation. In general, this method requires a lot of knowhow and experience, and very careful operation for optimal results. Salinity - An important problem in drip irrigation is the accumulation of salts in the interface between the irrigated and nonirrigated zones in the soil, whenever there is any appreciable salinity of the soil and/or of the irrigation water. Since the root zone itself is kept constantly at a high moisture level, there is no direct harmful effect to the crop, but in the next growing season these salts, if not leached away, may damage the crop if planted on top of that interface. When drip irrigation is practiced in the dry season and the rainy season provides more than some 300 mm of rainfall, the salts will generally be leached. Of course, good natural or artificial drainage is essential for that (as it is in all methods of irrigation); otherwise artificial leaching should be provided once every 1 or 2 years. This may be done by using the drip system itself, operating it at the highest allowable pressure and for a longer time, or else a portable sprinkling system has often been successfully used. Other problems - Other problems include the cost of the system, which is high in comparison with surface or portable sprinkling irrigation - but generally not high enough to be prohibitive. Also, the system is sensitive to damage by the sun, by passing vehicles and implements, by rodents and by birds (woodpeckers). Proper materials and design, together with some poison at the right time and amount, may solve most of these. Drip Irrigation System Elements Systems vary according to topography, size and shape of irrigated area, crop type and planting pattern, drip equipment, etc. However, a drip irrigation system will typically include most of the following elements (Figure 1): Main pipe - A rigid pipeline, generally steel, asbestos cement, concrete, or similar material, almost always buried underground, conveying the water from the source (such as a well, lake, regional pipeline or canal with a pumping plant) to the main control points in the field. Control head - The central control and operation point of the system, consisting of valves, discharge and pressure meters (means for control and regulation of discharges and pressures, including no-return valves and air vents), automation equip-

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FIGURE 1.

Schematic layouts of drip irrigation systems.

ment and control, filters, and dissolved fertilizer applicators (Figure 2). Each control head serves and controls an irrigation unit, having a unity of irrigation pattern and fertilizing regime. The unit size may vary, and if the field is not too large, it will be operated from one control head as one unit; otherwise it may be divided into smaller units of usually 10 to 50 dekares, each with its own control head, supplied by a main. Submain (or secondary) pipe - A many-valved pipe, distributing the water to the various subunits within the unit. Each subunit, controlled by a valve on the submain, is an area irrigated simultaneously from a single control point. Its size is determined

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LEGEND l MAN

8 PRESSURE

VALVE

3.WATER

METER AND VOLUMETER

4NON RETURN 5.lNLET PIPE TO 6.NR

REWCNG VALVE

9. FERTILEER M M FIPE

2.TAP

FERTLIZER

VALVE

7 3-WAY

VALVE

VALVE

PRESSB

H).WATER

FILTER

II. FLUSHING PPPLICATOR

IP.FIELD

(DRAW) VALVE

SLIPPLY

I3.FERTILIZER

VALVE

APPLICATOR TANK

GAGE

by considerations of field geometry and topography, water supply, and irrigation demands, as well as by uniformity requirements within the subunit. The submain is generally a rigid black polyethylene pipe, in most cases laid on top of the ground. The diameter can be anywhere between 32 and 90 mm, and the pressure rating 4 atm. Auxiliary (or manifold) pipe - A flexible (soft) or rigid pipe, generally of 20 to 75 mm diameter, distributing the water between the laterals that belong to a simple subunit. The manifold and its laterals are designed and operated as a single unified system, the unit drip system (UDS), which is controlled by a single valve. When possible, the manifold should supply laterals on both sides, but water supply characteristics as well as and topographical and geometrical considerations may limit the supply to laterals on one side only. Lateral (pipe) - As a rule, is a flexible (soft) polyethylene or PVC pipe, laid on top of the ground, carrying the emitters. Its diameter will generally be 12 to 25 mm, and its pressure rating 4 atm (unless the system is portable, when structural strength may dictate a 6 atm pipe). Sometimes a buried rigid PVC pipe may be used as a lateral. A typical drip irrigation system may have up to 1000 meters of laterals per dekare (i.e., 10 km/ha!) or even more. Emitter (or dripper) - A device for reducing the line water pressure to atmospheric pressure, providing water at a low, controlled discharge (2 to 40 P/hr). It is mostly made of injected hard plastic material, although brass emitters are still found. The Emitters The emitter, or dripper, is the device, or system element which makes drip irrigation possible by providing irrigation water at low flows and atmospheric pressure. Since the performance of the emitters determines to a large extent the efficiency of the whole system, and since their number is high (varying, typically, between 200 and 2000 per dekare), they should be 1. 2. 3.

Cheap; Uniform in structure and operation; Simple to manufacture, install and maintain;

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4. 5.

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Minimum problems (such as clogging, wear etc.) at standard operating pressures (3 to 30 m); and, while satisfying all the above requirements Able to produce a constant, low-rate water supply, as insensitive as possible to line pressure variations.

Emitters may be classified according to various criteria. The most important are: Emitter principle - Orifice, long path, perforated pipe, double-wall pipe. Flow regime - Laminar o r turbulent (or partially turbulent); this is strongly related t o emitter principle. Operation pressure (in the lateral) - "Low" (2 to 5 meters) o r "high" (8 to 15 meters). P a t h cross-section - "Narrow" (below 0.8 mm), "medium", o r "wide" (above 1.5 mm); related to sensitivity to clogging. Discharges - "Low" (below 4 P/hr), "medium" (4 t o 10 P/hr) and "high" (15 P / hr a n d more). The various types of commercially available emitters in wide use a t present will be described here, classified according to emitter principle (see Figure 3): Orifice emittersconsist of a n orifice producing a jet of water that strikes a cap which acts as a pressure dissipator. These generally operate a t low pressures (2 to 5 m) and have a small opening (0.5 t o 1.0 mm), and therefore are characterized by low application uniformity and frequent clogging, even with filtered water, by precipitation of dissolved salts o r organic matter. O n the other hand they are simple, comparatively cheap, easy to change when system operation is changed, and their turbulent flow provides low variation in discharge with considerable variation in pressure. Discharges vary from 6 t o 70 P/hr, usually u p to 15 !/hr. Their simplest form is just a perforation made in the pipe wall. More sophisticated are self-regulating nozzles, which enlarge as pressure drops, thus reducing the possibility of clogging. Long-path emitters are in principle long tubes allowing pressure drop by friction along the tubes and low discharges. They generally operate at "high" pressures (about 10 to 15 m) and with medium to high cross-sections (0.8 to 2.5 mm), and thus have reduced clogging problems and high application uniformity. They are comparatively expensive, must fit the size of lateral, a n d have nearly laminar flow (which is sensitive to pressure variations and thus requires shorter laterals). Discharges are generally 2 t o 12 P/hr. There are various types of this emitter, including the microtubes (or "spaghetti" tubes), long, narrow tubes extending out of the pipe in all directions (mostly simply pushed into holes made in pipe wall); a n d the screw-type emitter, where the tube takes the form of a helical thread between two sections of pipe one within the other. This last type is uniform, dependable, and insensitive to poor quality water. It may be found in two main forms: the side-emitter, which rides on the outside o f the lateral, connected t o it a t one point, a n d the in-line emitter, which is part of the lateral itself, with the water flowing under pressure inside its inner section. Another variation of this type is the multiple-outlet long-path emitters, working a t higher pressures and high discharges (10 t o 100 l / h r ) , divided into 5 to 10 flows by means of different lengths of tubes going in all directions. Their high discharges provide uniformity and reduce clogging. P o r o u s tubes are pipes with walls having minute pores, through which water may be drawn out by the soil suction. These tubes are buried in the ground and supply water throughout their lengths. They are very easily clogged. Double-wall pipesare two pipes, made of flexible polyethylene, one within the other. Water flows inside the inner tube a t high discharge rate and pressures varying between 3 to 15 m , a n d passes through small perforations in the inner pipe to the space between the two, from where it flows o u t at low pressure through larger perforations ("outlets") in the outer wall. Discharge per outlet is a function of pipe diameters, inlet

Volume 1

LATERAL

1

EMITTER

a. Long- path screw-type

255

LATERAL

emitter

( b ) Schematic representation of in4ine (top) and side (bottom) emitter position.

'L ( c ) Orifice

emitter

( d ) Multi -exit emitter:

with screw-plug A long-path type; Without screw -plug A - orifice type.

TUBING \

FIGURE 3.

Representative types of emitters.

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pressure, and ratio of numbers of holes between inner and outer pipes. Values may be between 1 and 5 P/hr. Outlet spacing is determined by field requirements. This method is cheap, comparatively, and may sometimes be used economically for one or two growing seasons and then discarded. Drip Irrigation Equipment Manufacturers Plastic pipe, in most cases flexible or rigid polyethylene pipe, is manufactured by many companies throughout the world, not necessarily in connection with drip irrigation. The same applies to fittings and appliances, such as connections, valves, pressure regulators, fertilizer applicators, and the like. Emitters are manufactured by various companies. Some of the more well-known are mentioned below. The list is not complete and does not signify quality of products. It is just a means of getting acquainted with some of the names in drip irrigation. Country U.S.

England Israel

Denmark

Company

Type

Drip - EZE@ Submatic, Watersaver@ Subterrain@, Spears@, Uniflow@ Cameron@ WollardB N e t a f i m a , LegoO NAANO Technoramm VolmaticO

Long-path emitters Orifice emitters. Self-regulating orifices. Orifices, long-path emitters and micro-tubes. Orifice with plastic tube. Side and in-line screw/labyrinth emitters. Nozzle with screw-path plug. Orifice and cap. Micro-tubes; orifice with perforated plastic-tube.

HYDRAULICS OF DRIP SYSTEMS General According to fluid mechanics, the flow regime is characterized by the Reynolds number, Re, which represents the ratio of inertia forces to viscous forces during flow. It is important wherever viscosity is important, when flow occurs in small, closed conduits, or around small objects. This is discussed fully in most texts and will be only mentioned here (see chapter on Pipe Flow). The Reynolds number is given by

where Re = Reynolds number, dimensionless; V = flow velocity, cm/sec; D = any characteristic length, such as flow section diameter, cm; and v = kinematic viscosity of water in cm2/sec, a function of temperature. At 20°C, v is close enough to 0.01 cmz/sec. It is about 0.013 at 10°C and 0.008 at 30°C. In most of the calculations that follow, a value of v = 0.01 cm2/sec will yield sufficiently correct results. For a circular flow-path, we can write (with Q in cm3/sec):

If we use "technical" units, i.e., D in mm, Q for pipes in m3/hr, and q for emitters in l / h r , we can calculate: Re = 3.5 37 X 103

Q DV

for pipes

(34

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257

and Re = 3.537

9 -

Du

for emitters

Taking v " 0.01 cm2/sec yields, respectively:

and

According to the Reynolds number, four regions of flow regime are specified: Laminar Unstable Partially turbulent Fully turbulent

Re G 2000 2000 < Re G 3500 or 4000 3500 < Re G 10,000 10,000 G Re

These types of flow regime have an effect on the relationship of friction head loss to flow velocity and conduit size. If we take the widely used Darcy-Weisbach formula:

where L = length of conduit in m; g = acceleration of gravity, on the average 980 cm/sec2; and h, = friction head loss in m, we can look for the dependence of f on Re on one hand and o n the conduit's relative roughness ( = e/D, where e = representative size of roughness), on the other hand. It has been found that: a.

Laminar flow - f is inversely proportional to Re, and unaffected by e/D (i.e. unaffected by the roughness). The following valve is used:

b.

Unstable flow - In this region discharge is unstable, and f cannot be calculated from either Re or e/D. Use of flow in this region is undesirable. Partially turbulent flow, and fully turbulent flow - f depends on both Re and e/D. Use is made of the Colebrook-White formula:

c.

which, for conduits with smooth boundaries, where f depends mainly on Re, assumes the form: 1 -

JE-

-

2 log (Re

a)

-

0.8

and for conduits with rough boundaries and fully turbulent flow, has the following form, independent of Re: 1 -- 2 log 6'

(:)

+ 1.14

= 1.14 - 2 log

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F o r plastic pipes, which generally show turbulent flow with smooth boundary conditions, Formula 7a should be used, o r Blasius' empirical formula for turbulent flow with smooth boundaries, which is simpler and straightforward:

This formula gives f values similar to (generally slightly higher than) those found by Formula 7a, as can be checked by plotting f vs. log Re on semilogarithmic paper according to both formulas. Relationship between pressure a n d discharge - Rewriting Equation 5 we can get, for a given pipe (i.e., for given L and D):

Substituting Q / A = Q/(nD2/4) for V

Under fully turbulent conditions, f depends only on pipe roughness, and not o n flow, so that for a given pipe K, = f X L/2g DSX (4/n)' = constant, and

But, under laminar conditions, f varies with the flow, according to

a n d thus L

hf = 16nvX - X 2g

42 --; X n

X D5 Q2

D

- =

Q

K2Q o r h f m Q

(llb)

where K, = 256 vL/2ng D4 = constant for a given pipe

In summary, for a laminar flow h, a Q , o r Q a h,, while for a fully turbulent flow h, a: Q 2 , o r Q a h,112. In actual practice, we find that in most complex flow conditions we seldom have such "pure" flow conditions, s o that m in the relationship

has a value somewhere between 1 and 0.5, or even out of this range! In drip emitters, the principle is that allavailable head is dissipated in the device, o r that h, = AH = H; thus we can write again

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259

T h e Emitter Orifice Emitter - The flow for a "pure'' orifice is theoretically given by

where q = discharge in cm3/sec, A = orifice area in cm2, C, = flow coefficient, H = pressure head in cm, a n d K, = A C,= constant for a given orifice. This corresponds to the assumption that the flow is fully turbulent. Actually, the emitter is not a freely flowing orifice, Equation 14 is not followed, and experiments result in

where C, is found empirically, and consists of the orifice area, the flow coefficient, and units transformation, s o that q and H may take the "technical units", L/hr and m, respectively; m = empirical exponent, with values mostly in the range 0.38 to 0.56. In a circular orifice, q is proportional both t o the square of the diameter and to Hm; therefore, if we have a line of similar orifices, the condition for a constant discharge for all would be D2 Hm

=

const..

q

o:

D2 Hm

(164

If one of the emitters gives the required discharge q, with D, and H., we can specify for all others (having different pressures) that

where

K, = D,

H F / =~ const.

In such a way a lateral with emitters can be designed for constant discharge, taking into account pressure variation both due to friction loss as well as t o topographical differences. In practice the required changes in D are not done continuously along the lateral, but only in 3 o r 4 sections, each section having uniform emitters corresponding to the value required a t its midpoint. (See the section on Uniformity and Efficiency of Application.) Microtube - Theoretically, the tube length L, required for the dissipation of a pressure head H in a given tube of diameter D can be related t o the discharge q by DarcyWeisbach's formula (Equation IO), rearranged as follows:

With L, in cm, D in mm, q in l / h r and H in m, we get

The value o f f depends o n the flow regime. Theoretically, in many cases of drip irrigation, the flow is laminar. By Equation 4b, Re = 353.7 q / D ; for laminar flow we require Re 2000, o r

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CRC Handbook of Irrigation Technology

Thus, f o r D = 0.5, q = 2, f o r D = 1.0, q = 4, o r D = 1.5, q = 8, the flow is laminar. In that case, we can use Equation 12 for calculating f, and, combined with Equation 19 obtain (in "technical" units):

Actually, experiments with microtube and with long-path screw-type emitters (which work on the same principle), have shown relationships different from either the purely Instead, the value of m in the laminar (q a H), or the purely turbulent (q a H0 equation

was found to vary between 0.56 and 0.81. For example, tests carried out on "NetafimO" screw-type emitters (1971) yielded m = 0.685,13 where (in "technical" units) the values of C 2were: Emitter nominal flow* (l/hr)

*

Fitting pipe of diameter (mm)

Value of C2in Equation 22

Emitter's "nominal" flow refers to the discharge of the emitter at some "standard" pressure, usually 2.5 m for "low" pressure emitters and 10 m for "medium" or "highm-pressure emitters. This is only approximately adhered to. In the example, for instance, "nominal" flows are obtained at about 8 m pressure head. Nevertheless, the "nominal" flow is an indication of the emitter size and its discharge. Usually this value may be used as the emitter's average flow in preliminary computations).

The discharge of an emitter is also influenced by the water temperature. This effect is small, mostly negligible when the flow is turbulent. In laminar and unstable flows it is quite pronounced. Since in laminar flow q is inversely proportional to v - as can be seen from rewriting Equation 11 b in the form:

then from calibrating the emitter at a certain temperature, we can correct for the temperature effect by multiplying by the inverse ratio of viscosities. For example, if (as is usually the case) the calibration was carried out at 20°C, the emitter's discharge at any other temperature t should be found from the relationship:

or: 4t

- E

q,,

1 100 ut(cmz/sec)

since v,, is closely equal to 0.01 cm2/sec. For example, if the emitter's discharge at 20°C was found to be 4.4 P/hr, its flow at 30°C ( v , ~= 0.00803 cm2/sec) would be:

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261

Table 1 DISCHARGE CORRECTION FACTORS FOR TEMPERATURE

When the flow is not purely laminar (and we have seen above that in most commercial emitters it is not), the temperature effect is smaller, and should be evaluated by experiment. For example, in the above-mentioned "Netafim" screw-type emitters, there is an increase of about 1% in q for each degree (Celsius) above 20°C, and a similar decrease for each degree below 20°C. It is clearly seen that the "laminar value" obtained by Equation 21 can serve at best only as a first approximation. Real values should be obtained empirically-such as C, and m in Equation 22, or C,' and m in Equation 25 where C,' = C, X L,:

It is seen that to obtain a constant value of q with varying H, it is required that L, a H". If the desired q is given by a certain emitter with L,, and H,, we can specify for all other emitters

where

K

=-

Lto H:

Multiple exit ("manifold") emitter - This type is a combination of two "stages". The first is a single emitter, orifice, or long-path, with a high discharge (10 to 100 P/hr), which flows, dissipating most of the pressure, into a small reservoir from which the water exits through a group of smaller emitters (which may be orifices, but are more commonly microtubes), with discharges of 1 to 10 P/hr each. These are much shorter than ordinary microtubes, since most of the pressure has already been dissipated in the first stage. The flow in the second stage is mostly laminar, with f in the order of 0.06. Re = 1000. Porous pipe - This requires a different theory and special experimental studies, which are at present being carried out in various locations. It shall not be discussed in the present work. Double-wall emitter - The hydraulics of this are purely empirical. The discharge depends on both diameters, on inlet pressure head, and on the ratio, R, of number of holes in the outer tube to the number of holes in the inner tube. Most manufacturers market only one size of double-wall emitter (i.e., only one pair of diameters), varying discharges and pressure heads by varying numbers and diameters of the hole in either tube. Typical formulas have the forms =

a R"

(Q/hr per hole)

(27a)

q' =

a R"

(?/h1 pcr meter of pipe)

(27b)

q

1

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C R C Handbook of Irrigation Technology

where a and n are empirical constants for given tube material diameters, and inlet pressures, and l is spacing o f the holes in the outer tube. Generally, n varies between 0.5 and l .O, and l between 0.25 and 1.5 m. The Lateral Types of Pipe In general, drip irrigation laterals are plastic pipes (mostly black polyethylene), rigid in the few cases when they are buried, flexible when they are laid on the ground. They are graded according to their test pressures: a pipe of grade 4, for example, has been tested a t 4 atm (or 40 m) pressure. Flexible pipes are available at the lower grades (4, 6, and sometimes 8), rigid pipes from grades 4 to 10. In most cases, for drip irrigation laterals laid on the ground, grade 4 is sufficient. In portable drip irrigation and for buried pipes, sometimes grade 6 is specified for its higher structural strength and durability. The pipes are described by their "nominal" diameters, which, in fact, are their outside diameters. This fact should be taken into account in hydraulic calculations, since these require the use of inside diameters. Nominal diameters of pipes used for drip laterals are 12, 16, 20, 25, and 32 mm. Inner diameters are given by

where D = inner diameter, D. = nominal (=outer) diameter, and t = wall thickness, all in mm. Wall thickness depends on the grade, determining the strength of the pipe. In a grade 4 flexible pipe, approximately t = 1/15 D. + 0.55; in a grade 6 pipe, t = 1/8 D,, more or less (except for D, = 12 mm, where t = 1.7 or 1.6 mm). In rigid pipes t is similar to that in flexible pipe, only the density is higher. Hydraulic Calculations Plastic pipes are very smooth, with a uniform inside diameter. The flow of water in them is generally turbulent with smooth boundaries. As mentioned above, friction in this flow is a function of the Reynolds number. We can use for calculations the DarcyWeisbach formula (Equation 5), with f calculated by Blasius' empirical formula (Equation 8) and obtain:

Using the "technical" units (h, in meters, Q in m3/hr, L in m, and D in mm), and taking v = 0.01 cm2/sec (at 20°C), we obtain

or:

Where J = hydraulic gradient, in % = 100 h,/L. A widely used formula for loss of head in pipes is the Hazen-Williams formula, which, in technical units, may be represented by

where C is a coefficient, representing the pipe-wall roughness. It is not recommended to use this formula for plastic pipes in general, and for drip laterals in particular, both because the dependency of C on pipe roughness (and not on Re) makes it suitable for rough-boundary turbulent flow only, and also because it is known to be good for pipes with diameters above50 mm. Nevertheless, some workers have been using it for plastic pipes, even in drip irrigation, with values of C varying between 140 and 150 for freely flowing laterals, and between 100 to 130 when emitters are so installed that they disturb the free passage of the water in the lateral. The best approach is, again, to test each type of pipe, with its emitters, and find empiricalvalues for the parameters K, n and n, in:

Note that here D, is used, for convenience, so that empirical values found are good only for a given wall thickness (or grade), which should be specified. In many of the empirical formulas, we find that n, = n + 3 , which fits the theory, (see, for example, Equation 29), but this is not a necessary condition. Even in HazenWilliam's formula this condition is not met exactly (n, = n + 3.019). Sometimes formulas of this type (Equation 31) are specified according to the flow regime, as represented by the Reynold's number. For example, values found for flexible, black polyethylene pipes, of grade 4, fit the following:

Thus, for example, for D. = 32, J = 100 h,/L = 0.55 or 0.48 Q'.81,respectively. Plastic pipe manufacturers generally supply, or request, diagrams showing friction head loss vs. discharge. Pay attention to the units of Q,, J, and D (e.g., whether Q is in m3/hr, P/min, U.S. gal/min, Imperial gal/hr; whether J is in decimals, %, or m/ km [ = O/o,]; or whether D is in mm, in., or cm). When such diagrams, or formulas representing them, are available, it is advisable to prefer them to any "theoretical" formula. Calculation of a Multiple-Outlet Pipe By the term "a multiple-outlet pipe" we shall denote a pipe which has outlets for water along its whole length, where the outlets are equally spaced and have similar discharges. As will be explained later, we try to achieve a uniformity in the application of irrigation water by minimizing the differences between the discharges of the various emitters. In such a case we can assume a more-or-less constant emitter discharge. Moreover, the pipe is supposed to discharge all its flow through these outlets, so that its far end is closed. Then, for a pipe of length L and incoming discharge Q, and with N emitters each discharging q, spaced 1apart, we can have the relationships (Figure 4).

CRC Handbook o f Irrigation Technology

264 Number

of

Discharge

of

emitter:

N

N-l

emitter:

q

q

Number of

section

Length of

section

N-2N-3N-4

g

q

q

...

i

...

4

3

2

1

...

q

...

q

q

q

q

.

I

ii-l

.

41 3

2

1

1

Dischorge in section

FIGURE 4.

The lateral, a multiple outlet pipe.

Since, as we have seen, friction head loss is proportional to Q", a decreasing discharge in the pipe will cause a decrease in head loss. Thus, the total friction head loss along such a pipe will be less than the head loss occurring when there is full flow throughout the length of the pipe. Similarly to the practice in sprinkling irrigation, friction head loss in a multipleoutlet lateral is obtained by multiplying the head loss in a fully flowing pipe by a factor F, which is the ratio (loss in multiple outlet pipe)/(loss in fully flowing pipe) suggested by Christiansen14. The following is a short explanation of how F is calculated (see Figure 4). The pipe is seen to consist of N sections (N being the number of outlets, or emitters), each of length 1, all with the same diameter and other hydraulic properties. The flow in the last section is q, in the second section from the end 2q, in the third 3q, and, in general, in the i-th section from the end, the flow is iq. In the N-th section, i.e., the one nearest to the entrance of the pipe, the flow is Nq = Q. Friction head loss for each section is calculated by a formula of the Equation 31 type; thus, for section i, that is to say, the i-th section from the end, we get

The total head loss for the whole pipe will be

and, incorporating the values from Equations 32 and 33

Comparing this value to the friction head loss, h,, in a fully flowing pipe, as given in Equation 31, we obtain:

1

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265

Note that F is found to be a function of n and of N, not of n,. When there may be any doubt, we write F = F (n,N); if there is no doubt (say, because we are using only onevalue of n), it is enough to write F = F(N). F is easy t o calculate when n is a whole number; thus:

It is much more difficult to compute F when n is not a whole number, as is generally the case (for example, when n = 1.75, or n = 1.852, etc). For such cases, Christiansen14 presented a formula, which is exact for n = 1 and n = 2, and correct to three decimal places for n = 3 and for intermediate values. The formula is:

Actually, at the above level of precision (3 decimal places) the first two terms of Equation 39 are sufficient for all N 2 20, so that calculation is easy. At any rate, F has been calculated and the results are presented for use in tables, such as Table 2 here (for 3 values of n: 1.75, 1.80, and 1.852). Note that in the calculation of F we assumed that the lateral begins one spacing ( = 1) before the first emitter, so that we have N emitters and N sections of pipes. This is not necessarily the case; generally the first emitter is either at some distance L, (>>1) from the valve, or is immediately near it. In the first case, we calculate head loss separately for the "blind" ( = without outlets) pipe, and then for the pipe with outlet, according to the second case. In the second case the calculation is as follows: We have a pipe o f length L, with N emitters. The spacing between emitters is L/ (N-l) ( N emitters with (N-l) spaces between them); the discharge of each emitter is, as before, q = Q/N. Head loss in any section i, will be hi = KlqnD-nl

in = K

And the total head loss will be

.

L N-l

D-n1 .N" Q"

in = K L Q"D-"I (N- 1)N"

in

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CRC Handbook o f Irrigation Technology

Table 2 SELECTED F VALUES

We thus see that in this case

Comparing Equation 42 to Equation 38, we can obtain:

That is to say, that once we have calculated F = F(n,N), we can easily calculate from it F' = F' (n,N), i.e. F' for the same values of n and N. Values of F' appear in Table 2, for the same three n values. Example - A level lateral is 100 m long. Starting from its far end there are 75 emitters, spaced 1 m apart. The pipe is flexible black polyethylene, grade 4, its nominal diameter is 16 mm, and wall thickness is 1.7 mm. Tests showed for this pipe loss of head given by

Flow into the pipe is 0.3 m3/hr, at a pressure of 1 atm ( = 10 m). Calculate the loss of head in the pipe, using both F and F'. Summary:

L=100 N=75 1 = 1 D. = 16 D = 12.6 J = 44Q" H = 10 Q = 0.3 Required: h, + h q = Q/N = 0.3/75 = 0.004 m3/h = 4!/hr Solution: J = 44 X 0.3' R = 5.038% = 0.05038 or h = 0.05038 L Given:

(1) Take L, = 25, L2 = L - L, = 75, F(75) = 0.364 h, + h = 0.05038 X 25 + 0.05038 X 75 X 0.364 = 0.05038(25 + 27.3) = 2.63 m

(2) Take L, = 26, L, = 74, F'(75) = 0.355 h, + h = 0.05038 X 26 + 0.05038 X 74 X 0.355 = 0.05038 (26 + 26.27) = 2.63 m As we shall see later, the ratio of pressure heads of the maximum and minimum emitters is important as an indicator of irrigation application uniformity. Let's calculate it: Head at first emitter: Head at last emitter: Ratio:

H, H, R,

= = =

10 - 0.05038 X 26 = 10 - 1.31 = 8.69 m 8.69 - 0.05038 X 74 x 0.355 = 8.69 - 1.32 8.69/7.37 = 1.18

=

7.37 m

Pressure and Discharge Variation along Lateral Pressure variation along a multiple-outlet pipe is not linear, and the average pressure is not (H, + H,)/2. It has been found that the pressure along the pipe (such as that shown in Figure 5) can be closely represented by:

or:

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CRC Handbook o f Irrigation Technology

FIGURE 5 .

Variation of pressure and discharge along a lateral

The average pressure will then be:

or:

N/4(N-1) equals about 0.26 for N = 20, and slowly approaches 1/4 for increasing values of N. Thus we can say that, very closely:

The emitter having this average pressure is found by equating [(i-l)/(N-1)13 1/4, which yields

to

This has a value of 13 (or 0.65 N) for N = 20, and approaches 0.63 N as N increases; that is to say, the emitter operating a t the average pressure is that located at 35 to 37% of the pipe, from the inlet end. The emitter having the average discharge is also near that point, and can, for convenience, be assumed to be that emitter operating at average pressure, s o that, from Equation 15 o r 22 we get

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269

Example - A multiple-outlet pipe has 100 emitters, an inlet pressure of 10 meters, and a pressure head loss equal to 15% of average pressure. Find the pressure at the farthest emitter, the average pressure and its location, and the average, maximum, and minimum discharge, assuming that the lateral is level; and that the emitter's discharge is given by:

Summary: Given: Required: Solution: Hence: or:

N = 100, H, = 10 h, = 0.15 (H) q = 0.9 H" H, E,i ( O ; s , cl,, q , H = H, - 0.75 h,= H, - 0.75 x 0 . 1 5 R H = H,-0.1125H = 10-0.1125i.i H = 8.99 = 9 m h, = 0 . 1 5 H = 1.35m H, = H, -h, = 10 - 1.35 = 8.65 m i(F) = 0.63 X 100 + 0.37 = 63.4 q = 0.9 (9)' 4.05 I / h r = 4.36 I / h r q, = 0.9 (10)" q, = 0.9 (8.65)' = 3.95 P/hr

-

Ratio of extreme pressures: R, = H,/H, = 1.156 Ratio extreme discharges: R, = qN/q, = 1.104 A plot of the above results is given in Figure 5.

=

(R,)O

Local Pressure Losses In addition t o the friction head loss, there are some other head losses in the lateral, the most important of which is due to the resistance to flow a t the lateral-emitter junction. This is more serious the smaller the diameter of the lateral, and is more pronounced in the case of "press-in" emitters (i.e., emitters which are pushed in into holes in the wall of the lateral, a n d generally interfere with the free flow of water in the lateral). This effect is generally presented in terms of the flow velocity head in the lateral, o r as K, in

Where h = head loss per emitter (m) and V = lateral flow velocity (m/sec). In "technical" units, with Q in m3/hr, D in mm, and h in m:

The values of K, (or, as a matter of fact, 6380 K,) are determined empirically. For a 20-mm pipe they may be negligible, while for a 12-mm pipe they may even exceed 10. For in-line screw-type emitters, valves of 0.5 to 0.75 were found. Generally, some of this effect is neutralized by the decrease in the lateral discharge at the junction point. At any rate, this effect is rarely taken into consideration in drip irrigation design. The Distribution System The manifold is really a multiple-outlet pipe, similar to the lateral, but with larger spacings, fewer outlets, and a higher discharge per outlet. It is therefore calculated and designed in a similar manner, using F(or F', as the case may be). The only important difference is that here the source of water is not necessarily at one end of the pipe (see later, in the discussion of pipe design).

CRC Handbook o f Irrigation Technology

270

The submains a n d mains are calculated according to the methods of common hydraulics, a n d there is hardly anything to add. These are not necessarily plastic pipes. If they are, they would generally be of grade 6, s o that higher pressures (and therefore smaller sized pipes) can be employed. Diameters would then be from 40 t o 90 mm. Rigid PVC pipes are often used. These are stronger and smoother, a n d their discharge, for the same outer diameter, is therefore higher. Calculations use the usual formulas, such as Hazen-Williams with C = 130 o r 140, o r (for plastic pipes) empirical formulas of the Equation 31 type. Uniformity a n d Efficiency of Application A correct design of a n efficient irrigation system must achieve a uniformity of water application to the soil, s o as to enable the application of the exact irrigation water requirement during the same time duration, throughout any part of the system that is operated as a single unit. In the case of drip irrigation this means that all emitters controlled by the same valve (or control point) will have as closely as possible the same discharge. Since emitter discharge is a function of the lateral pressure, then if we want (as is usually the case) t o use the same emitter throughout a single subunit, o r a whole unit, we require that pressure variation be reduced t o a minimum, o r at least remain within a specified range. The specification is generally given in terms of the permissible range of discharges. In most cases it takes one of the following forms: 1. 2.

3.

"The discharges of all emitters operated simultaneously as a single unit should have a variation of not more than X percent." "The discharge of the emitter with the highest flow should not be more than X percent higher than that with the lowest flow." "The discharges of all emitters operated as a single unit should be within k x/2 percent of the average discharge."

Each of the above has a distinct meaning and the statements are not always exactly interchangeable. The first form is not specific and unambiguous enough, and therefore is unsatisfactory. The second is the most commonly used; as a formula it would be

where R, = ratio of maximum t o minimum discharge, R,* = maximum permisible value of R, = 1 + x/100, where X = permissible variation, in %. Commonly X is taken as 10%, but sometimes stricter conditions require a narrower range, taking X = 7 o r even 5%. The third form relates the range t o the mean discharge, o r to the design value of q , q,, as in the inequalities:

o r , also

This is not equivalent t o Equation 50 f o r the same value of X. If we wanted t o express the specification (50) in the form of Equation 51a, we would have t o write

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271

(5 2a)

or, substituting the value of R,* = 1

For example, if

X =

+ x/100:

10%, Equations 51a a n d 52b would yield, respectively

and

We can thus see that, with the values of X we use, the two forms, though not equal, are similar a n d therefore interchangeable. (As a matter of fact, many assumptions we have made cause errors which are much larger than this difference!) A s a rule, we would generally use Equation 50 as the preferred form for this specification. The permissible range of pressures follows easily from the permissible range of discharges. Since q = C H", we obtain

where R, = ratio of maximum to minimum pressure. The permissible value of R, would then be

For example, for R,*

=

l . l 0 a n d m = 0.685, then:

Table 3 gives representative value of permissible ranges of discharge and pressure for various values of m . Note that the table values are values of X = 100 (R* - l ) , both for discharge a n d for pressure. A unit drip system (UDS) consists, generally, of a control valve, a manifold (auxiliary) line, a n d a number of parallel laterals with emitters (see Figure 6), and irrigates one subunit of the field. Its design should keep operating pressures within the range specified by Equation 54. O n level ground, the maximum emitter would be the one nearest t o the valve (marked "M" in Figure 6 ) , and the minimum emitter, the one farthest from the valve (marked m). The loss of pressure head between these two points, h, consists of two parts: h, along the auxiliary line, from the valve to the head

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CRC Handbook o f Irrigation Technology

Table 3 PERMISSIBLE DISCHARGE AND PRESSURE RANGES (%) m

x = 100(R,* - 1)

0.4

0.5 (fully turbulent)

0.685/ 0.7

1.00 (purely laminar)

0.85

-

Sub-main

6

Unit control vdve

l"l

I>Ern,ris

i

Manifold ,Lotemls,

mt

)m FIGURE 6 . A unit drip system (UDS) on level ground.

of the lateral, and h, along the lateral itself. The total loss, h the limitation in Equation 54. Thus we require that Hmax G

but since

Hmin

R;

then

Hmax Hmax

h G Hmax ( l

1 -

-h

G R;

=

h,

+ h,, must follow

(If the ground is not level, the pressure at each point is also affected by the topographic elevation, and the extreme-discharges emitters may be located anywhere in the UDS. See example in the Design section.) As an example, if R,* = 1.15 (range of pressure variation = 15%) and inlet pressure is 12 m. then

- 1.15, as specified

A recent study has shown that on level ground the economically optimal distribution of head losses is given by head loss in the manifold

= h,

= 0.55 h

head loss in the lateral

= hy = 0.45 h

\

(58)

or roughly, about one half of the pressure head loss in the UDS should occur in the manifold, and one half in the lateral. Uniformity of application may be measured, as in sprinkling irrigation,I4 by means of Christiansen's Coefficient of Uniformity, C,, defined by:

where

Id,(

=

the absolute difference (considered positive) between the discharge qi of the emitter and the average dischargebof all the emitters in the UDS, or id. I = 1 q . q I -

1

q = - Cq. N l

(604 (60b)

Specifying minimum permissible C. is another way of limiting the variation of emitter discharge along the lateral. Some workers, for example, specify that for emitters on the same lateral, a uniformity coefficient of at least 98% is desirable while a coefficient as low as 95% is still considered acceptable. Others even specify 95% as desirable and 90% as acceptable. Starting from Equation 44, it can be shown that, closely enough, also

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CRC Handbook o f Irrigation Technology

Then, if N is not too small, it can be shown that a good enough approximation (for design purposes) of C. is given by

-

If we remember (according to Equation 58) that in the same lateral we should allow only about one half of the head loss, then we should take R, = 1.05, and obtain C, 98.8%; that is to say that the least desirable value of uniformity coefficient o n a simple lateral should be 98.8%. The values of 98% and 95% mentioned above correspond t o R, = 1.08 a n d 1.21, respectively. Experimental studies resulted in a relationship similar to Equation 62:

-

-

98.6%, and for C. = 98% and 95% - R, 1.07 which yields for R, = 1.05, C, a n d 1.19, respectively - not a significant difference, s o that we can use either Equation 62 o r Equation 63 for preliminary design. Finally, a recently introduced uniformity measure is the emission uniformity (EU), which is defined as

In design work, q,,, is taken as the lowest discharge o n the lateral. In the case of a level lateral with a single type of emitter this would be q,. Under the previous assumptions. it can be shown that

that is t o say, E U will have values similar t o Christiansen's coefficient of uniformity (see Equation 62). When E U is calculated from field data, in the process of the evaluation of the performance of a n existing system, it is common to take q,,, as the average of the lowest fourth of the emitters, s o as to eliminate the danger of having one clogged emitter affect the total result. A t any rate, since the change of flow in the lower fourth is very slow, using this value for q,,, yields practically the same value for EU that was 90% as a obtained above for q,,, = q,. Authors using this measure specify EU value giving satisfactory uniformity of application. This corresponds t o R, = 1.45, which seems t o be somewhat high. Irrigation efficiency is clearly a function of the uniformity of application, since a high uniformity makes it unnecessary to overirrigate one part of the unit so that another part will receive sufficient moisture. This is true especially in drip irrigation, where most application losses (such as evaporation and runoff) are eliminated or greatly reduced. S o here irrigation efficiency depends mainly o n the uniformity of discharge of the emitters. This, in turn, depends o n the variation in pressure, as well as on the uniformity of emitter operation (due t o uniformity of manufacture, prevention of clogging, etc.). Another factor affecting efficiency through uniformity is the temperature, which, as has already been mentioned, affects the emitter's discharge. Fortunately, this effect is more pronounced in the emitters farther from the inlet (the water being warmed by the sun as it flows along the manifold and the lateral), so that this effect actually improves the uniformity by increasing discharge where pressure is lower!

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275

Calculations of drip irrigation efficiency sometimes use the concept of field application efficiency or application storage efficiency E, (%), which is 100 times the ratio of the depth of moisture stored within the root zone to the total depth applied. The average depth stored is calculated assuming that all moisture discharged from the emitters up to the full field capacity of the root zone is actually stored, while the excess is "lost" (or, may serve to leach salts) to deep percolation. With good management and full irrigation, it is expected that deep percolation will be of the order of 10% of application, so that

is an acceptable estimate for E, under these conditions. Achieving discharge uniformity may take either or both of two approaches: keeping pressure variations within the permissible range discussed above, or using different emitters within the same unit drip system (UDS). Keeping pressures within permissible range may be achieved by: 1.

2. 3.

Operating at higher pressures so that the friction head loss has a smaller relative effect. Higher pressures cost money, but sometimes high pressures are available. Moreover, higher pressures may reduce pipe sizes in the system, reducing a significant cost element. Reducing lateral length or, rather, decreasing the number of emitters per UDS. Increasing lateral diameter, wholly or in part. Use of more than one pipe size in a single lateral is not very common, but may be economically justifiable under certain conditions. The problem is to decide in what part of the lateral the diameter should be increased. Higher-diameter pipes lose less pressure, but cost more. The approach is generally to increase pipe diameter, starting from the inlet into the lateral, just enough so that pressure variation is at its maximum permissible value (given by RE ). The calculation must take into account the fact that the lateral is a multiple-outlet pipe, and that our method (using "F") of computation assumes zero discharge at lateral end. So, when we calculate the friction pressure head loss for a pipe with two diameters D, (with N, emitters) and D, ( T , o r even if N I > a T , it means that there should be more than one shift per day. The number of shifts per day does not have to be a whole number, since a n irrigation may start o n one day a n d finish o n the next, but in many cases irrigators prefer it t o be a whole number, a n d then its value is found by

which is the nearest lower whole number t o the value t'/t. N, is generally between 1 a n d 4. Combining Equations 108 and 109, we can see that

Small plots (or many shifts) are undesirable because they increase the amount of work involved in irrigation operation, a n d require more control units. O n the other hand, it may make possible the reduction o f network sizes a n d increase hydraulic efficiency. Example - An area of 250 da is irrigated once every 5 days with 40 mm of water. Irrigation duration is 10 hr and effective irrigation hours per day are 22. Find the size, shape, and number of shift plots and the required system capacity.

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293

Summary: Given:

A t

= =

250 da l 0 hr

d' t'

=

40 mm

T

=

Sdays

= 22 hr/day

Q

Required:

N,, Nz, At, L-,

Solution:

N, = [22/10]- = L2.21- = 2

For 2-sided manifold L, = d v = =158 m L,= 1 / 2 d m ' = 7 9 m Q = 40/10 x 25 = 100 m3/hr

For one-sided manifold L, = 3/2 d m = 237 m L, = 2/3 105 m

m=

Number of emitters of 4 I/hr:

or 1 emitter per I m'. Remember that most of the last formulas are inequalities, i.e., N, may be morethan 2 (though it cannot be less than 2), N , may be more than 10, and A, may be less than 25 da, and thus reduce also the required system capacity. Also the values for manifold and lateral length are only first approximations, as has been already stressed above.

Drip Irrigation Automation T h e goals of automated irrigation are the saving of work and time and ensuring precise application, without the risk of forgetfulness or of too early shut-off when the irrigator is anxious to return home after a hard day in the field. Drip irrigation lends itself very well to automation, provided that the whole field is permanently covered by the appropriate network. In drip irrigation automation we can discern three levels: 1.

2.

3.

Automatic shut-off, often by a clock, but much more preferably by means of a volumetric metering valve. Operation is started manually, and the valve is preset for a given water quantity. Shut-off is actuated by hydraulic action (or sometimes electrically). Follow-through operation, with a series of valves. All of these are pre-set to the required amounts, a n d the shut-off of one valve opens the next one (hydraulically o r electrically) until a complete cycle is finished. For hydraulic actuation, distance between adjacent valves should not exceed 200 m (preferably 100 m). Computer (or "control-board") operation, which opens and closes each valve, hydraulically o r electrically, according to any pre-designed program, and/or to super-imposed orders.

The fourth level (of a system operated by tensiometers or other soil-moisture sensors) is not suitable t o drip irrigation, because of the incompleteness of soil wetting. Levels (1) a n d (2) are simply installed, easily operated, reliable, and not too expensive. Their use is becoming more and more widespread. Level (3) is expensive, but has already been installed in various locations. Portable Drip Irrigation Most drip irrigation systems are solid (permanent) systems, with a full network,

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including laterals and emitters, installed in the field at the beginning of the irrigation season, and removed only when irrigation is finished (or not even then, when the system is used for more than one season). Such a system, which can be either manually or automatically operated, is a necessary condition for many of the advantages of drip irrigation. Nevertheless, there are portable drip systems in use and, properly designed, they are efficient and inexpensive. These are mainly used in lower-value field crops. In orchards they have been found to be most unsuitable and uneconomical. The portable parts are generally only the laterals and the emitters. Sometimes manifolds (or even submains) are moved. The portability may be partial (or semiportable), when laterals are pulled only inside the row, generally from one side of the manifold to the other. This saves the price of one half of the laterals and emitters. A fully portable system has the laterals wound-up on big drums and moved mechanically to another row. In this case the cost is reduced to that necessary for a single shift, or even less, but work is much increased. The pipes used in portable system care generally of grade 6, with diameters of 16 mm or more, and emitters of at least 4 P/hr. In most cases portable drip irrigation systems serve only as a temporary solution and are gradually converted into permanent systems. Thus costs are distributed over a longer time.

GENERAL CONSIDERATIONS Drip Irrigation of Various Crops Quite a wide variety of crops is showing good results when drip-irrigated, as compared to the "conventional" irrigation methods, with the yield improving in quantity, quality, and harvesting season, in addition to the water-saving and labor-saving involved. Each crop, in each region, in each type of soil, irrigated by water of a certain quality, would show a different response, and this should be determined experimentally under field conditions. Therefore the following are only summaries of general experience, indicating promising avenues and possibilities for further development.

Vegetables Vegetables are well adapted to drip irrigation, and its use is widespread. Good experience has been acquired in tomatoes, cucumbers, melons, eggplants, and strawberry. A permanent system is generally used, installed at the beginning of the growing season and transferred, or removed for tillage operations, after harvest. Spacing of laterals follows planting pattern (generally 1 to 2 m) - in most cases one lateral per row. Spacing of emitters is 0.5 to 1 m, or according to planting distances. Emitters used are generally small (2 to 4 P/hr) because of their small spacings. Orchards Drip irrigation has been found to be most suitable to fruit trees, where the root system is far from using the whole available area. Most deciduous fruits have been successfully drip irrigated, and so have olives, nuts, pomegranates, dates, vines, and bananas. An important part of commercial drip irrigation is in orchards. The system is permanent, with one or two laterals per row (one is generally enough if spacing between trees is less than 4 m), and with emitters concentrated around each tree, so that the whole area under the tree is uniformly wetted. With wide spacings (5 m or more), a frequent practice is to have one lateral on either side of the row, at a

Volume I

295

distance of 0.5 to 1.0 m (0.6 m for deciduous fruit trees), with 2 emitters per tree on each lateral. Emitters used are large (8 to 10 L/hr, or multiple-exit ones, giving 40 l / h r - in which case one, or at most two per tree are enough). However, the average intensity of application is low (0.5 to 2 mm/hr), so that the duration of irrigation will often exceed 24 hr. Depth application per irrigation is high (often 20 to 50 mm), sometimes double the practice in sprinkling.

Citrus Citrus is still in the experimental stage as regards drip irrigation, but there are some promising results. Irrigation is using a permanent system, L\;O laterals per row, with a 2- to 10-L/hr emitter every 1 m on each lateral (or one lateral per row, with a multiple-exit, 40-P/hr emitter every 4 m). With row spacing of 6 m, irrigation intensity is 1.5 to 2.5 mm/hr. Field Crops Drip irrigation is still making its first steps, and experience is limited. Cotton experiments in the U.S. showed a reduction of 10% in water use without change in yield or a reduction of 30% in water use with an 18% reduction in yield. Generally a portable system is used in field crops. Greenhouses In greenhouses, sprinkling irrigation not only provides water, but also regulates air humidity, temperatures, etc. When these additional effects are not necessary, drip irrigation is a good alternative to sprinkling, and is easier to operate (allowing other activities to be conducted simultaneously). Low discharges, small amounts per irrigation, and short intervals are required here. Drip irrigation has special advantages in irrigation of plastic-covered crops in the field, since the cover and the irrigation system do not interfere with one another. Soil and Water Salinity Use of saline soils and/or saline water is a source of problems in any irrigation method. In drip irrigation there are the additional problems of precise application with no excesses for leaching, and the interface in the soil between wet and dry zones, which is a "natural" location for salt accumulation. With a good design that ensures sufficient overlapping along the lateral there are no such interfaces between emitters on the same lateral, but longitudinal fronts exist between the wetted strip and the dry zones on both sides. If the irrigation system is well designed and operated, the irrigation zGne (or the crop root zone) is kept continuously at high moisture level, so that salt concentration and soil tension remain low throughout the irrigation season. This property, peculiar almost exclusively to drip irrigation, of keeping soil moisture continuously close to field capacity without compromising soil aeration, enables this method to use saline water with no subsequent salt concentration within the root zone, as long as irrigation is continued. The salts are not leached, but are accumulated and concentrated on the periphery of the wetted zone until the end of the growing season. At that time a good leaching is required, either by rainfall if available, or artificially. This last generally uses a portable sprinkling system (which out-of-season is available for such activities) drawing water from the same water-supply source as the drip irrigation system. In many cases there is enough rainfall during the rainy season to provide adequate leaching if drainage (natural or artificial) is adequate too. Sometimes the drip irrigation system itself may be used for leaching, by increasing the pressure (within the permissible limit) and the duration of operation. Care should be taken, since an

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C R C Handbook of Irrigation Technology

incomplete leaching may bring the salts back from the periphery to the center of the irrigation zone. It is interesting to note that experiments have shown indications that roots can develop much better barriers against ion penetration than leaves, and therefore when water of high salinity (and especially with toxic ions) is used, drip irrigation shows less harmful effects than sprinkling. Economics of Drip Irrigation There is no sense in an extensive discussion of this subject in a general work like the present one, since it changes from country to country (and from region to region within countries), from crop to crop, and from day to day. Each case should be dealt within its own context, using the usual methods of analysis. It is a well-known fact that drip irrigation systems are expensive, but in many cases (especially in vegetables and orchards) it has been found to pay for itself completely in one or two seasons. A complete analysis should take into account costs of: laterals and other pipes emitters fittings and equipment (control, filtering, fertilizing) labor for operation and maintenance against the values of: costs of alternative methods water saved increased yield value (quantity, quality, time, uniformity, etc.) labor saved The most expensive items of the system are generally the laterals and the emitters. The proportion between laterals and emitters varies according to type of emitter used, its size, and the spacings. The economics of varying lateral diameters are a function of the relative cost of pipes and of energy. If energy costs are especially high, we should prefer larger pipe sizes, so as to minimize head loss, while if pipe costs are the determining factor, we should take advantage of all the permissible head loss, by choosing the smallest pipe diameters feasible under this constraint.

UNITS AND NOTATION This work has attempted to use a consistent system of units conforming to the accepted practices in the design of irrigation systems in most countries using metric units. The one important innovation is the introduction of a new unit of land area - the dekare (using the symbol daa, or sometimes da) which is equal to 1000 m2 or 0.1 hectare, and is thus equivalent to the dunam that has been in use for many years in Mediterranean and Middle East countries. This is a convenient and practical unit of land area, reducing the need for using decimals in specifying areas, and has the additional advantage (in irrigation calculations) that 1 mm of water application = 1 m3/ da = 1 l / m 2 , which facilitates use o f the various units. The use of the dekare has been recommended by the American Society of Civil Engineers - Technical Committee on Irrigation Water Requirements16 for irrigation calculations in the metric system. Unless otherwise specified in the text, the following units (which will be referred to as the technical units) and notation will be used in this work:

Volume 1 Length:

D D. L L, l

Area: Volume: Time:

A V T t

S

Discharge: Water depth: Pressure:

-

d

-

P

-

Q

q

H h J Temperature: t Other units have been defined

297

pipe or orifice diameter, in millimeters (mm): inner diameter pipe nominal diameter, in millimeters (mm): outer diameter pipe length, in meters (m) microtube length. in centimeters (cm) emitter spacing along lateral, in meters (m) lateral spacing, in meters (m) land area, in dekares (da) Water volume, in liters (1) or cubic meters (m') in days (d) in hours (hr) discharge in pipes, in cubic meters per hour (m3/hr) discharge of emitter, in liters per hour ( l /hr) irrigation intensity, o r water volume per unit area, in millimeters (mm) air or water pressure, in (metric) atmospheres (atm) = kg/cml water head, in meters (m) head loss, or head difference, in meters (m) hydraulic gradient, in percent (%) = 100 h/L in degrees Celsius ( = Centigrade) ("C) in the text as used.

Conversions Within the metric system: 1 da = = 1 1 1 m3/hr = = 1 f/hr = 1 mm = 1 atm (metric)

1000ml=O.lha 1OOO cm3 = 1 dm3 = 10.' m' 1OOOf/hr 1/3.6 cm3/sec 1 m3/da = 1 !/m2 1 kg/cm2 = 0.9807 bar = 735.6 mm Hg = 10 m H 2 0

With "English " units 1 m 1 mm 1 l 1 da 1 mm2 1 l/hr 1 atm 1 ft 1 in. 1 U.S.gal 1 acre 1 in.' 1 U.S. gal/min = 1 psi (lb/in.') =

3.281 ft 0.03937 in. 0.2642 U.S. gal 0.2471 acre 1.550 X 10.) in.' 4.403 X 10.' U.S. gal/min 14.22 psi (Ib/in.') 0.3048 m 25.4 mm 3.785 1 4.047 da 645.2 mm' 227.1 l / h r 0.0703 1 atm

REFERENCES In the few years since the method has achieved popularity and recognition, there have appeared hundreds of booklets, articles, and research reports dealing with drip irrigation. These can be found mostly in the publications of universities and experiment stations or extension services and in many periodicals dealing with agricultural sciences, soil science, and engineering. Some of the main sources of information about drip irrigation, which have also been heavily drawn upon in this work, are mentioned below. This is a good occasion to acknowledge gratefully the contribution of these and other publications, as well as of my many colleagues in Israel and Brazil, to the present work.

298

CRC Handbook o f Irrigation Technology l . Karmeli, D. and Peri, G., Trickle Irrigation

- Design Principles, Technion Students Publishing House, Haifa, Israel. 1972, 112 pp. (Hebrew). 2. lrrigation Age(n1onthly journal) - Vol. 7(l l ) . June 1973: the whole issue deals with drip irrigation, including historical information, operation in\tructions, photographs, and a directory of USA manufacturers, Dallas, Texas. 3. Shani, M., Drip lrrigation - Methods and Equipment, Ministry of Agriculture, Tel-Aviv, Israel, 1973,67 pp. (Hebrew). 4. Trickle Irrigation, FAO Irrigation and Drainage Paper No. 14, Food and Agriculture Organization, Rome, 1973, 153 pp. 5. Keller, J. and Karmeli, D., Trickle irrigation design parameters, Trans. Am. Soc. Agric. Eng., 17, 678, 1974. 6. Merriam, J. L. and Keller, J., Farm Irrigation System Evaluation: A Guide for Management, Utah State University, Logan, 1978, Chap. 8. 7. Proc. 2nd Int. Drip lrrigation Congress - San Diego, California, Riverside Printer, Calif., 1974. 8. Manufacturers' literature. 9. Blass, S., Drip Irrigation, Tel-Aviv, November 1968 (mimeo; in Hebrew). 10. Goldberg, D., Gornat, B., and Rimon, D., Drip lrrigation - Principles, Design and Agricultural Practices, Drip lrrigation Scientific Publications, Kfar Shmaryahu, Israel, 1976. 11. Karmeli, D. and Keller, J., Trickle Irrigation Design, Rain Bird Sprinkler Manufacturing Corporation, Glendora, Calif., 1975. 12. Celestre, P., Irrigazione a goccia e techiche irrique affini ovvero irrigazione diuturna, L'lrrigazione, 19(1-2), 67, 1972 (Italian, English summary); Celestre, P., Drip irrigation system - higher efficiency and lower cost, in Commission Internationale de Genie Rural, Vol. 2, 6th Int. Cong. Agric. Eng., Lausanne, September 1964. 13. Nir, Dov, unpublished results 1971. 14. Christiansen, J. E., Irrigation by sprinkling, Univ. of Calif. Agr. Exp. Stn. Bull., No. 670, Berkeley, 1942. 15. Meyers, L. E. and Bucks, D. A . , Uniform irrigation with low-pressure trickle systems, J . lrrigation and Drainage Div., ASCE, 98, 341, 1972. 16. Technical Committee on lrrigation Water Requirements, Committee Report in Consumptive Use of Water and Irrigation Water Requirements, American Society of Civil Engineers, New York, 1974, 188.

Volume 1

299

PUMPS AND PUMPING Zeev Nir

INTRODUCTION With the expansion of irrigated agriculture and the general increase in all types o f water demand, there is increasingly greater use being made of water resources which lie below the level of the fields. These resources include ground water, river flow, freshwater lakes, recycled sewage effluent after treatment, and recycled drainage return flow. For all of these pumping must be used. Under prevailing conditions of energy shortage a n d high costs, pumping may become the major component of the cost o f irrigation. It is essential, therefore, that pumping should be designed for the greatest possible efficiency. For this reason the following exposition stresses first principles rather than mere rules of thumb so that the designer may have a more thorough understanding of what takes place in a pumping system.

CLASSIFICATION O F PUMPS P u m p s may be roughly subdivided into three classes (Figure 1): 1.

2. 3.

Rotodynamic, kinetic, o r impeller pumps Positive displacement pumps Other o r special pumps

In rotodynamic, kinetic, o r impeller pumps, a rotating element, the impeller, driven by a n outside driver, transfers energy to the liquid in o r o n it, through rotationaldynamic effects (sometimes also called centrifugal effects). The process is continuous, the flow of liquid through the machine is uniform (nonpulsating), and a closed valve on the exit from the p u m p does not cause adverse effects (such as mechanical damage, failure, o r breakage), beyond heating of the machine and of the liquid passing it.

ROTODYNAMIC PUMPS - TYPES AND ELEMENTS All rotodynamic pumps are equipped with a rotating element (impeller) by the aid of which energy is added t o the liquid. Figures 2 and 3 show a view and a section, respectively, of a typical impeller pump, with its elements and the appropriate terminology. T h e p u m p extends from its suction flange, where the suction pipe is connected and liquid enters the pump, to its delivery flange, where the delivery or pressure pipe is connected and liquid leaves the pump. The body of the p u m p o r the casing contains the rotating element o r impeller. The impeller is circular in form with one o r two shrouds or flat discs, on o r between which are the impeller- o r guide-vanes. Liquid enters the impeller at its central part, the impeller eye, is thrown outwards by centrifugal forces, leaves the impeller along its periphery, and enters the volute of the casing where the increasing (in the direction of flow) cross-section causes the flow velocity to decrease and the pressure, after Bernoulli's equation, to increase. The liquid at this increased pressure leaves the volute in the direction of the pressure o r delivery flange, there leaves the pump at increased energy, a n d enters the delivery pipe to continue o n its way. Sometimes the liquid is guided, upon leaving the periphery of the impeller, towards the volute by a set of

300 CRC Handbook of Irrigation Technology

Classification of pumps. FIGURE 1.

Volume 1

301

Delivery flange

/

lmpe'ler

eye

-- Suction FIGURE 2 .

Impeller eye

flange

Volute type impeller pump (view).

\ lmpeller

' Suction FIGURE 3.

shroud

flange

Volute type impeller pump (section).

stationary vanes, arranged in a diffusor-ring (Figure 4), and such a pump is termed a diffusor-type pump. In both the volute-type and the diffusor-type pumps the liquid enters the pump at the impeller-eye entrance in a n axial direction (direction of the axis of rotation of the impeller), and leaves the impeller, after turning by 90°, in a radial direction. Rotodynamic pumps containing such impellers are called radial-flow pumps or, quite often, also centrifugal pumps. At the other extreme, liquid entering the rotating element axially may also leave it axially, and pumps with such impellers are termed axial-flow pumps o r propeller pumps. In between are all the rotodynamic pumps where the liquid leaving the impeller does so neither in a purely radial direction nor in an axial direction. Such pumps are termed mixed-flow pumps.

FIGURE 4.

FIGURE 5.

P u m p impellers.

Diffusor-pump.

(A) Radial-flow; (B) mixed-flow; (C) axial-flow

Figure 5 shows three typical meridional impeller cross-sections of a radial flow, a mixed-flow, a n d a n axial-flow impeller. Pumps are just one element - the main element, indeed - in a pumping installation. Such a n installation is shown schematically in Figure 6, with the main elements of the installation outlined and identified. In the following hydraulic discussions the indexes a and b will refer, correspondingly, t o the beginning a n d the end of the path of a representative liquid particle; and the indexes S a n d d will refer to the entrance to the pump at the suction flange, and to the exit from it a t the delivery flange.

BASIC PARAMETERS The basic parameters employed in the description of pump performances are discharge, head, power, efficiency, rotational velocity, and torque. Each of these parameters will be defined, described, and explained in the following paragraphs.

Volume 1

Delivery

reservoir

Delivery

pipe

_R-

F, Throttling

One -way

valve

(check) valve

------- Delivery

I

l

303

flange

Suction flange Suction

pipe

Foot - valve Strainer Suction

reservoir

FIGURE 6. Typical pumping installation.

Table 1 VOLUMETRIC FLOW CONVERSION FACTORS ft3/sec cusec

m3/hr

Imperial gal/min

!/sec

Nore: 1000 barreldday (oil barrels of 42 U.S. gal) = 1.84P/sec.

=

U.S. gal/min

6.624 mJ/h

Discharge The amount of liquid passing through the pump in unit time, usually expressed as volume per unit time, is the discharge or volumetric discharge Q of the pump. The customary units for discharge are: in the Metric System, m3/h (or m3/hr), m3/sec (basic S1 unit), P/sec, and l/min; and in the English System, cfs or ft3/sec and gpm or gallons (U.S. or Imperial) per minute. The conversion factors for these units of discharge are given in Table 1. The discharge of pumps is usually measured by orifice, diaphragm, or Venturi-meters, commonly placed in the discharge line close to the pump.

Head The difference between the (specific) energy at the delivery flange, E,, and the (spe-

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CRC Handbook o f Irrigation Technology

FIGURE 7.

Energy relations in pumping installation

cific) energy at the suction flange, E,, at a discharge Q, is termed the head on the pump (see Figure 7):

where

and

The head H, being the difference between two values of specific energy, is measured and expressed in units of length (meters, feet, inches). It is customary to have manometers connected at or near the delivery and the suction flanges of pumps. With the possibility of having negative gauge pressures (under-pressures, vacuums) at suction flanges of pumps, there are often vacuum gauges, or even liquid- (mercury-) column manometers, connected there. The pump head H, as well as energy relations in general in a typical pumping installation, are shown schematically in Figure 7. The meaning of Equations 2 and 3, expressing the energies at the exit and entrance to the pump (delivery and suction flange, respectively) and the pump head H, Equation 1, should be made clear by inspection of Figure 7. Moreover, certain additional relations are illustrated. With the two water surface velocities V, and V, in the two large reservoirs being nearly equal t o zero, and the pressure on the open surfaces being actually equal t o zero, we have

Volume 1

305

(4)

and

Now, along the suction pipe:

and along the delivery pipe:

From Equation 1, and considering Equations 6 and 7: H = Ed - E,

=

b (Eb + C h,) d

S

-

(E,

-

C a

b

S

h,)

=

Eh

-

E, + (

a

h,

+ C h,) d

and, with the last expression in parentheses expressing the total head-(energy-) loss along the stretch of pipes from a to b:

we may write:

For the rather common case of large, open reservoirs, Equations 4 and 5 hold, and

where H,, is the so-called static or topographic head, which is simply the vertical distance to which the liquid is elevated by the pump. Introducing this into Equation 8 we see:

b

and, considering that in general both the pump head H and the pipe-characteristic f h, are functions of Q , we may write:

where h(Q) stands for

;h,. b

Power Power is defined as work performed in unit time. In every machine, power is, at

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CRC Handbook o f Irrigation Technology

one end, supplied t o the machine from a n external source (power input, P,), and, a t the other end, extracted (obtained) from the machine (power output, P,). If all conditions were ideal, and n o work o r energy were used for unwanted purposes (overcoming friction, heating, etc.) o r "lost", in the (rather incorrect) engineering terminology, the power input and the power output of a machine would be equal. But, for nonideal o r "real" conditions, the two values are different, with the power output always being less ("losses") than the power input. The p u m p head H , Equation 1, was given by:

Hence, H is the specific energy, o r energy per unit weight of liquid passing through the pump, transferred t o the liquid by the pump. At each unit of time, Q units of volume pass through the pump, and, with each unit of volume weighing y units of weight, the weight of liquid passing per unit time through the pump, is y Q . Now, the p u m p transfers t o the liquid H units of specific energy and therefore the energy (not specific energy) transferred t o the liquid per unit time (power) will be:

The conventional units used for expressing power are kg, m/s, lb, ft/s or horsepower, H P , metric o r English:

As has been seen, the two forms of horsepower are not identical, with the English unit being less than 1.5% larger than the metric unit. In S1 units (Systtme International d'unitis), adopted by more and more countries throughout the world, the unit of power is 1 W (watt) = l

](joule)

- N(newton)

-S

m

S

with

and lW

=

1.360 X 10-3 HPmet,

As stated above, the power input into the pump, provided by a n outside source of power, must be larger than the water-horsepower transferred. If W denotes the angular velocity of the p u m p impeller (see Rotational Velocity), and T the torque applied to the p u m p by the motor (see Torque), then the power transferred from the motor to the p u m p will be

Efficiency T h e total o r overall efficiency t o power input

of a p u m p is defined as the ratio of power output

Volume 1

307

and since always P , > P,, this ratio will be less than 1. Using the definitions for power output and power input, we will have for pumps, with Equations 12 and 13:

The power input, P,, required a t the coupling of a pump shaft exceeds the pump output, P,, by the losses due to leakage, vortex action, disk friction, clearance losses, and mechanical friction. Losses occurring in the power transmission or reduction gearing are not considered to be p u m p losses. In designing a pumping plant, the actual power requirement, P,, is calculated from the output, P,, and the efficiency, v, as follows:

A n estimate of the power input required to drive a pump (based upon cold water) is shown in Figure 8.

Rotational Velocity There are two customary ways of expressing the velocity of rotation of a rotating element: (a) the rotational velocity n, expressing the number of revolutions performed by the element in a unit of time, usually 1 min, and (b) the angular velocity w , expressing the angle, in radians, by which the element has rotated in 1 sec. The units o f rotational velocity n are rpm (r/min, revolutions per minute) and, less frequently, rps (r/sec, revolutions per second). The angular velocity w is expressed in rad/sec or, because the radian is nondimensional o r a pure number, also in l/sec. The connection between the two units, considering that one revolution equals 2n radians, is n

2rr W(rad/sec) = "(rpm) X

60

=

30 n(rpm)

Torque A single, nonbalanced force F, acting upon a body of mass m, will cause the body to translate with a linear acceleration a = F/m. Correspondingly, a couple of forces, resulting in a n unbalanced moment (torque) T, and acting o n a body with a polar moment of inertia (with respect to a n axis through 0) I, ( = JrZ drn = lr%dV ) (m)

(W

will cause the body t o rotate about this axis with a n angular acceleration a = T/I,. Power is transmitted from a motor t o a pump by means of torque (Equation 13). Torque is expressed in metric units in kg, m, in S1 units in N . m , and in English units in lb,ft.

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CRC Handbook o f Irrigation Technology

10

20

H [ m ] and

30

f'[d

40

M

FIGURE 8. Estimation of power, P,, required to drive a pump, based on pumping cold water. Example: given H = 23 m, Q = 400 3/h, q = 80%. From the chart: P, = 42.5 PS. (From KSB Pump Handbook, Klein, Schanzlin, and Becker Aktiengesellschaft, Frankenthal, West Germany, 1968. With permission.)

EULER'S FUNDAMENTAL EQUATION Introduction A schematic cross-section through a rotodynamic pump impeller is given in Figure 9, with only one representative guide-vane 1 - 2 shown. A t any point N on the guidevane the absolute velocity V of a liquid particle at a distance r from the axis of rotation through 0 , will be composed (vectorially) of the relative (to the guide-vane) velocity v, a n d the transport (together with the vane and the impeller) velocity U. In pumpimpeller notation it is customary t o denote everything connected with the inner circle (periphery of the impeller eye) with the index 1 , and everything connected with the

Volume 1

FIGURE 9.

309

Definition sketch for Euler's formula.

FIGURE 10. Impeller width b

outer circle (periphery of the impeller) with the index 2 (thus 2 is downstream from 1). In this notation the impeller-eye radius is r,, and the impeller radius is r, = D/2. From the vector diagram of velocities in Figure 8, we can write:

and

v= =

U=

V,

=

V cos a =

V,

=

V sin a

U

=

IW

+ V=

- ~ U cos V p U

-

= v

v cos p

sin p

(17) (18) (19)

(20)

Every one of these equations will be valid with indexes 1 a t r = r,, and with indexes 2 a t r = r, (except for W, which is constant). If the impeller is of a changing width b (Figure 10), the discharge through it is Q and the widths of the vanes are neglected; then at any distance, r will be

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CRC Handbook o f Irrigation Technology

In Figure 9 the absolute path of a liquid particle is also shown (line 1 - 2). Preservation of Angular Momentum From fluid mechanics, the expression

for the preservation of angular momentum will be remembered. Applying this equation to the liquid in the pump-impeller shown in Figure 9, we see, first, that both a t the outflux of momentum (along the outer rim of the impeller) and a t the influx into it, the mass discharge Q is equal and may hence be extracted from the two expressions in parentheses: C M = pQ [X(: X !)out

-

X(? X

We see also: C(f X V_),,*

=

'1

X

V,

- -

=

-rl

X

1,

and C(r X V)in

Now, for radial flow impellers, both r a n d Vare in the plane of the impeller disc (plane and t ( r x _V),, are parallel and both in axial of paper in Figure 9); hence t ( ~ _V)x, direction, a s is also the sole moment, the torque, = T. With both vectors in the brackets a t the right side of Equation 23 parallel, we may substitute absolute values (magnitudes) instead of vectors, both on the right side and o n the left side of Equation 23:

and, observing again Figure 9,

Y Q ( r 2 v zCOS a z - r1 V, T = g

COS

a,)

(24)

Equation 24 expresses the torque T transferred from the irnpeller to the liquid in o r o n it. Equation 13 gave the power input into the impeller as P , = w T and, if the machine be considered ideal, this will also be the power transferred to the liquid (Equation 12).

Using the two equations above a n d the expression for T, Equation 24, we will have:

Volume 1

FIGURE 1 1 .

31 1

Theoretical H(Q) relationship.

or, with H,, showing that the expression derived applies to a theoretical, ideal case, and remembering that r,w = U, and r,w = U,, we may write: U,

Hth =

V, cos a, -

U,

V , cos a ,

g

This expression is the basic equation for pumps. An expression, almost identical with Equation 24 and applicable to turbines, was developed by L. Euler in 1754, and is known as Euler's fundamental equation for rotodynamic machines. Theoretical H(Q) Curve When designing pumps, rotational velocities n are usually prescribed by motor characteristics, especially in the case of electric motors of the more common type where the rotational velocity is usually a whole multiple of the line frequency (usually 50 or 60 Hz) multiplied by a so-called slip-factor (cos ty < 1). The impeller-eye radius r,, together with n (or W),determines the tangential velocity U,, while the design discharge Q and the width b,, determine the magnitude of the entrance velocity V,. By choosing a suitable vane-angle a , , the direction of V, can be determined such that it be a shockfree continuation of the radial approach velocity inside the impeller eye. So, at design conditions, we have a, = 90" and Equation 25 reduces to U,

Hth =

V, cos a, g

(26)

Considering Equations 18 and 20, and reviewing Figure 9, we may write

and this represents a linear relation between H,, and Q, with constants K, and K2(at a given rotational velocity n, and hence W = const.), with a parameter /l2, which is the so-called exit blade- (or vane-)angle. (A, is the exit area from the impeller, roughly 2nr2 . bZand is also constant). Equation 27 is shown in Figure 11 for three cases of P2.The three cases of Ij2 are shown in Figure 12, and refer, correspondingly, to (A) back-swept vanes, (B) rightangle vanes, and (C) forward-swept vanes. Example 1 A pump impeller of diameter D = 2r2 = 300 mm, rotates at n = 1200 rpm. A

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FIGURE 12. Exit vane-angles p,. (A) Back-swept vanes; (B) right-angle vanes; and (C) forward-swept vanes.

discharge Q = 500 m3/hr of water passes through the pump. The net exit area from the impeller is A2 = 750 cm2 and energy losses are given (a) through the impeller as 2.8 Vz2/2g, and (b) through the rest of the pump passages as 0.4 VZ2/2g.Two angles are given, a , = 90" and /l2= 20". Calculate the pump efficiency. Q V, sin 0, = v, sin p, = -

A,

v, =

V, =

500 3600 X 750 X 10.~ X sin 20°

J U: + v:

= J18.850~

H+, =

500 3600 X 750 X 1 0 - ~

U,

-

+ 5.414,

v,

COS

2u, v, cos p, -

a? -

=

5.414 m/sec

=

2 X 18.850 x 5.414 X cos 20" = 13.887 lnlsec U, (U,

- v2 cos P2)

-

18.850 X (18.850- 5.414 cos 20') 9.81

= 26.445 m

CHARACTERISTIC PUMP DIAGRAMS Basic Pump Characteristics Figure 11 showed the theoretical relation between the head H developed by the pump and the discharge Q. It was obtained under the assumption that there are no losses of energy inside the pump and in the liquid; that there are no losses of liquid (leakage, internal recirculation); and that the angle a , remained 90°, as if every value of Q were the (one only) design value for which the impeller was designed. With this in mind, the expected shape of a real H(Q) curve can be predicted (Figure 13). Part of the losses in H will be proportional to Q2, and part of them will increase

Volume 1

i

Q design

0 FIGURE 13.

l

d

313

-b

Q

Actual H(Q) relationship.

FIGURE 14.

Pump characteristics.

because of the deviation of the actual Q from the design value, Q-design. After subtracting the losses from the /j2 < 90' curve, the shape of the expected H(Q) curve is obtained (Figure 13) a n d it is very closely representative of curves actually measured. By means t o be shown later, the values of head H and of power (input) P, for various values of Q (including Q = 0) are measured at a constant n (design value), and plotted in a diagram (Figure 14). The measured values of H and Q and the known specific weight y of the liquid make it possible (Equation 12) t o calculate the power output, P,

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+ Operating FIGURE 15.

4

region

Operating region o f pump.

= yQH; and the measured values of power input, or required power, P i make it possible (Equation 14) to compute and plot in Figure 14 the q(Q) curve, too. The three curves shown in Figure 14, H(Q), P(Q), and q(Q), are the so-called pump characteristics, and they are measured and presented graphically for particular major pumps and for random samples of pump types, in smaller, production-line pumps. The diagram is given for a constant value of n which is usually the design value of n 0.r a multiple of it (half or double the value of the design-n, for example, 1450 rpm and 2900 rpm). Remembering the definition of pump head, Equation (1): H = E, - E, (Equations 2 and 3), it may be seen that the pump will develop a head, even when the throttle valve at the exit from the pump (see Figure 6) is closed ("shut-off" conditions). Then the discharge will be Q = 0. Hence V, = V, = 0, and the head for Q = 0, the socalled "shut-off head", will be

The larger the discharge Q , the smaller will be the head H developed by the pump. There is a value of Q (see Figure 14) for which H = 0. At these two extremes, for shut-off head with Q = 0, and for the value of Q where H = 0, the value of efficiency, as defined by Equation 14, will be q = 0. Between those two zero values the continuous, nonnegative value of q must pass through a maximum value, q,,,. The value of discharge for which q = q,.,, and the corresponding values of head and power, are the so-called nominal values of the pump characteristics, Q,, H,, and P, (Figure 14). Theoretically, a pump will operate at best economic conditions at its nominal discharge, with = q,.,. However, we d o concede the efficiency of the pump t o recede to some lower value than q,,,, say 0.9 qmar(or 0.8 qm.J at the engineer's discretion. Then (see Figure 15) we arrive at a region, the so-called operating region, where for all values of Q , Qmi,< Q < Q,.,; with Q, included, the efficiency will not drop below a predetermined value kq,,, (k < 1). Oak-Leaf Diagram Let Figure 16 present an H(Q) curve for a certain pump, operated at n = n,

=

FIGURE 16. Alternative presentation of efficiency

const. revolutions per minute, a n d q(Q) the familiar q(Q) curve. As shown in Figure 16, points of certain discrete values of q can be determined, projected upon the H(Q) curve, a n d there identified by listing the value of next t o the point. Such a presentation saves a separate q(Q) curve, while giving all the necessary information, as required. A p u m p may be operated at any desired rotational velocity, and, as will be seen later, the H(Q) curves at those different values of n will be similar to each other, with larger values of H a t a given Q when n is increased, a n d smaller values when n is reduced. Power and efficiency curves may also be plotted for those values of n, and the efficiency projected upon the corresponding H(Q) curves, as outlined above (Figure 16). If now several of those H(Q) curves, with numbered efficiency values upon them, are plotted o n a single diagram and the points of equal efficiency are connected by smooth lines, a so-called iso-efficiency diagram, Figure 17, is obtained. Because of a similarity between the iso-efficiency lines and oak leaves, the diagram is sometimes called a n oak-leaf diagram. It appears, a n d may be shown theoretically as well, that all maximum efficiency points o n the various H(Q) curves lie o n a parabola with its apex a t the origin (dotted in Figure 17). If the iso-efficiency lines be considered as topographic (equal) elevation lines, it may easily be seen that there is a "peak" o n the iso-efficiency "hill". This peak is the point of maximal maximum-efficiency (in Latin: "maximum maximorum") - the highest possible efficiency at which the given pump can be operated. An H(Q) curve can be plotted through this point (dotted in Figure 17), and this will be the optimal H(Q) curve for the given pump. By interpolation, the corresponding optimal rotational velocity can be estimated, and this should be (good engineering and design provided) as near to the design-n as possible. (For the hypothetical values in Figure 17 we would obtain no,, = 1450 rpm.)

Selection Diagram Sometimes a manufacturer produces a line of pumps with similar characteristics but of different sizes a n d , hence, different capacities. Moreover, a certain pump of the series will be best suited a t certain operating conditions. T o show all the various pumps

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Optimal H(Q ) curve, at

Maximum efficiency points Maximum rnaximorumU

FIGURE 17.

Iso-efficiency or oak-leaf diagram

n = 1470 rpm

Q FIGURE 18.

Selection diagram

of the series, for a wide range of discharges and heads, so-called selection diagrams are prepared (Figure 18). For practical reasons the Q-scale, and sometimes the H-scale too, are chosen to be logarithmic. The optimal region of a pump-type is limited by full lines, with data on the pump (type designation, delivery/suction flange diameters)

Volume 1

FIGURE 19.

317

Pump and model: (A) prototype; (B) model

listed in it, and equal-power (input) lines shown. If for a certain application a couple of values (H, Q) is given, the point on the crossing of appropriate lines falls within a pump-type area, e.g., A - 5"/12" in Figure 17. The power requirement can be read off the diagram immediately, a n d the efficiency calculated.

SIMILARITY LAWS General Let Figure 19 show a prototype p u m p impeller and its model. For the two impellers t o be geometrically similar, the ratio of all lengths must be equal:

For kinematic similarity, homologous velocity triangles must be similar, i.e., angles must be equal, a , = a,, p, = p,, . . . , a n d corresponding velocities must be at a constant proportion:

Now, recalling Equation 26

v*

Ha-

g

and, with V a nD, it may be said that

T h e discharge Q = AV, o r Q a D 2 V a D2 nD

=

n D 3 , and

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Finally, P

=

yQH or P,

=

y, Q, H, and with Equations 30 and 31

Equations 30, 31, and 32 express the similarity laws or laws of affinity for pumps. The values of efficiency at homologous points on characteristics of pump-prototype and model are equal. If a pump itself be operated at different rotational velocity the different cases may be considered as models of a prototype pump of unchanged size, i.e., D, = 1. Then Equations 30, 3 1, and 32 will reduce to

and again: q, = 1. Specific Speed Let H,, Q,, P, be the nominal values of a centrifugal pump at its design velocity n. Let a model of this pump be found such that it will carry a discharge Q,, against a head H, when working at a rotational velocity n,. No requirements are set on D,, but it should be clear that it will have to be different from D. Equations 30 and 31 were H, = n,2 D,' and Q, = n, D.: TO eliminate D, we write H? = n,6 D,6 and Q,' = nrZ D / . Dividing the two expressions

From here

If H, be a unit length, and Q, a unit discharge, the velocity n, is called specific speed and serves as an identifying parameter for rotodynamic pumps:

Unfortunately, n, is not a pure (nondimensional) number, and much confusion is connected with numerical values for n,, depending on the units chosen to express Q, and H,. Common units are 1 m for H, and 1 m3/sec or 1 m3/hr for Q,. In English units it is customary to express H, = 1 ft, but Q, may be 1 ft3/sec, l gal/min, etc.

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319

Lazarkiewicz and Troskolafiski (Reference 2, page 120) have proposed a nondimensional form for specific speed which would be (somewhat modified):

and is called "nondimensional shape number". In this expression o is in rad/sec, Q in m3/sec (or ft3/sec), g in m/sec2 (or ft/sec2) and H in m (or ft). As may be seen by inspection of Equations 37 or 38, a small specific speed indicates a pump carrying a small discharge against a large head, whereas a large specific speed indicates a large discharge and a low head. Actual measurements show that radial rotodynamic pumps have low specific speeds (W, = 0.2 + 1.5), mixed-flow pumps have medium specific speeds (W, = 1.5 + 2.8), and axial-flow or propeller pumps have high specific speeds (o, = 2.5 t 6).

EXAMPLES Example 2 A centrifugal pump carries 350 l/sec of water against a head of 64 m when operated at 1450 rpm. Calculate the discharge, the head, and the power required by the pump (in kW) when it is operated at 960 rpm and the efficiency in both cases stays 88%.

Example 3 A reduced model of a centrifugal pump is built to scale 1:lO. The model was tested at 3600 rpm, pumping 3 m3/hr of water against a head of 40 m. If the prototype pump, working with water against the same head, achieves an efficiency of 91%, compute the rotational velocity of the prototype, the discharge carried, and the power required by the prototype pump.

nm

=

3600 rpm

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Example 4 The specific speed of a certain centrifugal pump is given by ns = 34.6

rpm

Jm3 /sec ,,,3/4

Assuming that this pump operates at 75% maximum efficiency while carrying 80 m3/hr of water at 2900 rpm, find the rest of its nominal values (head and power) and the torque applied to the pump.

Example 5 A discharge of 120 m3/hr of water has to be pumped against a head of (a) 50 m with a centrifugal pump operating at 1450 rpm. What type of rotodynamic pump will be suitable for this task? And what type, if the pumping head be reduced to (b) 4 m?

FIGURE 20.

Operating point

A radial-flow pump will be suitable.

A mixed-flow pump should be considered.

PUMP OPERATION Operating Point Discussing the idea of pumping-head, we arrived (page 305) at Equations 10 and l l :

or more general, Equation 24,

stating that the head H developed by the pump must supply the energy necessary to overcome the energy difference E. - E,, or the static head, H,,, and the friction losses b in the piping

2 hf a

= h(Q)

Let Figure 20b show the pump characteristic H(Q) of the pump P in Figure 20a, lifting liquid to a height H,,. As shown in Basic Pump Characteristics, the stretch char-

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CRC Handbook o f Irrigation Technology

FIGURE 21.

Changing water level

acteristic for the piping (suction a n d delivery) a n d all possible fittings on the pipes, h(Q), can be calculated a n d is shown in Figure 20b (with apex through the origin 0). According to Equation 11, repeated here above, there is one discharge for which the variable head H(Q) developed by the pump exactly equals to the sum of static head H,, a n d the stretch characteristic, h(Q). This discharge is found graphically in Figure 20b, a t the intersection A of the H(Q) curve and the H,, + h(Q) curve, obtained by vertical superposition. Point A is the so-called operating o r workingpoint of the pumping system consisting of p u m p P and the connected stretch of pipes. The corresponding discharge Q, a n d head HA, are the operating discharge and the operating head, and as seen in Figure 21b, H A = H,, + h(QA). If Q A exactly coincides with the nominal discharge, o r discharge a t maximum efficiency, Q,, Figure 14, then the choice of pump for the given conditions may be considered the very best. However, even if Q, f Q,, but stays within the operating region (Figure IS), the choice will still be considered good. If the valve in Figure 20a was fully open, the discharge Q, was the maximum possible discharge obtainable in the system without lowering the high-water level or enlarging some of the pipes in the stretch. However, if the valve were partly closed, the stretch characteristic should be calculated anew a n d replotted as a steeper curve h'(Q) (Figure 20b). A new operating point A ' would be obtained, with new operating discharge Q'A (