Laboratory Work in Hydraulic Engineering [1 ed.] 9788122423204, 9788122418101

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Copyright © 2006 New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved. No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher. All inquiries should be emailed to [email protected]

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Dedicated to my brothers

Ratan, Giriraj, Satya Narayan, and Manak

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Preface In engineering learning, seeing and doing are as necessary as reading and listening. Unless one has an opportunity of testing or applying principles of a subject learned in classrooms (or from text books) one’s assimilation of the subject remains incomplete. Laboratories (providing controlled reproduction of various physical phenomena associated with the subject or course of the laboratory) and summer training (on real-life projects) provide the learner an opportunity of seeing and doing. Therefore, the laboratories play a very important role in making the learner to understand complex physical phenomena and, very often, are the only source of knowledge in solving complex field problems. Learning of hydraulic engineering (or hydraulics) is no exception. Although most courses on hydraulics have now been replaced with courses in the mechanics of fluids, the contents of the two courses remain almost the same with no change whatever in the laboratory work as far as hydraulic engineering is concerned. In almost all technical institutions of learning, the laboratory work in any subject runs concurrently with the course in theory of the subject. Consequently, the students perform the laboratory work mechanically without intellectual involvement in the work. It is, therefore, necessary that the students, before conducting the experimental work, are familiarized with elementary theoretical and other aspects relevant to the experimental work. This book is an attempt to serve this objective. The contents of the book include description of elementary terms of fluid mechanics, fundamental equations governing fluid motion, introduction to open channel flow, basic facilities in hydraulic engineering laboratory, a note on writing laboratory reports, and instructional description of several experiments including those on basic hydraulic engineering (or fluid mechanics), pipe flow, open channel flow, boundary layers, and hydraulic structures. Instructional description of each experiment includes the object(s), brief theoretical background, description of one typical set-up for the experiment, procedure for conducting the experiment and carrying out computations. The required graph sheets have also been provided in order to make the book self-contained. The book is expected to be useful to the under-graduate students of Civil Engineering, Chemical Engineering, and Mechanical Engineering and other students who study hydraulic engineering. The forbearance of my wife Savi during the period I was busy writing the text for this book is appreciated. The excellent work done by the editorial staff of the publishers also deserves appreciation.

G.L. ASAWA

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Contents

Preface .......................................................................................................... (v) 1.

Elementary Terms of Fluid Mechanics .................................................................. 1

2. 3.

Fundamental Equations governing Fluid Motion ..................................................... 8 Open Channel Flow .......................................................................................... 12

4. 5.

Basic Facilities in Hydraulic Engineering Laboratory ............................................. 18 Writing Laboratory Reports ............................................................................... 22

6.

Viscometer ...................................................................................................... 23

7. 8.

Surface Tension ............................................................................................... 26 Centre of Pressure ........................................................................................... 30

9. 10.

Metacentric Height ........................................................................................... 33 Bernoulli’s Equation .......................................................................................... 36

11.

Impact of a Fluid Jet ........................................................................................ 40

12. 13.

Horizontal Water Jet through an Orifice .............................................................. 43 Orifice Meter ................................................................................................... 48

14. 15.

Venturi Meter ................................................................................................... 53 Triangular Weir or V-notch ............................................................................... 57

16.

Viscous Flow Analogy ...................................................................................... 60

17. 18.

Electrical Analogy ............................................................................................ 62 Effect of Vorticity ............................................................................................ 66

19. 20.

Forced Vortex Flow .......................................................................................... 72 Flow through Porous Medium ........................................................................... 76

21.

Stokes’ Law .................................................................................................... 82

22.

Transition from Laminar to Turbulent Flow ........................................................ 86

x

Contents

23. 24.

Velocity Distribution in Pipes ............................................................................. 90 Frictional Head Loss in Smooth and Rough Pipes ................................................ 97

25. 26.

Minor Losses in a Pipeline ............................................................................... 101 Bend Meter .................................................................................................... 104

27.

Boundary Layer over a Flat Plate ...................................................................... 110

28. 29.

Drag around a Cylinder .................................................................................... 116 Uniform Flow in a Channel.............................................................................. 124

30. 31.

Velocity Distribution in a Channel ..................................................................... 126 Vertical Contraction in a Channel...................................................................... 132

32.

Horizontal Contraction in a Channel.................................................................. 136

33. 34.

Broad-Crested Weir ........................................................................................ 140 Hydraulic Jump .............................................................................................. 146

35. 36.

Free Overfall ................................................................................................. 151 Horizontal Expansion in a Channel.................................................................... 155

37.

Reservoir Flood Routing ................................................................................. 159

38. 39.

Submerged Hydraulic Jump ............................................................................. 163 Forced Hydraulic Jump ................................................................................... 167

40. 41.

Vertical Fall .................................................................................................... 173 Ogee (Overfall) Spillway ................................................................................. 178

42.

Sediment Distribution at Offtakes .................................................................... 186

43.

Scour around Spurs ....................................................................................... 190

C h a p t e r

Elementary Terms of Fluid Mechanics

1 .

1.1 FLUID Fluid is one of the two states in which a matter may exist. Liquid and gaseous states of matter are jointly named as fluid state. Fluid is a substance which deforms continuously on application of tangential (or shear) stress irrespective of the magnitude of the stress. 1.2 FLUID MECHANICS Fluid mechanics deals with the behaviour of fluids subjected to a system of forces. It is a subject parallel to the mechanics of solids. The fundamental laws of motion, as used in solid mechanics, are used in the mechanics of fluids. 1.3 MASS DENSITY In fluid mechanics, one is more interested in mass per unit volume of a moving fluid at any point of observation rather than the corresponding total mass. The mass per unit volume of a fluid is known as the mass density of the fluid and is designated by the symbol ρ (rho). 1.4 SPECIFIC WEIGHT Weight (force of attraction exerted on any mass or body by the earth) per unit volume of a fluid is known as specific weight (or weight density or unit weight) of the fluid and equals ρg. Here, g represents the acceleration due to gravity. 1.5 SPECIFIC GRAVITY Specific gravity (or relative density), S is the ratio of the mass density (or unit weight) of the fluid to the mass density (or unit weight) of pure water at 4°C. 1.6 VISCOSITY Viscosity is the property of a fluid which is responsible for resisting deformation of the fluid. In a moving real fluid, shear stress always exists. This gives rise to fluid friction which opposes the sliding of one particle past another. These friction forces are due to a property of the fluid which is called viscosity (or dynamic viscosity) and is represented by the symbol µ (mu).

2

Laboratory Work in Hydraulic Engineering

1.7 KINEMATIC VISCOSITY The ratio of the dynamic viscosity and mass density of a fluid is called kinematic viscosity of the fluid and is denoted by the symbolν (nu). Thus, = µ/ρ 1.8 PRESSURE Pressure means force exerted upon a fluid surface of unit area. Assuming that a column of crosssectional area A is filled upto a height h by a fluid having unit weight equal to ρg , it may be seen that the force per unit area exerted by the fluid on the bottom of the column is given by ρgAh p= = ρgh A Thus, in a body of liquid, the pressure at any depth h is equal to ρgh (taking the atmospheric pressure at the surface as reference pressure). Assuming ρg to be constant, one can state that the pressure is equivalent to a height h of the liquid of constant specific weight ρg. In fluid mechanics, it is more convenient and common to express pressure in terms of height of coloumn of a liquid (or fluid) rather than in terms of force per unit area. Thus, h = p/ρg. Here, h is termed as the pressure head and has the dimension of length. Pressure can be measured by using pressure gauges, pressure transducers, piezometers, and manometers. Pressure gauges and pressure transducers need careful calibrations. The use of piezometers and manometers for pressure measurement is simple, direct, and reliable provided that certain requirements are fulfilled. Piezometer consists of a small diameter tube, having one of its ends open and the other connected suitably to the flow system in which the liquid can rise freely without overflowing. The height of the liquid column in the tube measured above the point under consideration will give directly the pressure head (see Fig. 1.1).

Figure 1.1 Piezometer

Figure 1.2 Open-end manometer

Elementary Terms of Fluid Mechanics

3

For higher pressures, the piezometer may not be suitable. The simple manometer, shown in Fig. 1.2, is used for this purpose. The U-tube of the manometer is filled with some heavy liquid, usually mercury. The pressure at A, pA may be determined by writing down the gauge equation as follows: p A − ρ A gZ − ρm gy = 0 pA ρm y+z = ρ Ag ρA

or

Here, subscripts A and m refer, respectively, to the liquid (or fluid) under consideration and the manometer liquid. This simple manometer can also be used to measure the pressure in gases. In many cases, only the difference in pressure at two different sections is desired. For this purpose, a differential manometer, shown in Fig. 1.3, is used. Writing down the gauge equation, pA − ρA g Z A − ρm gy + ρ B g Z B = p B If ρ A = ρ B = ρ, i.e., the same fluid at A and B, then, p A − pB  ρm   − 1 y = ρg  ρ 

...(1.1)

Figure 1.3 Differential manometer

1.9 DISCHARGE It represents the volume of a fluid flowing past a section per unit time. In other words, it is the volumetric rate of flow of a fluid. The letter Q is used to represent the discharge. Discharge of liquids can be measured either gravimetrically or volumetrically. For smaller discharges, gravimetric method is considered suitable. For larger discharges, volumetric method should be used. For still larger discharges, a standard flow rate meter such as weir (Art. 3.20), venturi meter (Chapter-14), bend meter (Chapter26) etc. may be used.

4

(a)

Laboratory Work in Hydraulic Engineering

Gravimetric Method

The discharging liquid is collected in a container (usually a bucket) for a known duration of time in seconds (s). Volume (m3) of liquid so collected is divided by the duration of collection to obtain the discharge (m3/s). Volume may either be measured directly or computed by dividing the weight of the collected liquid with the weight density of the liquid. (b) Volumetric Method

In volumetric method, the volume of the discharging liquid in a known duration of time is measured and thus the volumetric flow rate or the discharge is estimated. For this method, one may employ large tanks of known geometric form. The capacity of such a tank should be large enough to accommodate the largest expected rate of flow in a time interval large enough for the desired degree of accuracy in flow rate measurement. The discharging liquid is collected in a container whose internal dimensions have been accurately measured. By noting down the time required for rise of liquid level between predetermined elevations, the rate of flow may be calculated. The rise in the liquid level in the collection tank is measured either by a piezometer tube fitted to one of the tank walls or by means of a pointer gauge (Art. 3.18). Following steps illustrate the computation of discharge. Surface area of tank = A t in m2 Initial water level reading = Gi in m Final water level reading = Gf in m ∴

Rise in water level, G = (Gf – Gi) in m

∴ ∴

Volume of water collected = GA t in m3 Duration of collection = T in seconds GAt Discharge, Q = in m3/s T

(c)

Flow Rate Meters

Alternatively, one may install flow rate meters or, simply, flow meters (such as bend or elbow meter, orifice meter, venturimeter, nozzle meter, contraction meters etc.) in the supply or the exit pipe to measure the fluid discharge. If the flowing fluid in the set-up is liquid and is discharging into a channel, one can install suitable weir in the exit channel for this purpose. The basic principle of a flow rate meter is that the discharge through the meter is proportional to hn. Here, h is easily measurable suitable head difference (or piezometic head difference) between two definite sections in the flow and n is an index. A calibration graph (a plot between Q and h) or a mathematical relationship between Q and h is normally available in fluid mechanics laboratory for such a flow rate meter. Having measured h, the discharge can be estimated using the graph or the relation. (For more details about flow rate meters, see chapters 13-15, 26, and 33). While flow rate meters are convenient to use, the gravimetric and volumetric methods are still the most reliable and accurate methods of discharge measurement.

Elementary Terms of Fluid Mechanics

5

Suggested computation tables for these three methods are given below: (i) Gravimetric Method Weight of bucket, Wb = …………… Unit weight of water, ρ w g = …………. Weight of bucket and water, Wbc (N)

Duration of collection T (s)

Discharge (m3 /s) Wbc − Wb Q = ρ gT w

(ii) Volumetric Method Area of discharge tank, A t = …………………………………………… Water level reading on pointer gauge/ piezometer

Initial,Gi (m)

(iii)

Discharge (m3 /s) At (G f − Gi ) Q= T

Final, Gf (m)

Flow Rate Meters

Head or piezometric head difference h (m)

1.10

Duration of collection T (s)

Discharge, Q (as read from calibration graph or computed from suitable relation) (m3 /s)

VELOCITY

The velocity of a fluid particle is the length traversed by the particle in a given direction and in a unit time. The mean velocity, V, for a flow section is obtained when the rate of flow, Q, is divided by the area of flow cross-section, A. Thus, V = Q/A

6

Laboratory Work in Hydraulic Engineering

Obviously, the mean velocity is inversely proportional to the area of flow cross-section. Velocity at the point in a flow section is commonly measured by means of a Pitot-static tube (Art. 2.2) or a current meter (Art 3.19). 1.11

REYNOLDS NUMBER

It is a dimensionless parameter which is a measure of the relative importance of inertial force and viscous force prevailing in the flow of a fluid. It is equal to the ratio of the inertial force to the viscous force per unit volume. This means that a large value of Reynolds number signifies less viscous effects and vice versa. Reynolds number, R e, for flow in a pipe of diameter D, is expressed as VD/ν for pipe flow. 1.12

PROPERTIES OF FLUIDS

In S.I. (System International) units, the units of mass, length, and time are kilogram (kg), metre (m), and second (s) respectively. The unit of force is Newton (N). Units of some major physical quantities are given in Table 1.1. Table 1.2 lists the values of ρ, ρg , and γ for some ccommon fluids, while Table 1.3 lists the values of kinematic viscosity of water and air at different temperatures. Table 1.1: Dimensions and units of some physical quantities

Physical Quantity Length Mass Time Force or weight Mass density Specific weight Energy Power Pressure Dynamic viscosity Kinematic viscosity

Dimension

S.I. Unit

L M T MLT –2 ML–3 ML–2 T–2 ML2 T–2 ML2 T–3 ML–1 T–2 ML–1 T–1 L2 T–1

Metre (m) Kilogram (Kg) Second (s) Newton (N) Kg/m3 N/m3 Joule (J) Watt (W) N/m2 or Pascal (Pa) Kg/m.s or N.s/m2 or Pa.s m2 /s

Table 1.2: Properties of some common fluids at 20°C and atmospheric pressure

Fluids Water Air Alcohol Glycerin Mercury Carbon Tetra Chloride

Mass Density, ρ (Kg/m3 )

Specific Weight, ρg (N/m3 )

1000 1.207 789 1268 13533 1594

9800 11.83 7732 12426 132623 15621

Kinematic Viscosity, ν (m2 /s) 1.0 × 10–6 1.5 × 10–5 1.5 × 10–6 6.3 × 10–4 1.16 × 10–7 6.04 × 10–7

Elementary Terms of Fluid Mechanics

7

Table 1.3: Mass density of air and kinematic viscosity of water and air at different temperatures

Temperature °C

Mass Density of air

Kinematic Viscosity of Water(10–7 m2 /s)

Air(10-6 m2 /s)

12 14 16 18 20 22 24

1.241 1.234 1.221 1.214 1.207 1.196 1.189

12.48 11.78 11.17 10.60 10.05 9.58 9.17

14.34 14.54 14.74 14.93 15.11 15.30 15.48

26 28 30

1.183 1.172 1.165

8.77 8.40 8.05

15.66 15.84 16.03

C h a p t e r

Fundamental Equations Governing Fluid Motion

2 As in solid mechanics, the laws of conservation of mass and energy hold good in case of fluid mechanics also. These result into two of the three fundamental equations of fluid motion. The third equation is obtained by using the Newton's second law of motion. The three equations are individually known as the continuity equation, energy equation, and momentum equation. 2.1 CONTINUITY EQUATION If the mass density of the fluid does not change, then, the volume rates of flow past all flow crosssections must be the same, i.e., V 1 A 1 = V 2 A 2 = ……………………………. V N A N ...(2.1) Here, V and A represent, respectively, the mean velocity and area of cross-section of flow. Subscripts have been used for indicating different sections, Fig. 2.1. Equation (2.1) is known as the continuity equation and is based on the law of conservation of mass. This form of the continuity equation is valid only for such flows in which flow parameters at a section do not change with time (i.e., steady flows).

Figure 2.1. Sudden expansion in a horizontal pipe

Fundamental Equations Governing Fluid Motion

9

2.2 ENERGY EQUATION At any section in a flowing fluid, total energy is the sum of the pressure energy, potential (or datum) energy and kinetic energy. In fluid mechanics, energy is commonly expressed as energy per unit weight of a fluid and is termed as 'head' of the fluid. Thus, the total energy is expressed as 'total head' and the energy loss is termed as the 'head loss'. It is evident that the energy expressed in this manner will have the dimensions of length. 1 2 Kinetic energy of a body of mass m moving with a velocity V is equal to   mV . Since weight 2 V2 of this mass is mg, kinetic energy per unit weight is, therefore, . This quantity is termed as the 2g velocity head (or the kinetic head). If the pressure, as measured by a piezometer or some other means, is p, then the corresponding pressure energy per unity weight of water is equal to p/ρg and is termed as the pressure head. Datum head (z) corresponds to the potential energy of the fluid mass under consideration and is equal to its height z above a certain datum. Since one is generally concerned with the difference in energy between two points, the datum may be chosen arbitrarily. Energy can neither be destroyed nor created. Only its form may be changed. It may, therefore, be stated that, if between two sections of a flow system, there is neither addition nor subtraction of energy then the total energy (or the total head) at the two sections must be the same. If the two sections are designated as 1 and 2 then, z1 +

i.e.,

z+

p1 V12 p 2 V22 + + = z2 + ρg 2 g ρg 2 g

...(2.2)

2 p V + = Constant. ρg 2 g

This form of the energy equation assumes uniform velocity distribution and is known as the Bernoulli's equation. However, if there is some loss of energy (i.e., head loss) between the two sections, then, the energy equation is written as follows: z1 +

p1 V12 p 2 V 22 + z + + + hL = 2 ρg 2 g ρg 2 g

..(2.3)

where, hL is the amount of head loss between the upstream section 1 and the downstream section 2. Applying the energy equation, Eq. (2.3), for the case of sudden expansion in a pipe, Fig. (2.1), one obtains, p1 V12 + ρg 2 g

=

p2 V 22 + + hL ρg 2 g

...(2.4)

as z1 = z2 (pipe being horizontal). Here, hL is the head loss caused due to sudden enlargement of the flow section (friction losses are comparatively small in this case and, hence, neglected). Sum of the pressure head and the datum head is known as the piezometric head, h, and is directly measurable with the help of a piezometer by determining the height of the liquid level in the piezometer above a reference datum.

10

Laboratory Work in Hydraulic Engineering

The total head at any point in the flow section can be measured by inserting a small diameter tube having a short right-angled limb facing the flow, Fig. 2.2. The height of the liquid level in this tube, called the total head tube, or the stagnation tube, above a reference datum is the total head. Difference of the total head and the piezometric head (both measured with respect to the same reference datum) gives the velocity head, V 2/2g, and, hence, the velocity at the point under consideration may be estimated. These two tubes, the total head tube and the piezometer (the static head tube) can be suitably combined and the difference in the total head and the piezometric head can, then, be read on a manometer. The device so prepared is known as Prandtl (or Pitot-static) tube, shown in Fig. 2.3, which is used for measuring the velocity of flow. This device consists of a total head tube (or a stagnation tube), surrounded concentrically by a closed outer tube (static head tube) with annular space in between the two tubes. Small holes are drilled (transverse to the flow direction) through the static head tube to measure the static head, p/ρg. The total head tube in the centre measures the total head (or the stagnation head), which is the sum of the static head, p/ρg, and kinetic head, V 2/2g. When the two tubes are connected to a suitable differential manometer, the resulting difference in the manometer liquid levels measures the velocity (or kinetic) head.

Figure 2.2 Total head and static head tubes

Figure 2.3 Pitot-static tube (or Prandtl tube)

Fundamental Equations Governing Fluid Motion

11

Using the notation of Fig. 2.3, and Eq. (2.2), 2 pt ps V +0 + = ρg ρg 2 g

V2 or

2g

=

pt − p s ρg

...(2.5)

Writing down the gauge equation p s − Yρg + Xρ m g = pt − Yρg + Xρg p t − p s  ρm − ρ  X ρg =  ρ  From Eqs. (2.5) and (2.6), or

V2 2g

=

...(2.6)

pt − p s ρg

 ρm  ...(2.7) V = 2g  ρ −1 X   Here, ρm and ρ are the mass densities of the manometer fluid and flowing fluid, V the velocity and g the acceleration due to gravity. Velocity at any point can be computed by measuring the manometer reading X and then using Eq. (2.7). or

2.3 MOMENTUM EQUATION Momentum equation is based on Newton's second law of motion which states that the algebraic sum of all external forces applied to a control volume of a fluid in any direction is equal to the rate of change of momentum of the fluid in that direction. The external forces include the component of the weight of the fluid and that of the forces exerted externally upon the boundary surface of the control volume in the direction under consideration. Momentum equation, in its simplest form, is written as, ∑ Fx = ρQ (V x2 − V x1 )

...(2.8)

where, ∑ Fx represents the algebraic sum of the external forces applied on a control volume in the xdirection , and V x1 and V x2 are x-direction components of mean velocities at sections 1 and 2, respectively.. Applying the momentum equation, to the control volume for the case of sudden expansion in a pipe, Fig. 2.1, and considering the control volume ABCD (shown by dotted lines), ∑ Fx = p1 A 2 – p2 A 2 = ρ V 2 A 2 (V 2 – V 1) p1 − p2 V 2 (V 2 − V1 ) or = ...(2.9) ρg g Combining Eqs. (2.4) and (2.9), one obtains an expression for hL , as follows: hL =

(V1 − V 2 ) 2 2g

...(2.10)

C h a p t e r

Open Channel Flow

3 The flow of a liquid in a conduit (closed or open) may be either open channel flow (also termed as free surface flow or gravity flow) or pressure flow (i.e., closed conduit flow or pipe flow) depending upon the presence or absence of the free surface. Open channel flow must have a free surface (i.e., top surface of flow is in contact with the atmosphere) while pressure flow has no free surface. In pressure flow, fluid confined in a closed conduit flows under pressure. In open channel flow, liquid exerts no pressure other than the atmospheric pressure and that caused by its own weight. Open channel flow occurs under the influence of gravity and, hence, is also known as gravity flow. 3.1 CHANNEL A channel is a conduit in which liquid flows with a free surface which is subjected to the atmospheric pressure. A channel may be either natural (such as a river) or artificial (such as a canal or laboratory flume). 3.2 CANAL A canal is a long and mild sloped open channel usually built into or on the ground. 3.3 FLUME A flume is a channel having walls made of wood, metal, glass or masonry and supported on or above the ground. 3.4 DEPTH OF FLOW The depth of flow, h, is the vertical distance of the lowest point of a channel section from the free surface. 3.5 DEPTH OF FLOW SECTION The depth of flow section, d, is the depth of flow normal to the direction of flow. Thus, from Fig. 3.1, d1 h1 = cos θ and for θ ≈ 0, h1 = d1.

Open Channel Flow

13

Figure 3.1 Definition sketch for open channel flow

3.6 TOP WIDTH The top width, T is the width of channel section at the free surface. 3.7 AREA OF FLOW CROSS-SECTION The flow cross-section area, A, is the water area on a plane normal to the direction of flow. 3.8 WETTED PERIMETER The wetted perimeter, P, is the length of the line of intersection of the channel wetted surface with a cross-sectional plane normal to the direction of flow. 3.9 HYDRAULIC RADIUS The hydraulic radius, R, is the ratio of the flow cross-sectional area to the wetted perimeter, i.e., R = A/P. 3.10

HYDRAULIC DEPTH

The hydraulic depth, D, is the ratio of the flow cross-sectional area to the top width, i.e., D = A/T. 3.11

GEOMETRIC ELEMENTS FOR A RECTANGULAR CHANNEL

For a rectangular channel section of width B and depth of flow h ( ≈ d when θ ≈ 0, θ is the angle of inclination of the channel bed), Fig. 3.2, the expressions for various geometric elements, defined above are as follows: T = B; A = Bh; P = B + 2h A Bh R = P = ( B + 2 h ) ; and

D=

A Bh = =h T B

14

Laboratory Work in Hydraulic Engineering

Figure 3.2 Rectangular channel section

3.12

CLASSIFICATION OF OPEN CHANNEL FLOW

Open channel flow may be classified as steady or unsteady when changes in flow conditions are considered with respect to time. Steady flow occurs in a channel, if the flow parameters at a given location do not change with respect to time. The flow becomes unsteady, if the flow parameters vary with time. Using space as the criterion, open channel flow may also be classified as uniform or varied (nonuniform) flow. A uniform flow occurs in a channel when, at a given time, the flow conditions remain the same at every section along the channel. In varied flow, the flow conditions, at a given time, vary from section to section along the length of the channel. Varied flow can be further classified as rapidly varied flow or gradually varied flow. In gradually varied flow, the change in flow conditions takes place gradually over a comparatively large distance. 3.13

FROUDE NUMBER

Froude number, F r is a dimensionless parameter which is a measure of relative influence of the inertial force and gravity force on the flow. It is defined as the ratio of the inertial force to the gravity force and is expressed as, V Fr = gD where, and 3.14

V = the mean velocity of flow, g = the acceleration due to gravity, D = the hydraulic depth. EQUATION OF CONTINUITY

For steady open channel flow in which there is neither addition nor withdrawal of water, the equation of continuity explained in Art. 2.1 holds good. 3.15

ENERGY EQUATION

As in pipe flow, the total energies at two different sections of channel flow will differ by an amount equal to the energy loss between the two sections. For a mild sloping channel (i.e., θ ≈ 0 ), Fig. 3.1, the energy equation is expressed as,

Open Channel Flow

15

z1 + h1 + 3.16

V12 V 22 + hL = z 2 + h2 + 2g 2g

...(3.1)

SPECIFIC ENERGY

The total energy at any section with channel bed as reference datum (i.e., datum head z = 0 ) is termed as specific energy, and is represented by the letter E. Thus, at any section, V2 E = h+ 2g or

Q2 E = h+ 2 g A2

...(3.2)

Q ; Q being the discharge and A, the area of flow cross-section. A Since A is a function of h, it can be concluded that for a given channel section, E depends upon h and Q. The graphical representation of Eq. (3.2), shown in Fig. 3.3, is known as the specific energy curve. as

V=

Figure 3.3 Specific energy curve

If the flow conditions, for given Q and E, are represented by the point C (corresponding to the minimum specific energy) on the specific energy curve, then the flow is said to be ‘critical’ and the corresponding depth hc and velocity V c are termed, respectively, as the critical depth and critical velocity. If the depth of flow, h < hc as at point 1, the flow is termed supercritical flow. On the other hand, if the depth of flow, h > hc as at point 2, the flow is subcritical. The two depths h1 and h2 for the same specific energy, as obtained from the specific energy curve (except at E = E c), are known as alternate depths.

16

Laboratory Work in Hydraulic Engineering

It is also of interest to know that for a given specific energy E, the discharge flowing in a channel will be maximum if the flow is critical, i.e., the depth of flow is hc. 3.17

MOMENTUM EQUATION

For open channel flows also, the momentum equation, Eq. (2.8), explained in Art. 2.3 holds good. 3.18

MEASUREMENT OF LIQUID SURFACE ELEVATIONS

A pointer gauge or a hook gauge, Fig. 3.4 is the simplest method of measuring the liquid surface elevation. While using the hook gauge, the hook is first lowered below the liquid surface and then raised until the point of the hook just breaks the liquid surface. The liquid surface elevation is read on the vernier scale provided on the hook gauge mounting. In using the pointer gauge, the point is lowered until it touches the liquid surface or appears to touch its reflection in the liquid surface. It is preferred to use these in a stilling chamber (or well) at the side of the channel where the fluctuations of liquid surface are much less.

Figure 3.4 Hook gauge and pointer gauge

Electrical gauges are also available. In such gauges the variable capacitance between a fixed plate and the liquid surface is the measure of the liquid level. 3.19

MEASUREMENT OF VELOCITY

Velocity of flow in open channel can be measured by using either a Pitot-static tube, described in Art. 2.2 or a current meter. Current meter is a mechanical device which consists mainly of a rotating element (usually series of cups or vanes) whose speed of rotation varies with the local velocity of flow. The relation between the speed of rotation and the velocity of flow is found by calibration and, in most cases, supplied by the manufacturer. Speed of rotation is measured by noting down the number of revolutions (read from the battery operated counter or by counting the number of clicks heard through a head phone provided for this purpose) in a known duration.

Open Channel Flow

3.20

17

MEASUREMENT OF DISCHARGE

The discharge in an open channel is measured by means of a weir. Weir is an obstruction built across a channel section with water flowing over it. Weirs are of different shapes, but the sharp-edged rectangular weir is commonly used for discharge measurement in the laboratory. A sharp-edged rectangular weir is made of a steel plate fixed across the entire width B of the discharging channel. The top edge of the weir plate is made sharp. In Fig. 3.5, h is termed as the head over the weir and is measured at a distance of about 3h to 4h upstream of the weir. W is the height of the weir crest, above the channel bed. For free flow conditions (i.e., when the downstream water level is below the weir crest level), the discharge Q flowing over the weir is given by the expression, 3 2 Cd B 2 g h 2 ...(3.3) 3 where, Cd is the coefficient of discharge of the weir and is obtained by using the expression,

Q=

Cd = 0.611 + 0.075 [h/W]

...(3.4)

Alternatively, a calibration graph (Q v/s h), if available, may be used for estimating the flow rate.

Figure 3.5 Sharp-edged rectangular weir

It should be noted that Eq. (3.3) is based on the assumption that the atmospheric pressure prevails on both sides of nappe (water sheet falling from the weir is termed nappe). Therefore, the underside of the nappe is ventilated by means of holes made in the channel wall immediately downstream of the weir. Alternatively, the triangular sharp-edged weir (or V-notch) can be used for measuring the discharge. For V-notch, the expression for discharge is 8   θ  5 2 Q = 15 Cd 2 g  tan  2   h    Here, θ is the notch angle.

...(3.5)

C h a p t e r

4

Basic Facilities in Hydraulic Engineering Laboratory

4.1 GENERAL Hydraulic engineering (or hydraulics or fluid mechanics) laboratory in any engineering institution, imparting education in Civil, Mechanical, Chemical, and Aeronautical Engineering, is an important facility. It enables the students to grasp and appreciate basic principles of fluid mechanics and hydraulic engineering. The laboratory work in hydraulic engineering is, thus, complementary to the classroom lectures in fluid mechanics, hydraulics, pipe flows, and open channel flows. In general, hydraulic engineering laboratory serves one or more of the following needs: (a) Undergraduate teaching (b) Post-graduate teaching and research (c) Research for sponsoring agencies (d) Consultancy work for sponsoring organisations Laboratory work for teaching purposes is generally aimed at: (a) Visualization of various flow phenomena (b) Verification of theoretical relationships (c) Calibration and use of flow meters (d) Prediction of flow characteristics using principles of dimensional analysis and physical modelling Basic facility of any effective laboratory is uncluttered space. While setting up a new laboratory or even for an extension, provision should be made for future expansion so that, even at a later date, the laboratory gives a look of clean, dry, and well-painted hall. A hydraulic engineering (or hydraulics) laboratory would generally require water and air as experimental fluids. In addition, oil, glycerin, and other fluids may also be used as experimental fluids for specific purposes. Air possesses the advantage because of its availability everywhere without any requirement of its storage. Water would require storage space (in the form of sumps and overhead tanks). Oil too would require proper storage in some containers with tight joints and arrangements to collect any leakage of oil from the containers or the set-ups that may still occur. The water reservoir may be below the laboratory floor or may be sited alongside the laboratory. The reservoir should have sufficient quantity to fill all the experimental set-ups and equipments, and still maintain adequate depth of submergence at pump inlets. Arrangements for overflow (required in case of careless overfilling) and waterway (in the form of bottom outlet connected to sewer for cleaning purposes) should always be provided.

Basic Facilities in Hydraulic Engineering Laboratory

19

Constancy of flow in the experimental set-ups and equipments must be ensured by electric control of the motor speeds for pumped supplies and overflow in case of overhead tanks. The freeboard (above the constant head in the overhead tank) and capacity of the return pipe of return channel taking overflow back to the reservoir should be large enough to take the entire discharge of the pumps when all the experiments have been stopped. A common pipe supplying water to more than one experimental set-ups, to be operated simultaneously, would affect the flow in all the experimental set-ups when the flow is varied in any one of the set-ups. Therefore, a separate pipe should be used for supplying water to any experimental set-up. Laboratories usually provide for both qualitative and quantitative experimentation. For quantitative experimentation, the hydraulics laboratory must have provisions of flow measurement besides other kinds of measurements like dimensions of a body, temperature of the surroundings, and fluid properties such as viscosity etc. For volumetric rate of flow, i.e., discharge, one can employ either gravimetric method or volumetric method or a suitable flow meter. Other primary flow quantities to be often measured in any experiment are pressures and velocity. For measuring pressures, piezometers and manometers are generally used. However, when pressures are expected to fluctuate considerably, one should use pressure transducers. It would be desirable that each experimental set-up has a separate piezometer or manometer dedicated to itself. One to two units of pressure transducers and the associated equipment would usually be adequate for any hydraulics laboratory. Most commonly used device for measuring the local velocity of flow of a fluid is Prandtl or Pitot tube along with a manometer. Number of Pitot tubes and dedicated manometers would depend on the number of experimental set-ups which would run simultaneously and would also require measurement of velocity. The measurement of the fluctuating velocity (and the associated turbulence) would, however, require instruments such as hot-wire (for gases) or hot-film (for liquids) anemometers, laser-Doppler anemometer, acoustic-Doppler velocimeter etc. In addition, the hydraulics laboratory would also require adequate number of stop watches, thermometers, pointer gauges (for measuring water surface levels), weighing balance etc. The hydraulics laboratory should also have a small dedicated workshop to fabricate specific set-ups and models of the object to be investigated, and carry out necessary maintenance works. 4.2 COMPONENTS OF HYDRAULICS LABORATORY Main components of a hydraulic engineering (or hydraulics) laboratory are sump(s), overhead tank (s) calibration tank, pump room, workshop, office space, computer room, instrumentation room, store room, sanitary block, indoor (main) laboratory and outdoor space (for physical models). If one is required to set up a hydraulic engineering laboratory, one should visit an established good hydraulics laboratory in the region to discuss all aspects of the laboratory with its in-charge. While planning, ample provision should be kept for future expansion of the laboratory as the need arises or funds are made available. 4.2.1 Sump

Capacity of the sump(s) and overhead tank(s) should be decided keeping in mind future expansions of the laboratory. The sump capacity can be estimated by determining the volume of water in pipes, return channels and all the flumes when they have maximum depth of flow. To avoid formation of vortices there should be at least 1.0 m depth of water above the pump intake. As a thumb rule, sump capacity

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Laboratory Work in Hydraulic Engineering

should be provided at the rate of 1 m3 for each 1.0 l/s of the laboratory discharge. Depending upon the extent of future expansion, the sump capacity may be kept 50 to 100 per cent higher than the present requirement. In case of non-availability of space for open tank, one can plan the sump under the floor of the laboratory. 4.2.2 Discharge

The discharge for the laboratory would depend upon the number of experimental set-ups to be run simultaneously. If model studies are likely to be regular feature, relatively higher discharge would be required. For a medium size laboratory, one should have about 500 l/s discharge which may be supplied by three or more pumps. 4.2.3

Overhead Tank

The overhead tank is provided at 6.0 m to 10.0 m above the floor level of the laboratory. For every 5.0 l/s of the laboratory discharge, one should provide 1.0 m3 overhead tank capacity. In order to maintain constant water level in the overhead tank (so that the flow in the set-ups is steady) an overflow arrangement is necessary. The inlets from pumps to the tank and outlets from the tank should be suitably spaced and located so that there is no short-circuiting. Therefore, the overhead tank should be large. In addition, the inlets may be baffled and the outlets shielded properly. 4.2.4 Pipe System

In order to have steady flow conditions in each of the experimental set-ups, a separate pipeline should be installed for each set-up. If desired, one may have a separate overhead tank for a group of four or five set-ups requiring smaller discharge. But, then also, a separate pipeline would be desirable for each of those set-ups. It would be economical if two or three different standard sizes of pipes (and valves and flow measuring devices) are used. Valves should be located downstream of the flow measuring devices. If the bends are unavoidable in the pipeline, the bends can be used as discharge measuring device. The pipes can be laid underneath the laboratory floor. The exposed pipelines should be so placed that the view of pipelines is aesthetically pleasing. Unnecessary sharp bends should be avoided to reduce the losses. If unavoidable, flow vanes may be used to reduce the losses. 4.2.5

Flow Measuring Devices

For pipelines, one may use either orifice meter or venturi meter or 90° pipe bend for measuring the discharge. A sharp-crested weir (rectangular or triangular) is generally used for measuring the discharge in a channel. 4.2.6 Flumes

Fixed bed flumes with glass side walls are required for the experiments on open channel flows. The flumes can be of different widths (say, 15 cm to about 1m) and depths (say, 15 cm to 60 cm). The bed of the flume can be smooth or rough. At the inlet end, flow straighteners and turbulence dampeners are placed. At the downstream end, a tail gate (vertical strips) is provided for controlling the depth of flow in the flume. The flume should be of sufficient length so that its central section is unaffected by the entrance and exit conditions. In order to have supercritical flow, one can have a small reservoir at the upstream end of the flume and a sluice gate to control the outflow from the reservoir into the flume. The flumes should have a railing on its walls for enabling measurements of depth of flow and velocity of flow at different sections. The outflow from the flume may fall in the return channel that may have a weir for measuring the discharge. At least one tilting bed flume should always be provided in a hydraulics laboratory.

Basic Facilities in Hydraulic Engineering Laboratory

4.2.7

21

Wind Tunnel

The advantage of working with the fluid air is obvious as one need not have any storage for air since it is available everywhere. For this purpose, one requires closed ducts (usually of rectangular or square cross-section) which are known as wind tunnels. Studies relating to boundary layer formation, drag around a cylinder can be easily carried out using a wind tunnel. A wind tunnel would have an entrance (designed suitably to have a streamlined flow), a test section, and the exit section. A fan would be required and is provided at the exit end. The side walls of the test section are made transparent. Usually, open-circuit wind tunnels are considered suitable for wind tunnel studies. For uniform flow conditions, test section of length of 1 m to 4 m is enough. 4.2.8

Measuring Equipment

There are several kinds of measuring devices for various flow quantities. Most commonly used devices in the hydraulics laboratory are stop watch, weighing balance, pointer gauges, Pitot tubes, piezometers, manometers, total head tubes, thermometers, scales etc. In addition, one may have precision equipments such as pressure transducers, anemometers (hot-wire or laser-Doppler type), strip-chart recorders, data-acquisition systems etc. Depending upon the objective, many other types of equipments may also be required.

C h a p t e r

Writing Laboratory Reports

5 Laboratory work is undertaken to (a) test and expound theory, (b) provide practical experience and data for solving certain problems, (c) develop design concepts, and (d) allow conclusions to be drawn from the observed results. The laboratory report on any experimental work should contain (a) details of the experiment such as objective, theoretical background etc., (b) description of the set-up and equipment used, (c) an accurate record of all observations (both visual and numerical) and measurements taken during the conduct of the experimental work, (d) computation, and (e) results (in tabular or/and graphical form as required) and conclusions including summary or discussions or comments etc. The laboratory notebook should be reasonably neat and page-numbered with an index at the beginning. The observation/computation/result tables should preferably be set out vertically and suitably titled. Heading of each column must include, where relevant, the units of the quantity being entered. Any text massage (like, “measurement could not be taken” or “test not performed” etc.) can be written as footnote. For graphical presentation of results, the horizontal axis (or X-axis, i.e., abscissa) is, usually, used for the quantity that is being controlled or adjusted (i.e., independent), and the vertical axis (i.e., Y-axis or ordinate) is used for the observed dependent quantity. Scales should be carefully chosen and the units for the quantity being plotted, mentioned. A full report would generally contain the following: 1. (a) Name (b) Group (c) Experiment Number (d) Date 2. Title of Experiment 3. Object of the Experiment 4. Introduction and Theoretical Background 5. Description of the Experimental Set-up 6. Method or Procedure 7. Results 8. Conclusions, Discussions, and Comments

C h a p t e r

Viscometer

6 OBJECT To measure the viscosity of a given liquid. INTRODUCTION AND THEORY Viscosity (Art. 1.6) can be measured by using Newton's law of viscosity, i.e., du τ = µ ...(6.1) dy in which, τ is the shear stress, µ is the viscosity (or dynamic viscosity) of the liquid and du/dy is the velocity gradient. A cylinder of radius R 2 rotates at a speed of N revolutions per minute (rpm) with respect to an inner concentric stationary cylinder of radius R 1 such that the small annular space between the two cylinders (Fig. 6.1) is filled with the liquid whose viscosity is to be determined. One can determine the velocity gradient du/dy assuming that the velocity in the annular space varies linearly. Thus du 2πR 2 N ...(6.2) dy = 60b The equation assumes that b 6.0) have been derived by Karman and Prandtl and, hence, the same are known as Karman-Prandtl equations. Here, k and δ′ are, respectively,, the mean surface roughness height and thickness of laminar sublayer, the meaning of which is explained in Chapter-27. For turbulent flow near smooth boundaries, velocity distribution is expressed as: V V y 5. 75 log * + 5.5 ...(23.1) V* = ν Corresponding equation for rough boundaries is expressed as, V y 5.75 log + 8.5 ...(23.2) V* = k Here, V is the velocity at a distance y from the boundary, V* the shear velocity which is equal to τ 0 being the wall shear stress, Fig. 23.1, and ρ is the mass density of the fluid.

Figure 23.1 Velocity variation near boundary

τ0 ρ ,

Velocity Distribution in Pipes

91

For a given boundary and fluid, the velocity distribution in the case of turbulent flow follows the logarithmic law and thus, one can write, V ∝ log y or V = A log y + B ...(23.3) where, A and B are some suitable constants. It may be noted that the logarithmic law does not yield realistic value of the velocity at y = 0. This form of the velocity law is equally valid for turbulent flow in pipes. Its alternative approximate form for turbulent flow in pipes is expressed in the form of a power law as follows : m V y   V0 =  R  ,

...(23.4)

where, V 0 is the centre-line velocity (at y = R) and the index m varies from 1/7 to 1/10. The velocity distribution laws, Eqs. (23.3) and (23.4) can be verified by plotting either V v/s log y on an ordinary graph paper or V/V0 v/s y/R on a log-log graph paper. Each of these plots should yield a straight line whose slope and intercept on y-axis in the former case give A and B, respectively, while slope of the line in the latter case gives the value of m. Considering a small elemental strip of thickness dy, Fig. 23.1, at a distance of (R-y) from the centre of the pipe, the discharge dQ can be written as dQ = {2π( R − y ) dy}V R

or

Q=

∫ 2π (R − y ) V dy 0

Writing this equation in terms of finite difference quantities, Q=

∑ 2 π ( R − y )V ∆ y

...(23.5)

Having plotted the velocity distribution, the velocity can be integrated, graphically, to get the discharge. EXPERIMENTAL SET-UP The set-up consists of a straight pipeline of diameter about 100 mm and length about 5 to 7 m. Supply to the pipe is controlled by means of an outlet valve. A Pitot-static tube attached to a suitable mounting and a manometer are used to measure the velocity at different points along a vertical section in the pipeline. At the outlet end of the pipeline is placed a collection tank of about two cubic meter capacity for measuring the discharge. PROCEDURE 1. Note down the reading on the gauge, to which Pitot-static tube has been fixed, when the Pitot-static tube just touches the lower pipe wall. This reading on the gauge corresponds to y = d/2, where d is the diameter of the Pitot-static tube. 2. Open the inlet valve fully and close the outlet valve. Remove air bubbles, if any, in the manometer tube. 3. Open the outlet valve and let the flow stabilize. 4. Note the manometer readings for different positions of the Pitot-static tube. Near the wall,

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the interval between successive positions of Pitot-static tube may be kept small, say, 2-3 mm and near the centre this interval may be increased to about 3-5 mm. 5. Measure the discharge. FIGURES TO BE PREPARED AND FURTHER COMPUTATIONS 1. Plot on a simple graph paper, V v/s y with V on x-axis and fit-in a smooth curve. Integrate the velocity profile to get the computed value of discharge for the run taken. Compare the value with the measured value of discharge. 2. Plot on a simple graph paper V v/s log y, with V on y-axis for all the data upto y = R = D/2 only. Fit-in a straight line and compute the values of A and B, respectively, in Eq. (23.3). Mention the values of A and B for the run taken. A = …………………….. B = …………………….. 3. From the plot V v/s y, read the value of the centre line velocity, V 0, for the run taken and compute V/V0 v/s y/R upto y/R = 1 for all the data points of the run. Record these in Table and plot V/V0 v/s y/R, with y/R on x-axis, on a log-log graph paper. Fit-in a straight line to the data points and find its slope. Thus, m in Eq. 23.4 is obtained. m = ………………………. 4 Also obtain the values of the energy and momentum correction factors (see chapter-30) for the velocity profile observed.

and

where,

3

1 α = πR 2

∫

1 β = π R2

∫

1 π R2

∫

Va =

OBSERVATIONS AND COMPUTATIONS

R 0

V    2 π rdr = ....................  Va  2

R

0

R 0

V    2π rdr = ....................  Va  V (2π r ) dr = Q A Date: ………..

Radius of pipe, R = …………………………………………………. Diameter of Pitot-static tube, d = …………………………………. Mass density of manometer liquid, ρm = …………………………. Mass density of water, ρ w = ………………………………………. Initial reading of Pitot-static tube gauge, Gi = ……………………

Velocity Distribution in Pipes

93

Discharge Measurement

Discharge, Q (Measured) Discharge, Q (Computed from velocity profile) Velocity Profile Measurements

V Sl. No. ↓ Unit →

Gf

y

=

ρ  2 g  m −1 (h1 − h2 )  ρw  h1

h2

d  y = G f − Gi +   2 RESULTS AND COMMENTS Values of A and B for Eq. (23.3): A = .............., B = ...................... Values of m for Eq. (23.4) = ....................... Discharge Q from Eq. (23.5) = .......................... Average velocity, V a = Q/πR 2 = ......................... Energy corection factor, α = .......................... Momentum corection factor, β = .......................

V

V/V 0

y/R

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Laboratory Work in Hydraulic Engineering

Velocity Distribution in Pipes

95

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Laboratory Work in Hydraulic Engineering

C h a p t e r

Frictional Head Loss in Smooth and Rough Pipes

24 OBJECT To study the variation of friction factor, f for turbulent flow in smooth and rough commercial pipes. INTRODUCTION AND THEORY For steady uniform flow in a pipe of diameter D and length L, Darcy and Weisbach obtained the following relationship by equating the pressure force exerted on the flow with the boundary shear force: hf = f

L V2 D 2g

...(24.1)

This relation is known as Darcy-Weisbach equation for the head loss due to friction in a pipe. Here, hf is the head loss on account of friction, V the mean velocity of flow, and f is the friction factor. The friction factor depends on Reynolds number, Fe (= Vd/ν ) and the relative roughness, k/D. Here, k is the equivalent sand grain roughness of the roughness projections on the surface of the pipe. Nikuradse's experimental investigation on artificially roughened pipes demonstrated perfectly the same relationship among f, R e and k/D. The results of his investigations have been summarized below: 1. For laminar flow (Chapter -22) i.e., R e < 2000, f = 64/R e. This means that the head loss in laminar flow is independent of the surface roughness and depends only on R e. 2. For turbulent flow (i.e., R e > 3000) there exists a curve f v/s R e for different values of k/D. 3. Following are the equations for friction factor in turbulent flow. For hydrodynamically smooth turbulent flow in a pipe, 1 f

= 2. 0 log Re

f − 0. 8

...(24.2)

and for hydrodynamically rough turbulent flow in a pipe, 1

D 2. 0 log + 1.74 f = 2k

...(24.3)

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Laboratory Work in Hydraulic Engineering

A surface is said to be hydrodynamically rough if k δ′ > 0.6. If k δ′ < 0.25 the surface is said to be hydrodynamically smooth. Here, δ′ is the thickness of laminar sublayer (Chapter-27). For a hydrodynamically smooth pipe, the following equation, suggested by Blasius, is also in agreement with Nikuradse's data in the range 3000 < R e < 105. f=

0.316 Re0. 25

...(24.4)

Since Nimuradse's experiments were conducted on the sand-coated pipes, these results cannot be applied directly to the commercial pipes. However, Colebrook and White, starting from Nikuradse's equations, derived the following equation that can be used for obtaining friction factor values for the commercial pipes.  k/D 1 2.51 = −2.0 log  + f  3.7 Re f

  

...(24.5)

This equation has been plotted by Moody in the manner shown in Fig. 24.1. Here, k is the equivalent sand grain roughness, defined as the diameter of such uniform sand grains which, when coated on a pipe wall, would yield the same limiting value (i.e., independent of R e) of f for rough conditions as that given by the pipe.

Re Figure 24.1 Variation of Friction factor for commercial pipes (Moody's diagram)

Frictional Head Loss in Smooth and Rough Pipes

99

EXPERIMENTAL SET-UP The set-up consists of two pipes. One of these pipes is hydrodynamically smooth and the other is hydrodynamically rough for the flow range in the set-up. The diameter of these pipes may range between 15 mm and 25 mm. These pipes may be about 5 m long. The discharge is regulated by means of a valve provided near the outlet end of each pipe. One common inlet valve for both pipes is also provided in the main supply line. For measuring the head loss hf , two pressure taps, about 3 m apart, are suitably located on each of these pipes. These pressure taps are connected to a manometer. PROCEDURE 1. Open the inlet valve and keep the outlet valve closed. Remove the air bubbles from the manometer tubes. 2. Open partially the outlet valve of one of the two pipes and keep the common inlet valve fully open. 3. Wait for some time so that the flow is stabilized. Take the manometer readings h1 and h2. 4. Measure the discharge. 5. Repeat steps (2) to (4) for different discharges. 6. Repeat steps (2) to (5) for other pipe also. FIGURE TO BE PREPARED AND FURTHER CALCULATIONS Plot the computed values of f against the corresponding Reynolds numbers, R e on Moody's diagram, Fig. 24.1. Use different symbols for the two sets of data. Check whether the hydrodynamically smooth pipe data are in agreement with the Blasius curve for smooth pipe. The data of hydrodynamically rough pipe should follow around one of the curves for hydrodynamically rough pipes shown in Fig. 24.1. Using the rough pipe data and Moody's diagram, determine the value of k/D and thus compute k. k = ………………………… RESULTS AND COMMENTS

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Laboratory Work in Hydraulic Engineering

OBSERVATIONS AND COMPUTATIONS SHEET

Temperature of water = ……………

Date: ………

Kinematic viscosity of water, v = ………. Pipe 1

Pipe 2

Area of cross-section, A Distance between pressure points, L Hydrodynamically rough/smooth

Pipe Run No. No.

↓ Unit → 1

2

Manometer Readings

Discharge Measurement Q

h1

hf h2

Re

C h a p t e r

Minor Losses in a Pipeline

25 OBJECT To determine the loss coefficients for different pipe fittings. INTRODUCTION AND THEORY Losses due to change in cross-section, bends, elbows, valves and fittings of all types fall into the category of minor losses in pipelines. In long pipelines, the friction losses are much larger than these minor losses and, hence, the latter are often neglected. But, in shorter pipelines, their consideration is necessary for the correct estimate of losses. The minor losses are, generally, expressed as V2 ...(25.1) 2g where, hL is the minor loss (i.e., head loss) and KL , the loss coefficient, which is practically constant at high Reynolds number for a particular flow geometry. V is the velocity of flow in the pipe (in case of an abrupt contraction, V is the velocity of flow in the contracted section). For an abrupt enlargement of the pipe section, however, use of the continuity equation, Bernoulli's equation, and momentum equation (see Art. 2.3) yields, hL = K L

2   d 2  V 2 V (V − V 2 ) 2 hL = = 1 −  D   2 g = K L 2 g ...(25.2) 2g     Here, V 2 and V are the velocities of flow in the larger diameter (= D) and smaller diameter (= d) pipes respectively.

EXPERIMENTAL SET-UP The experimental set-up consists of a pipe of diameter about 25 mm fitted with (a) a right-angled bend or an elbow, (b) a valve, (c) a sudden expansion (larger pipe having diameter of about 100 mm), and (d) a sudden contraction (from about 100 mm to about 25 mm). Sufficient length of pipeline should be provided between various pipe fittings. The pressure taps on either side of these fittings are suitably provided and the same may be connected to different manometers or a multi-tube manometer. Supply

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Laboratory Work in Hydraulic Engineering

to the pipe line is made through a storage tank in which water level should remain at a constant level. The discharge is regulated by means of an outlet valve provided near the outlet end. PROCEDURE 1. Open the outlet valve and let the flow become steady. 2. Connect the manometer tubes to a pair of pressure taps provided for all the pipe fittings, one by one, and record the difference of manometer readings. It should be ensured that there is no air bubble left in the manometer tube while taking manometeric observations. 3. Measure the discharge. 4. Repeat the above steps for different openings of the outlet valve. OBSERVATIONS AND COMPUTAIONS

Diameter of main pipe, d = ………… Diameter of enlarged pipe, D = ……… Area of cross-section of main pipe, a = …………………………………………….. Area of cross-section of the enlarged pipe, A = ……………………………………

Run No.

Unit

Discharge Measurement Discharge, Q

Velocity of Flow V = Q/a

V2=Q/A

Minor Losses in a Pipeline o

90 bend/elbow hL

KL

103

Valve hL

Sudden contraction* KL

hL

KL

Sudden expansion* hL (measured)

KL

(V–V2 )2 /2g

* Head loss h Lfor sudden contraction and expansion requires application of Bernoulli's equation, Eq (2.3)

RESULTS AND COMMENTS Average values of the loss coefficients for various pipe fittings, as obtained experimentally, are as follows: Pipe fitting Loss Coefficient, KL Bend/Elbow -------------------------------------------Valve -------------------------------------------Sudden contraction -------------------------------------------Sudden Expansion --------------------------------------------

C h a p t e r

Bend Meter

26 OBJECT To study the flow behaviour in a pipe bend and to calibrate the pipe bend (i.e., bend or elbow meter) for discharge measurement. INTRODUCTION AND THEORY When a fluid flows through a pipe bend, there occurs a change in the direction of flow that requires, irrespective of the magnitude of the radius of bend, an increase in pressure intensity in the flow field along the outside of the bend and a decrease along the inside.

Figure 26.1 Pressure and velocity variation in a pipe bend.

Figure 26.2 Secondary flow in a pipe bend

Bend Meter

105

Figure 26.1 indicates the typical head distribution for flow along the outer and inner wall of the bend. Also shown in the figure is the distortion of velocity profile from a uniform variation just upstream of the pipe bend. Because of the transverse pressure gradient, the fluid near the pipe wall, moving with relatively smaller velocity due to boundary layer formation, starts moving from the outer wall to the inner wall. To satisfy the continuity requirement their will also be a flow from the inner wall toward the outer wall in the central region. This secondary flow, as shown in Fig. 26.2, in combination with the main flow gives rise to a spiral motion which persists for some distance. Thus, the velocity in the pipe may require a length as much as about 100 pipe diameters downstream from the bend to become normal again. The characteristics of flow in a pipe bend, viz., the change in flow direction requiring a pressure gradient along the radial direction irrespective of the radius of the bend, can be used to employ the bend as a flow measuring device. It is, then, called as bend meter or elbow meter. It should be noted that just as other flow measuring devices, such as orifice meter and venturi meter, use the relation between the fall of piezometeric head and the flow rate, the bend meter also utilizes the relation between the flow rate and the fall of piezometeric head between the outer and inner limits of the flow in the pipe bend, Fig. 26.3. For this purpose, an equation has been proposed in the following form: 2  po   p  + Z0  −  i + Zi  = ∆ h = C k V  2g  ρg   ρg 

...(26.1)

in which the coefficient Ck ranges between 1.3 and 3.2, the actual magnitude depending upon the size and shape of the bend. This equation, when solved for V and multiplied by the area of cross-section of the pipe A to obtain the flow rate Q, yields. Q = C A 2 g ∆h where, C =

...(26.2)

1 C k and is termed as the coefficient of discharge of the bend (or elbow) meter..

Figure 26.3 Set-up for pipe bend

EXPERIMENTAL SET-UP The set-up consists of a suitable pipe bend fitted in a pipeline of about 50 mm diameter. Pressure points are provided on the inner and outer walls extending well upstream and downstream of the bend. All the pressure points are connected to individual piezometer tubes that are fitted on a board having a graph

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Laboratory Work in Hydraulic Engineering

sheet fixed on it for reading the elevations of the piezometer levels. Discharge is regulated by means of an outlet valve. PROCEDURE 1. Open the inlet valve fully and close the outlet valve. Check if there is any air bubble in the tubes connected to piezometers. If so, remove the same. 2. Open the outlet valve partially and let the flow stabilize. 3. Take all the piezometer readings. 4. Measure the discharge. 5. Repeat steps (2) to (4) for one more opening of the outlet valve. 6. Repeat steps (2) and (4) for different openings of the outlet valve and take the corresponding piezometer readings only for the two pressure taps fitted on the inner wall and outer wall at the middle of the bend. Let these be represented as hout and hin, respectively. FIGURES TO BE PREPARED Plot the variation of [(h0 – h)/(V 2 / 2g)] for outer side and inner side of the pipe bend, for both the runs taken. Here, h is the piezometeric head at any pressure tap and h0 is the piezometeric head for the pressure tap upstream of the bend. Mark the variation by a smooth curve for both outer and inner side of the pipe bend. Also, plot on a log-log graph paper, Q v/s ∆ h and fit-in a straight line with a slope of ½. This is the calibration curve for the bend meter. OBSERVATIONS AND COMPUTATIONS SHEET

Date: ……...........

Diameter of pipe, D = ……………………………….. Area of pipe cross-section, A = ……………………. Radius of pipe bend, r = ……………………………. (A)

Calibration of Bend Meter Run No.

Discharge Measurement Q

Piezometer reading , h ou t

Unit

Average value of C = ......................................

Piezometer reading, hin

∆h = hout – h in

C=

Q A 2g ∆ h

Bend Meter

(B)

107

Pressure Distribution Run No.

(1)

(2)

Discharge, Q Velocity of flow, V = Q/A Piezometer reading at a section upstream of bend, h 0

Inner Side

Outer Side

Pressure Distance tap No. of the tap Piezometer reading, h

RESULTS AND COMMENTS

Run No. 1 h0 – h

Run No. 2

h0 − h V2 2g

Piezometer reading, h

h0 – h

h0 − h V2 2g

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Bend Meter

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Boundary Layer over a Flat Plate

27 OBJECT To study the boundary layer velocity profile, and to determine the exponent in the power law of velocity distribution, nominal boundary layer thickness, and displacement thickness. INTRODUCTION AND THEORY Because of viscous characteristics of a fluid flowing past a stationary body, the fluid has a tendency to adhere to the body. As a result, 'no slip' condition prevails and the fluid at the boundary has zero velocity and away from the boundary, the velocity increases gradually. Thus, there is a thin layer in the vicinity of the boundary within which the velocity has been affected because of the boundary and viscous effects. This thin layer is termed the boundary layer. Consider a fluid flow past a flat plate which is placed parallel to the flow as shown in Fig. 27.1. At the leading edge, x = 0, of the plate, the thickness of the boundary layer zone is zero. Thickness of this zone increases with increase in x. In the initial portion of the flat plate (i.e., small values of x), the flow within the boundary layer is laminar (i.e., the fluid moves in parallel layers) and, accordingly, the boundary layer is termed the laminar boundary layer. After some distance downstream of the leading

Figure 27.1 Boundary layer development

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111

edge, the flow within the boundary layer is, however, turbulent (i.e., the fluid does not move in parallel layers but moves in the way that the fluid particles have transverse motion as well) and, accordingly, the boundary layer is called the turbulent boundary layer. In the turbulent boundary layer zone, there still exists a very thin layer near the boundary in which the flow is laminar. This thin layer is called laminar sublayer. In between the laminar boundary layer zone and turbulent boundary layer zone, there exists a transition zone. Velocity distribution in the laminar boundary layer zone follows parabolic variation while in the turbulent boundary layer zone the velocity variation is logarithmic. The extent of viscous effects near a boundary is measured in terms of boundary layer thickness. Two commonly used thicknesses are the nominal thickness and displacement thickness of the boundary layer. The nominal thickness of a boundary layer, δ is defined as that value of y (see Fig. 27.2) at which the velocity of flow is 99% of the free stream velocity. In other words, at y = δ , u = 0.99 U0. Here, u represents the velocity of flow at a distance y from the boundary and U0 is the free stream velocity.

Figure 27.2 Boundry layer thickness

Displacement thickness, δ * is defined as the distance by which the boundary should be shifted so that the resulting volume of fluid flowing with uniform velocity distribution is the same as that of the actual flow. Obviously, from Fig. 27.2, δ* =

Area ABC U0

Here, area ABC represents the reduction in flow rate (per unit width of plate) due to the boundary effects.

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Velocity variation in a turbulent boundary layer is often expressed as : n u  y   U0 =  δ 

...(27.1)

in which n varies from 1/7 to 1/10. EXPERIMENTAL SET-UP It consists of a wind tunnel (open circuit type) having a test section of size 400 mm × 300 mm (approx.). A longer test section will result in large thickness of the boundary layer and is, therefore, desirable. A Prandtl tube fitted to a suitable manometer is provided at the downstream end of the test section for measuring the velocities at different points along a vertical. Alternatively, a total head tube fitted to a pointer gauge and a pressure point on the tunnel bottom (to measure static pressure) may be used. Instead of using lower wall of the wind tunnel as a flat plate, one may, alternatively, place a metallic plate in the wind tunnel and measure the velocity profile near the downstream end of the plate. PROCEDURE 1. 2. 3. 4.

Start the wind tunnel and let the Prandtl tube touch the bed of the plate. Take manometer readings h1 and h2. Raise the Prandtl tube by 1 to 2 mm and repeat step (2). Repeat step (3) till the centre of the tunnel is reached or when no change in manometer readings is observed for three different successive positions of the Prandtl tube.

FIGURES TO BE PREPARED AND FURTHER CALCULATIONS Plot y v/s u (with u on x-axis) on a simple graph paper. Fit-in a smooth curve to the plotted data points. This is the velocity profile. Determine U0 i.e., the free stream velocity. Find out the value of y at which u = 0.99 U0. This value of y is the boundary layer thickness δ . Thus, δ = ………………………. Estimate the area ABC, as marked in Fig. 27.2, on the plotted velocity profile. Then, δ* =

Area ABC = ……………………….. U0

Using the values of U0 and δ complete the last two columns of the observations and computations sheet for y ≤ δ . Now plot u/U0 v/s y/ δ (with y/δ on x-axis) on a log-log graph paper. Fit-in a straight line to these plotted points. The slope of the line is the exponent in Eq. (27.1). Thus, n = …………………………… OBSERVATIONS AND COMPUTATIONS

Date: …………….

Diameter of Prandtl tube, d = ……………………………………………………… Slope of the inclined manometer, sin θ = ………………………………………….. Mass density of the manometer liquid, ρm = ………………………………………. Mass density of air, ρair = …………………………………………………………….

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113

Conversion factor for converting manometer liquid head into equivalent air head, C′ =

 ρm     ρair 

= ……………………

Initial reading of the pointer gauge when Prandtl tube touches the tunnel bottom or the plate, Gi = ……………………… Sl. No.

Pointer gauge reading, Gf

y= Gf – Gi +d/2

Unit

RESULTS AND COMMENTS

Manometer Readings Limb 1, h1

Limb 2, h2

∆h = C´( h1 – h 2) × sin θ

u= 2g∆ h

u U0

y δ

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Drag Around a Cylinder

28 OBJECT To measure the pressure distribution around a cylinder placed in a wind stream and to calculate the coefficient of drag for the cylinder. INTRODUCTION AND THEORY When an object is placed in a fluid flow, the former experiences a force whose component in the direction of motion is known as the drag force. The drag (or drag force) on a body consists of one or all of the following three types of drag (or drag force): 1. Friction drag: It depends upon the viscosity of the fluid and the surface roughness of the body. 2. Deformation drag: It results due to deformation of the flow pattern (with respect to the basic flow pattern) due to presence of the body. Deformation drag consists of friction drag at the boundary and the pressure drag due to variation of pressure caused by deformation of the flow pattern. With the increase in the Reynolds number, the extent of deformation zone reduces and the resistance of motion is mainly due to viscous shear in the boundary layer. 3. Form drag: At high Reynolds number, if the flow condition and shape of the body result in separation (a phenomenon produced due to the combined effects of adverse pressure gradient and boundary layer formation, due to which a reverse flow is set near the boundary) a low pressure zone is created in the rear portion of the body. As a result of this pressure difference, between the front and the rear of the body, from drag is caused. Consider a body placed in a flow. The total drag force on the body, F is the sum of the pressure drag, F p and friction drag, F f . If p and τ 0 represent, respectively, pressure and shear stress acting on an elemental area dA of the body, shown in Fig. 28.1, then the total drag on the elemental area dA of the body can be written as, dF = dFp + dFf dF = p cos θ dA + τ 0 sin θ dA This may be integrated to yield the drag force F on the body, i.e, or

Drag Around a Cylinder

117

F=

∫ p cos θ dA + ∫ τ A

in which, the symbol

∫

0

sin θ dA

...(28.1)

A

represents integral over the surface of the body..

A

Figure 28.1 Flow around a body

If the body under consideration is a cylinder with a smooth surface and the Reynolds number is sufficiently high (R e > 100), then, as a further approximation, friction drag can also be neglected and then total drag force, F is equal to the pressure drag F p , i.e., F=

∫ p cos θ dA

...(28.2)

A

The coefficient of drag, CD is defined as, CD =

F ρV2 Ap 2

...(28.3)

where, A p is the projected area of the body on a plane normal to the direction of flow, ρ the mass density of the fluid, and V is the ambient (or free) stream velocity. EXPERIMENTAL SET-UP It mainly consists of a wind tunnel having a square (or rectangular) test section of size of about 300 mm and capable of producing a wind velocity equal to about 10 m/s. A brass cylinder of diameter of about 15 to 20 mm and length equal to the width of the test section is fixed in the test section such that the axis of the cylinder is normal to the direction of flow. An arrangement is made so that the cylinder can be rotated and the amount of rotation can be read on a protractor with the help of a pointer fixed at one end of the cylinder. A small hole is made on the surface of the cylinder somewhere at the centre. This hole acts as a pressure point and is connected to an inclined manometer with the help of an attachment made of copper. The wind speed is regulated by means of a rheostat. For measurement of the wind speed, a pressure point is provided near the upstream end of the test section of the tunnel. This enables measurement of the static pressure in the tunnel to be used as reference pressure.

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PROCEDURE 1. Adjust the wind speed with the rheostat. 2. Take the reading on the manometer for static pressure at the upstream end O of the tunnel. 3. Take the protractor reading and the corresponding manometer reading for static pressure, at some location of the cylinder along a circumference. 4. Rotate the cylinder by, say 20°, and repeat step (3) for obtaining pressure at another locations of the cylinder along a circumference. 5. Repeat step (4) in order to measure the pressure distribution around the cylinder. OBSERVATIONS AND COMPUTATIONS

Date: ………………

Diameter of cylinder, D = ………….. Temperature of air = ………………… Kinematic viscosity of air, ν = ………..… Free stream velocity, V = ………….. Inclination of manometers : θ 0 = ……………………………………∴ sin θ 0 = ………………………………… θ = …………………………..…………∴ sin θ = …………………………….……

Sl. No.

Manometer Reading

Protractor Reading Manometer

Manometer

∆p

( 12

∆p ρV 2 )

Drag Around a Cylinder

119

Referring to Fig. 28.2, the pressure point at section O enables measurement of the static pressure of the ambient stream and the pressure point C on the cylinder enables measurement of the pressure on the surface of the cylinder. Since both pressures are measured using an inclined U-tube manometer having one end of the U-tube open to the atmosphere, the difference of the two readings (provided that both manometers are at the same elevation) should enable one to compute

∆p ( p − po ) i.e., where ρg ρg

ρ is the mass density of air. Alternatively, both pressure points can be connected to the same manometer and

( p − po ) can be determined. Again, referring to Fig. 28.2 and applying Bernoulli's equation at ρg

section A and O (for estimation of the velocity V of flow in the tunnel). 2

2

p a Va p V + = 0+ ρg 2 g ρg 2 g

...(28.4)

Figure 28.2 Set-up for drag on a cylinder

where, suffix a refers to the atmospheric conditions. The atmospheric air can be considered to be almost still and, hence, V a can be approximated as zero. Therefore, from Eq. (28.4),  pa po  V2 =  ρ − ρ  2  

...(28.5)

po can be measured by a suitable manometer and, hence, the velocity of flow in the tunnel V can be determined from Eq. (28.5). ∆ p If the values of ( 1 ρ V 2 ) (here, ∆ p is (p - po) and p is the pressure at a given point on the 2 surface of the cylinder) as obtained by measurements are plotted along the circumference of the section of the cylinder, the resulting plot will appear similar to the one shown in Fig. 28.3. In order to ∆ p find the value of CD from the distribution of ( 1 ρ V 2 ) one needs to integrate the distribution profile. 2

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Laboratory Work in Hydraulic Engineering

The method of integration is as follows: Consider any point P 1 on the surface of the cylinder as shown in Fig. 28.3. The magnitude of ∆ p 1 ( 2 ρ V 2 ) at this point is equal to the magnitude represented by radial distance P 1R 1. This ordinate is redrawn as p1' r1' on the diameter a'c' as shown in Fig. 28.4. Proper care should be taken with regard to the sign. In this way, the curve a' e1' a1' b1' c1' d1' c' is traversed for the left half of cylinder. The same is repeated for the right half of the cylinder and a curve such as a ′′ e′′ b′′ c ′′ is obtained on the diameter a′′ c′′ , Fig. 28.5. The algebraic sum of these two areas ( a' e1' a1' b1' c1' d1' c' and a ′′ e′′b′′ c ′′ ) divided by the diameter D of the cylinder yields the value of CD as shown below:

Figure 28.3 Variation of ∆ p/(ρ V 2/2) along the surface of cylinder

Drag Around a Cylinder

121

Figure 28.4 Variation of ∆p/(½ρV2) along the diameter (upstream side)

Figure 28.5 Variation of ∆p/(½ρV2) along the diameter (downstream side)

Considering unit length of cylinder, 1 CD = D

∫

ABP1 C

1 = D

∫

ABP1 C

∆p 1 ρV 2 2

∆p 1 ρV 2 2

1  = D   ABP1 C

∫

=

cos θds

(ds cos θ ) +

∆p dy + 1 ρV 2 2 AP C

[

s1 = area a'1b1' c1' s2 = area a'1e1' a'1 s3 = area c'd1' c1'

and

2

∫

AP2C

∆p 1 ρV 2 2

s4 = area a ′′ e′′ b′′ c ′′

(ds cos θ)

 ∆p  dy 1 ρV 2  2 

1 Area a' e1' a1' b1' c1' d1' c' + Area a′′ e′′ b′′ c ′ D

C D = 1 [s1 − s 2 − s 3 + s 4 ] D where,

∫

1 D

] ...(28.6)

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FIGURE TO BE PREPARED AND FURTHER COMPUTATIONS ∆ p ∆ p Plot the distribution of ( 1 ρ V 2 ) as shown in Fig. 28.3. Integrate the plotted distribution of ( 1 ρ V 2 ) 2 2 as explained earlier and thus get the value of CD using Eq. (28.6). Compare this value of CD with the standard value of CD at the corresponding Reynolds number =

VD (Fig. 28.6). ν

Figure 28.6 Variation of CD with Re for a cylinder

RESULTS AND COMMENTS

Drag Around a Cylinder

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Uniform Flow in a Channel

29 OBJECT To determine the Manning's coefficient of roughness n for a given flume. INTRODUCTION AND THEORY An open channel flow is said to be uniform if the flow characteristics do not change from section to section at any instant of time. This means that the depth everywhere in the reach of a prismatic channel under consideration is the same at any instant of time. One primary condition for the uniform flow to exist is that the driving force (due to gravity) is equal to the resisting force (due to friction) in the channel. For uniform flow in an open channel, the discharge, Q (m3/s) is given as, 2 1 1 Q= AR3S2 ...(29.1) n where, n is the Manning's coefficient of roughness and is dimensionless, R (=A/P) the hydraulic radius (m), A the area of flow cross-section, P the wetted perimeter, and S is the slope of the channel bed. Equation (29.1) is known as the Manning's equation in which 1 is a dimensional constant. EXPERIMENTAL SET-UP It consists of a glass-walled rectangular flume about 10 m long, 0.6 m wide and 0.8 m deep having honeycomb walls at the entrance, tail gate at the outlet end, and top rails for the movement of a pointer gauge. The bed of the flume is made rough. Discharge is regulated by means of a supply valve fitted at the outlet end of the supply pipe. Pointer gauge and a scale are additional equipment needed. PROCEDURE 1. Select three different sections in the central part of the flume. These sections may be about 1 to 2 m apart. Take the pointer gauge readings for the bed levels at these sections. 2. Open the supply valve. Adjust the discharge and the tail gate so as to get a suitable depth of flow in the flume. 3. Wait until the flow becomes uniform at which condition the depth of flow at the sections chosen in step (1) must be approximately the same. Take the pointer gauge readings for the water surface elevations at these sections.

Uniform Flow in a Channel

125

4. Measure the discharge. 5. Repeat steps (2) to (4) for other values of discharges. Take about 3 to 5 sets of observations. OBSERVATIONS AND COMPUTATIONS

Date: …………….

Width of flume, B = ………………… Slope of flume, S = ……………… Initial pointer gauge reading for the bed level at (i) section 1, y1i = ……………… (ii) section 2, y2i = ……………… (iii) section 3, y3i = ……………… Run No.

1

Discharge Measurement Q Pointer gauge reading for the water surface elevation at (i) Section 1, y1f (ii) Section 2, y2f (iii) Section 3, y3f Depth of flow at section 1, y1 = y1f – y1i Depth of flow at section 2, y2 = y2f – y2i Depth of flow at section 3, y3 = y3f – y3i Mean depth of flow, h = (1/3) (y1 + y2 + y3 ) A = Bh P = B + 2h R = A/P Manning’s n (Eq. 29.1)

RESULTS AND COMMENTS Average value of n

2

3

4

5

C h a p t e r

Velocity Distribution in a Channel

30 OBJECT To study the velocity distribution in an open channel and to estimate the energy and momentum correction factors. INTRODUCTION AND THEORY Velocity distribution along the depth of flow in a channel is nonuniform due to the boundary layer formation. This nonuniformity of the velocity affects the computations of energy and momentum terms based on the uniform velocity distribution. To account for the nonuniform distribution of velocity, V2 , computed on the basis of the mean velocity V, is multiplied by a correction factor, α 2g i.e., the energy correction factor to obtain the true kinetic energy head corresponding to the actual velocity profile. Similarly, the momentum term, ρQV computed on the basis of the mean velocity V is multiplied by another correction factor, β i.e., the momentum correction factor to obtain the true momentum rate corresponding to the actual velocity profile. Both α and β are always greater than unity for nonuniform velocity distribution. If v indicates the velocity at a distance y from the bed, V the mean velocity and A is the area of flow cross-section, then, it can be shown that, the head,

∫ α=

v 3 dA

A

and

β =

...(30.1)

V 3A

∫

A

v 2 dA ...(30.2)

V 2A

∫

where, dA is an elemental area of the flow cross-section A and A indicates the integration over the entire area of the flow cross-section A. Considering unit width of the channel and writing down the differential terms in terms of finite difference quantities, Eqs. (30.1) and (30.2) can, alternatively, be written as, α =

∑v

3

∆y

V 3h

...(30.3)

Velocity Distribution in a Channel

127

α =

and

∑v

2

∆y

...(30.4)

2

V h

Therefore, if plots of v 3 v/s y and v 2 v/s y are made, then the areas of these plots will, respectively, yield Σv 3 ∆ y and Σv 2 ∆ y. Here, h is the depth of flow. The mean velocity,, V is expressed as, V=

∑

v∆y

...(30.5)

h

where Σ v ∆y is the area of the plot v v/s y i.e., the velocity profile. EXPERIMENTAL SET-UP It consists of a glass-walled rectangular flume about 10 m long, 0.8 m wide, and 0.6 m deep, having top rails for the movement of instruments, honeycomb walls at the entrance, and a tail gate at the outlet end. A sluice valve is provided at the outlet end of the supply pipe. A Pitot-static tube connected to two inclined piezometers is used for the purpose of velocity measurement. A scale and a stop watch (in case, current meter is used) are also needed. PROCEDURE 1. Open the sluice valve and let the flow attain steady and uniform flow conditions. Tail gate may be used for adjusting the depth of flow. 2. Select a suitable section, centrally located in the flume. 3. Measure the depth of flow, h at this section. 4. Take Pitot-static measurements at the mid-width and quarter-widths of this section so as to obtain three velocity profiles at the chosen section. FIGURES TO BE PREPARED AND FURTHER COMPUTATIONS Plot all the three velocity profiles. Calculate the velocities V 1, V 2 and V 3 using Eq. (30.5). Thus, V 1 = ………………………………… V 2 = ………………………………… V 3 = ………………………………… ∴ Mean value of velocity, V = (1/3) (V 1 + V2 + V3) = ………………………….. Hence, discharge, as obtained from velocity profiles, Q = VBh = ………….. Measured value of discharge, Qm = ……………………………………………. Similarly, plot v 3 v/s y and v 2 v/s y on a graph paper for all the three profiles and compute α1 , α 2 , α 3 , β1 , β2 , and β3 using Eqs. (30.3) and (30.4). α1 = …………………………

β1 = ……………………………..

α 2 = …………………………

β2 = ……………………………..

α 3 = …………………………

β3 = ……………………………..

∴ α = (1/3) ( α1 + α 2 + α 3 ) = ……………

β = (1/3) ( α1 + α 2 + α 3 ) = ………………

Velocity Distribution in a Channel

RESULTS AND COMMENTS

129

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Velocity Distribution in a Channel

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Vertical Contraction in a Channel

31 OBJECT To study the flow over a hump placed in an open channel. INTRODUCTION AND THEORY Let a hump of small height ∆ z be placed on the bed of a rectangular channel carrying a discharge Q under uniform flow conditions as shown in Fig. 31.1. As a result of this, flow conditions in the vicinity of the hump are no more uniform. The specific energies E 1 and E 2 at sections 1 and 2 are related as follows: E 2 = E 1 − ∆z ...(31.1) where,

V12 Q2 h + = h + E1 = 1 2 g 1 2 g Bh12

Figure 31.1 Flow over a hump in a channel

...(31.2)

Vertical Contraction in a Channel

133

V22 Q2 E 2 = h2 + 2g = h2 + 2 g Bh22

and

...(31.3)

in which, B is the width of channel. Here, the energy loss between sections 1 and 2 have been considered negligible. By increasing the value of ∆ z suitably, the flow conditions, for a given discharge, Q, over the hump can be made critical i.e., Froude number,

V2 gh2

is unity. Let this height be ( ∆ z )c . If ∆ z exceeds

( ∆ z )c , the flow conditions upstream will be modified and the flow conditions over the hump will be that of critical state. New conditions of flow on the upstream of the hump will be given as, E1′ = E c + ∆ z

...(31.4)

where, E1′ is the new value of E 1. If ∆ z < ( ∆ z )c , the upstream conditions remain unaffected and Eq. (31.1) holds good, If ∆ z = ( ∆ z )c, the upstream conditions remain unchanged but the flow over the hump is in the critical state. Then, E 2 = E c = E1 - ( ∆ z )c ...(31.5) EXPERIMENTAL SET-UP It consists of a glass-walled horizontal rectangular flume about 4 m long, 0.2 m wide, and 0.40 m deep having a honeycomb wall at the inlet end, tail gate at the outlet end, and top rails for the movement of a pointer gauge. Two suitably curved wooden humps of about 25 mm and 50 mm radius with their flat surface on the flume bed are used as humps. Pointer gauge and a scale are additional equipment needed. PROCEDURE 1. Establish uniform flow with depth of flow about 150 mm in the flume by adjusting discharge and the tail gate position. 2. Measure the depth of flow in the absence of any hump at few locations from slightly upstream of the hump location to the downstream of the hump location along the centre line of the flume. 3. Place hump no. 1 on the bed transverse to the flow leaving no gap between the flume boundary and the hump. 4. Take pointer gauge readings for water surface and bed elevations at different stations upstream and downstream of the hump along the centre line of the flume. 5. Measure the discharge. 6. Replace hump no. 1 by hump no. 2 and repeat steps (4) and (5).

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OBSERVATIONS AND COMPUTATIONS Discharge, Q = …………………………….; width of flume, B = ……………………. Location, x h V=

Q Bh

E=h+

V2 2g

Hump No. 1 Location, x

Depth, h

Sp. Energy E

Hump No. 2 Depth, h

Sp. Energy E

FIGURE TO BE PREPARED AND FURTHER COMPUTATIONS Plot on a graph paper the following: (1) The longitudinal water surface profile showing the hump on the bed.  Q2  (2) The specific energy curve E v/s h for the discharge, Q using E = h +  2   (2 g A )  (3) The experimental observations on E v/s h curve. RESULTS AND COMMENTS

Vertical Contraction in a Channel

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Horizontal Contraction in a Channel

32 OBJECT To study the flow through a horizontal contraction in a rectangular channel. INTRODUCTION AND THEORY For a steady flow in a horizontal channel, the specific energy E through a horizontal contraction can be treated as constant if the energy loss is negligible. The specific energy E is related with the discharge per unit width q and the depth of flow h as follows:

or

 q2   E = h +  2   2gh 

...(32.1)

q = h 2g( E − h)

...(32.2)

The curve q v/s h for a specified specific energy is as shown in Fig. 32.1. The depth of flow at which q is maximum is the critical depth hc.

Figure 32.1 Variation of q with h for given E

Horizontal Contraction in a Channel

137

Figure 32.2 Horizontal contraction in a channel

EXPERIMENTAL SET-UP The set-up, Fig. 32.2, consists of a horizontal rectangular flume about 4 m long, 0.2 m wide, and 0.4 m deep incorporating a contraction in the central portion such that the cross-section remains rectangular at all stations. The flume should have some wave dampeners at the inlet end, tail gate at the outlet end, and arrangement for the movement of depth-measuring gauge. PROCEDURE 1. Record the channel width at different stations/locations. 2. Adjust the supply suitably and let the flow stabilize. 3. Measure that flow rate Q and the depths at different stations. FIGURE TO BE PREPARED 1. Plot the water surface and specific energy profiles along the contraction. 2. Prepare q v/s h curve using Eq. (32.2) for average value of the observed specific energy (E =………………..) 3. Mark the experimental values on q v/s h curve. OBSERVATIONS AND COMPUTATIONS Observed specific energy = .................................. Depth of Flow, h Discharge per unit width q, Eq. (32.2)

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Discharge, Q = ............................................ Station No.

Distance downstream of station 1

RESULTS AND COMMENTS

Channel width, B

Depth of flow, h

Discharge per unit width, q

Specific energy, E

Horizontal Contraction in a Channel

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Broad-Crested Weir

33 OBJECT To calibrate a broad-crested weir and study the pressure distribution at the upstream end of the weir. INTRODUCTION AND THEORY A control section in an open channel is that section at which there exists a definite relationship between the depth of flow and the corresponding discharge. At the critical state of flow, relationship between the depth of flow and the discharge is expressed as, Q 2T =1 ...(33.1) gA3 where, Q represents the discharge, T the top width, and A is the area of flow cross-section. For a given channel shape, A and T are dependent on depth of flow, h only and, hence, at critical state of flow, Q is a function of h alone. Equation (33.1) indicates that at the critical state of flow, the Q v/s h relationship is theoretically independent of the channel roughness, slope and other uncontrolled conditions. Therefore, a critical flow section can be termed as a control section which enables one to predict the discharge by making one simple measurement of the depth of flow, h. A control section in a channel can be created in various ways. One way to obtain a control section is by putting an obstruction of adequate height across the entire channel width, having sufficient length along the flow direction. Such a control section is termed as broad-crested weir which is widely used for measuring the flow rates in a channel. The pattern of flow over a broad-crested weir has been shown in Fig. 33.1. It should be noted that the curvilinear flow at the entrance and the outfall of the weir prevents the critical depth from occurring at any one section for all flow rates. Therefore, in practice, the flow rate is related to the upstream head, H and using this relation, the flow rate can be predicted by measuring the head, H. Using the energy equation and introducing a coefficient, C, one can express the relation between the upstream head, H and the flow rate, Q as, Q = CB g H

3

2

...(33.2)

where, B is the width of the weir, and equals the width of canal for suppressed weirs. It should be noted that on account of curved streamlines the pressure at the upstream of the weir is non-hydrostatic.

Broad-Crested Weir

141

Figure 33.1 Broad-crested weir

EXPERIMENTAL SET-UP It consists of a rectangular channel whose bed and walls are plastered with cement. The channel is about 5 m long, 0.5 m wide, and about 0.6 m deep. A honeycomb wall at the inlet end and top rails for the movement of the pointer gauge are also provided. A broad-crested weir having length about 0.4 m and height about 0.15 m is constructed sufficiently upstream of the outlet end of the channel. Its surface is also plastered with cement. The upstream and the downstream corners are rounded. If the supply to the channel is through a main feeder channel, a gate is used for controlling the discharge in the channel. If the supply is made through a supply pipe, a sluice valve is provided at the outlet end of the supply pipe. Pointer gauge and a scale are also needed. Few pressure taps are provided in the upstream wall of the weir along the centerline of the weir. These taps are connected to a multi-tube manometer. PROCEDURE 1. Locate a section in the channel upstream of the weir where the water surface will have almost no curvature even at the maximum discharge. This can be done by opening the sluice gate fully and observing the water surface. 2. Adjust the position of the sluice gate and when the flow becomes steady, take the pointer gauge reading for the water surface elevation at the section fixed in step (1) above. 3. Measure the discharge. 4. Repeat steps (2) and (3) for other different positions of the sluice gate i.e., other discharges. 5. Also take pressure measurement for some of the above runs so as to be able to sketch the pressure distribution along the upstream wall of the weir. The water surface profiles may also be measured for these runs. OBSERVATIONS AND COMPUTATIONS

Date: ………...............

Width of the broad-crested weir, B = …………………………………… Length of the broad-crested weir, L = …………………………………… Height of the broad-crested weir, Wb = ………………………………… Pointer gauge reading for the crest level of the broad-crested weir, hbi = …………

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Run No. Discharge Measurement

Broad-crested weir Q

h bf

H

Unit

hbf = Pointer gauge reading for the head over broad-crested weir. H = Head over the B.C. weir = hbf – hbi Depth of flow at the upstream face of weir: Run 1: …………… Run 2 : …………..

Sl. No.

Height of the pressure point from channel bed, y

Run – 1 Hydrostatic pressure head

Observed pressure head

Run – 1 Hydrostatic pressure head

Observed pressure head

Broad-Crested Weir

143

FIGURES TO BE PREPARED Plot H v/s Q (with H on x-axis) on a log-log graph paper. Fit-in a straight line with a slope of 1.5 to the data points. Estimate the value of C in Eq. (33.2). Also plot the observed pressure variations along the upstream wall of the weir and compare these with the corresponding hydrostatic variations. RESULTS AND COMMENTS

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Hydraulic Jump

34 OBJECT To study the characteristics of a hydraulic jump. INTRODUCTION AND THEORY When supercritical flow meets subcritical flow there forms what is known as hydraulic jump which is accompanied by violent turbulence, eddy formation, air entrainment, and surface undulations. Hydraulic jump is a very useful means to dissipate the excess energy of flowing water which, otherwise, would cause damages downstream. Consider the flow situation, shown in Fig. 34.1, in which section 1 is in supercritical zone and section 2 is in sub-critical zone. Assuming the channel bed to be horizontal, friction forces to be negligible, and flow to be two-dimensional, one can write, using the momentum equation, P 1 – P 2 = ρ q (V 2 – V1) ....(34.1) where, q = Q/B, in which B is the width of channel and P represents the hydrostatic force per unit width of the channel. Substituting the values of P 1 and P 2 for a rectangular channel, in Eq. (34.1), one gets, ρ g h12 ρ g h22 − = ρ q (V 2 −V1 ) 2 2

Figure 34.1 Hydraulic jump

...(34.2)

Hydraulic Jump

147

where, ρ is the mass density of water. From the continuity equation, q = V2 h2 = V1 h1. ...(34.3) Combining Eqs. (34.2) and (34.3) and then , solving for h2 /h1 one obtains the following Belangar’s equation : h2 = h1 in which, Fr 1 =

V1

1 2

 −1 + 1 + 8 Fr 21   

...(34.4)

and is termed as Froude number of the incoming flow at section 1. The depths

g h1

h2 and h1, as related by Eq. (34.4), are known as conjugate or sequent depths. A jump forms in a rectangular channal when Eq. (34.4) is satisfied. Because of eddies and flow decelerations that accompany the jump, considerable head loss occurs. This head loss, hL may be calculated by using the energy equation. Thus,



hL = E1 − E2 =  h1 +



V12   V22  −  h2 +  2g   2g 

...(34.5)

From Eqs. (34.2), (34.3), and (34.5), it can be shown that, (h2 − h1 ) 3 hL = 4 h1 h2

...(34.6)

Height of jump, hj is defined as the difference between the depths of flow after and before the jump, i.e., hj = h2 – h1 ...(34.7) The variations of hj /E 1 and hL /E 1 with F r1 has been shown in Fig. 34.2. Here, E 1 is the specific energy at Section 1. EXPERIMENTAL SET-UP It consists of a glass-walled rectangular flume about 5 m long, 0.40 m wide, and 0.8 m deep having a sluice gate at the inlet end, a tail gate at the downstream end, and top rails for the movement of pointer gauge. A sluice valve is provided near the outlet end of the supply pipe. Scale is also required. PROCEDURE 1. Adjust the supply valve, sluice gate, and the tail gate, so that there forms a stable hydraulic jump in the flume. 2. Take the pointer gauge readings for the bed levels and water surface elevations at pre-jump section (1) and post-jump section (2). 3. Measure the discharge. 4. Repeat steps (1) to (3) for other positions of valve, sluice gate, and tail gate. FIGURES TO BE PREPARED 1. Plot h2 /h1 v/s F r1 on a simple graph paper. On the same plot also draw the line represented by Eq. (34.4). Note the scatter of the observed data points.

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Figure 34.2 Variation of hydraulic jump parameters

2. On Fig. 34.2, mark the data points of hL /E1 and hj/E1 for various values of F r1. Note the scatter of the experimental data points from the standard curves. RESULTS AND COMMENTS

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Free Overfall

35 OBJECT To study the characteristics of flow over a free overfall in a channel and also to determine the end depth. INTRODUCTION AND THEORY When the bottom of a channel is discontinued, as shown in Fig. 35.1, the specific energy concepts indicate that the section of minimum energy should be the critical flow section and, hence, the depth of flow at the end of the channel (section of minimum energy) must be equal to the critical depth. In practice, however, this is not true. Rouse has found that for rectangular channels, the critical depth, hc obtained on the basis of parallel flow assumption, occurs a short distance (3 to 4 hc) upstream from the channel end and the end depth he (also known as brink depth and is the “true” critical depth) is about 71.5 percent of the critical depth hc. This departure from theoretical prediction is on account of the fact that the specific energy derivations are based on the assumption of parallel flow and are only approximately applicable to situations, such as in the vicinity of a fall, where the streamlines are curvilinear, as a result of which the pressure distribution is non-hydrostatic.

Figure 35.1 Flow over a fall

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EXPERIMENTAL SET-UP It consists of a glass-walled rectangular flume about 3 m long, 20 mm wide, and 30 mm deep having a honeycomb wall at the entrance and top rails for the movement of the pointer gauge. A sluice valve is provided near the outlet end of the supply pipe. Pointer gauge and a scale are also required. PROCEDURE 1. Take pointer gauge readings for the flume bed elevation along the centre line of the flume starting from the fall (i.e., end of the channel) to well upstream where the flow will become almost uniform even for the highest value of available discharge. 2. Open the sluice valve and let the flow become steady. 3. Take pointer gauge readings for the flume bed elevation along the centre line of the flume starting from the brink to sufficiently upstream where the flow is almost parallel. Also measure the discharge. 4. Repeat steps (2) and (3) for other different openings of the sluice valve. Note: - Sections for taking the pointer gauge readings in steps (1) and (3) above should, preferably, be the same.

FIGURE TO BE PREPARED AND FURTHER COMPUTATIONS 1/3

 q2  Plot h/hc v/s x/hc on a simple graph paper for all three runs. Here, hc =   . These data points must  g  result in a single smooth curve. From this plot find the value of h/hc at the fall or channel end where x/hc = 0. This gives ratio of he to hc. Also determine the value of x/hc where h/hc = 1. This gives the value of x in terms of hc at which distance upstream of the fall will occur the critical section. at

x h hb = = ................................... = 0, hc hc hc

at

h x = ................................... = 1, hc hc

Alternatively, a plot can be prepared between (h – he) / (hc – he) versus x/x1. Here x1 is the length scale which is the value of x (from the brink point) at which (h – he) is equal to 0.75 (hc – he). RESULTS AND COMMENTS

hi

hf

h = h f–h i

(1)

h/h c

h f = Pointer gauge water surface elevation

h = Depth of flow

h i = Pointer gauge reading for elevation of flume bed

x =Distance upstream of fall

x

h c = (q 2 /g)1/3

q = Q/B

Discharge Q

Run No.

Width of flume, B = ........................................

OBSERVATIONS AND COMPUTATIONS

x/hc

hf

h = h f–h i

(2)

h/h c

x/hc

hf

Date:................

h = h f–h i

(3)

h/h c

x/hc

Free Overfall 153

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Horizontal Expansion in a Channel

36 OBJECT To study the velocity distribution downstream of an expansion (with and without splitter plates) in a channel. INTRODUCTION AND THEORY Open channel transitions (i.e., a contraction or an expansion) have to be provided in the vicinity of hydraulic structures. Open channel expansions cause the flow to separate from the side walls giving rise to excessive turbulence and asymmetry of flow. The velocity distribution downstream of an expansion is often irregular and erratic and affects adversely the erosion characteristics of an unlined channel in the vicinity (downstream) of the expansion. In order to improve the velocity distribution downstream of an expansion, either the channel section is expanded gradually or some auxiliary devices such as splitter plates are used. These splitter plates are placed vertically along the flow in the expansion so as to divide the channel section into number of compartments. Fig. 36.1.

Figure 36.1 Channel expansion with splitter plates

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EXPERIMENTAL SET-UP A rectangular channel section of about 30 cm width is expanded to a width of about 50 cm through a straight transition of central angle of about 25o. An assembly of 3 or 5 mild steel plates acts as a set of splitter plates. Arrangements for supply of water and its measurement and tail gate to control the depth in the channel are made. Velocity measurements are carried out by using a Pitot-static tube or a miniature current meter. PROCEDURE After letting a suitable discharge flow in the channel with a suitable depth, measure the local velocity at different fixed points along the width at 2 or 3 different elevations at a section slightly downstream of the expansion. Now fix the splitter plates assembly and again measure the local velocities at all the previous points at the same section and elevations. The discharge flowing in the channel should also be measured. The two sets of velocity distribution (i.e., with and without splitter plates) are taken with the same discharge and depth of flow. FIGURE TO BE PREPARED Plot the velocity distributions along the channel width and compare these for the two cases (with and without splitter plates) and comment on the observed improvement in the velocity distribution due to the presence of the splitter plates. RESULTS AND COMMENTS

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Reservoir Flood Routing

37 OBJECT To study the effect of reservoir on an inflow hydrograph. INTRODUCTION AND THEORY There are many ways of routing a flood through a reservoir. The basic equation for this purpose is Inflow = storage + outflow ...(37.1) for any interval of time. A plot of discharge, Q versus time t is known as hydrograph. Figure 37.1 shows an inflow and an outflow hydrograph for a reservoir. The shaded area between these two curves for any interval of time (t2 - t1) indicates the change in storage of the reservoir during the interval (t2 – t1).

Figure 37.1 Inflow and outflow hydrographs for a reservoir

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EXPERIMENTAL SET-UP The set-up consists of a tank of suitable size with arrangements for inflow and outflow. Inflow to the tank (i.e., reservoir) is through a supply pipe and the discharge in this pipe can be varied with time and measured with the help of an orifice meter or venturi meter. Outflow from the tank is measured by means of an orifice suitably located in the tank wall. An average value of the coefficient of discharge (or the calibration curve, Q versus h) for the orifice is determined. Suitable instrument (say, automatic water level recorder) for the measurement of water levels in the tank should be made available. Likewise, the measurement of inflow should also be recorded continuously with time. PROCEDURE Adjust a suitable inflow and outflow and start making measurement of inflow and water level in the tank alongwith time while the inflow is being varied. The inflow is first continuously increased and after attaining a peak value, it is decreased in the same way. From water level measurements, outflow from the tank can be computed at different instants of time. Also, the storage in the tank can be estimated. If the facilities for continuous measurements are not available then the inflow can be changed at a convenient interval (say, 1 to 2 minutes) and the measurements for inflow and water level can be made at the middle of each interval. The hydrographs can, then, be prepared in the form of a bar diagram. Suitable curves can be sketched for the bar diagram for computation purposes. OBSERVATIONS AND COMPUTATIONS Inflow Sl. No.

Time since beginning

Meter reading

Discharge Q 3 m /s

Water depth in the tank

Outflow 3 m /s

Storage in the tank since beginning

Reservoir Flood Routing

161

FIGURE TO BE PREPARED Plot inflow and outflow hydrographs and compute total inflow and outflow at 3 to 4 different times since the beginning (t=0). Obtain areas under the inflow and outflow hydrographs upto these times and check whether the basic equations, Eq. (37.1) is satisfied or not. RESULTS AND COMMENTS

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Submerged Hydraulic Jump

38 OBJECT To study the effect of submergence on the discharge through a sluice gate. INTRODUCTION AND THEORY The discharge (per unit width) q through a sluice gate is given as q = C d a 2gH 1

...(38.1)

where, a is the sluice gate opening, H1 the head upstream of the sluice gate, and Cd is the coefficient of discharge that can be functionally expressed as,  H1 H2 C d = f1  a , C c , H  1

  

in which, H2 (> a) is the depth of flow downstream of the sluice gate and Cc is the coefficient of contraction. However, for free flow conditions,  H1  , Cc  Cd = f 2  a   Assuming that the coefficient of contraction Cc is not affected by the submergence, the ratio of Cds (coefficient of discharge under submerged conditions) and Cdf (coefficient of discharge under free flow condition) depends only on H2 /H1 (i.e., submergence ratio) for a given value of H1 /a i.e., C ds H f 2 C df =  H 1

  

This also means that C ds H2  qs = C = f  H  qf df  1

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Figure 38.1 shows the variation of Cd for a sluice gate under submerged and free flow conditions. From this figure, a curve between Cds /Cdf (or qs/qf) and H2 /H1 can be sketched for a specified value of H1/a. Obtain Cdf for given H1/a and Cds for given H1/a and H2 /H1. Therefore, Cds /Cdf versus H2/H1 for given H1/a can be prepared.

Figure 38.1 Variation of Cd with H1/a for sluice gates

EXPERIMENTAL SET-UP The set-up (Fig. 38.2) consists of a rectangular flume or channel about 0.3 m wide, 0.8 m deep, and 5.0 m long having a sluice gate near the entrance section and a tail gate at the exit section. Arrangements for controlling and measuring the discharge are provided.

Figure 38.2 The experimental setup (free flow condition)

PROCEDURE 1. Adjust the sluice gate opening, a and the head H1. Establish free flow condition and measure Qf (=qf B). Here, B is the width of the channel. 2. Increase the depth H2 by means of the tail gate to submerge the hydraulic jump.

Submerged Hydraulic Jump

165

3. By reducing the supply restore the head H1. 4. Measure the discharge, Qs (=qsB). 5. Repeat steps (2) to (4) for other positions of the tail gate. OBSERVATIONS AND COMPUTATIONS

Date:………

Initial reading of the pointer gauge (for H2) H2i = ……………………………………. Sluice gate opening, a = ………………………………………………………………. Head, H1 = ……………………………………………………………………………….. Discharge under free flow condition, Qf = ……………………………………………. Run No.

Submerged Flow

Qs

H2f

H2

H2/H1

Qs /Qf

H2f is the final gauge reading for H2. And H2 = H2f – H2i FIGURE TO BE PREPARED Sketch the curve Cds/Cdf v/s H2/H1 (for the chosen value of H1/a) as obtained from Fig. 38.1. Plot Qs Qf

 q s C ds = =  q f C df 

   v/s H2 /H1 on this figure for the observed data. 

RESULTS AND COMMENTS

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Forced Hydraulic Jump

39 OBJECT To study the effect of friction blocks on formation of hydraulic jump and its energy loss. INTRODUCTION AND THEORY Excessive kinetic energy of flow downstream of hydraulic structures, such as spillways, canal falls etc., will result in considerable damage on the downstream side. The dissipation of this excess kinetic energy can be achieved with the help of a hydraulic jump (Chapter -34). In order to stabilize the hydraulic jump and achieve effective energy dissipation, a stilling basin with or without appurtenances such as friction blocks is constructed at the toe of the hydraulic structure. If the bed downstream of the stilling basin consists of erosive material then the magnitude of scour can be taken as a measure of the effectiveness of the stilling basin.

Figure 39.1 Stilling basins

The relationship between pre-jump depth h1 and post-jump depth h2 for a hydraulic jump in a horizontal rectangular channel without appurtenances is expressed as (Eq. (34.4)), h2 = h1

1 2

 1 + 8 F 2 − 1 r1  

...(39.1)

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Here, F r1 is the Froude number for pre-jump flow. The value of the post-jump depth in case of a hydraulic jump formed with appurtenances structures is less than the value of h2 given by Eq. (39.1) for the same pre-jump conditions. EXPERIMENTAL SET-UP The set-up consists of a channel which is divided symmetrically into two channels each of which is about 0.3 m wide, 0.8m deep, and 5 m long. For both these channels, one sluice gate is provided in the upstream region. In one of the channels, friction blocks are put in the stilling basin downstream of the sluice gate. The stilling basin of the other channel is not provided with any appurtenances. In both channels, the erosive bed is provided downstream of the stilling basin. Tail gate provided at the downstream end of the erosive bed in both channels enables one to control the tail water depth. The discharge in the main channel is controlled and measured, respectively, by a valve and a bend meter fitted in the supply line. PROCEDURE 1. Open the supply valve and when the flow is stabilized, measure the discharge. 2. Adjust the tail water depths in two channels so that the hydraulic jump forms near the sluice gate. 3. Measure pre-jump and post-jump depths h1 and h2 in both channels. 4. Also measure the maximum scour depth Ds in both channels after, say, 10 minutes. 5. Repeat steps (1) to (4) for other different values of discharge. FIGURES TO BE PREPARED  1. Prepare Fr 1  = V1  gh1 

  v/s h2/h1 diagram using Eq. (39.1) and plot on it the measured values  

using different symbols for the hydraulic jumps with and withou t friction blocks (Here, V 1 = Q/Bh1). 2. Prepare F r1 v/s HL /E 1 diagram for hydraulic jumps with and without friction blocks. Here,  V12   h + H L = (E 1 − E 2 ) =  1 2 g  −   3. Prepare Q v/s Ds diagram RESULTS AND COMMENTS

2    h2 + V 2   2 g  

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Vertical Fall

40 OBJECT To calibrate a vertical fall and to study the effect of cistern length on the energy dissipation. INTRODUCTION AND THEORY The ground slope is generally higher than the designed bed slope of a channel. Therefore, a fall has to be provided. A vertical fall is the simplest of all the falls. Once calibrated, a fall can also be used to measure the discharge. For vertical falls one can write, Q=

3 2 Cd B 2 g H 2 3

...(40.1)

Here, Cd is the coefficient of discharge, B the width of fall, and H is the head over the fall. Thus, if Cd is known, one can predict Q by measuring H alone. Alternatively, a calibration graph plotted between H and Q should enable one to determine the flow rate. Proper dissipation of excess kinetic energy, which is the consequence of providing the fall, forms one of the main objectives of the designer of a fall. Scour depth, Ds , downstream of the fall can be taken as the measure of energy dissipation. Lesser scour depth means larger energy dissipation and vice versa. The scour depth, Ds depends mainly on the discharge Q, length of cistern (that portion of the structure in which the surplus energy of water leaving the crest is destroyed) Lc , size of the bed material d, and the tail water depth h. Thus, for a constant tail water depth h and a given bed material size d, Ds = f (Q, Lc) ...(40.2) EXPERIMENTAL SET-UP It consists of a vertical fall, Fig. 40.1, constructed in a rectangular channel of about 0.5 m width, 0.8m depth, and 5 m length. Just downstream of the fall, a cistern is provided. The length of the cistern should be adjustable. Channel bed downstream of cistern consists of erosive material. Arrangements for measuring and controlling the flow rate in the channel may consist of a bend meter and a valve in the supply line or some other suitable device. A tail gate is provided at the downstream end of the channel to adjust the tail water depth.

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Figure 40.1 Flow over vertical fall

PROCEDURE (A)

Calibration

1. Locate a section in the channel upstream of the fall where the water surface will have almost no curvature even at the maximum discharge. This can be done by allowing the maximum discharge (intended to be covered in the experiment) to flow and, then, observing the water surface. 2. Adjust the control valve for a suitable discharge, and when the flow becomes steady, take the pointer gauge reading for the water surface elevation at the section fixed in step (1) above. 3. Measure the discharge 4. Repeat steps (2) and (3) for other discharges. (B)

Energy Dissipation

1. Adjust the tailwater depth, h and the cistern length, Lc at one flow condition. 2. Measure the scour depth, Ds at the end of 10 minutes. This may be assumed as the maximum scour depth. 3. Vary the discharge twice and adjust the tail gate so that the tailwater depth is the same as in step (1). Level the bed and repeat step (2). 4. Repeat steps (1) to (3) for four more values of Lc, but at the same three discharges, and the tail water depth h which was used for the first value of Lc. For this experiment, it is advised that the discharge should be varied from low to high and Lc from high to low. OBSERVATIONS AND COMPUTATIONS

Date:…….

Width of channel or fall, B = ………………………………………………………… Pointer gauge reading for the crest level of vertical fall, hbi = …………………….

Vertical Fall

(A)

175

Calibration of Vertical Fall

Run No.

Discharge Measurement Q

Head on Vertical Fall hbf

H = hbf - h bi

hbf = Pointer gange reading for the head over the fall H = Head over the fall (B)

Energy Dissipation

Tail water depth, h = …………………… Bed material size, d = ……………………. Discharge measurement Q Cistern length, Lc Scour depth, Ds

FIGURES TO BE PREPARED 1. Plot H v/s Q (on y-axis) on a log-log graph paper and draw a straight line of slope 1.5 which best fits the data points. Substitute the values of Q and H of any point on this line in Eq. (40.1) to obtain the value of Cd. 2. Prepare a plot of Ds v/s Lc (on x-axis) with Q as third parameter. RESULTS AND COMMENTS Mean value of Cd = …………………………………………

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Vertical Fall

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Ogee (Overfall) Spillway

41 OBJECT Objectives of this experiment are: (i) to calibrate the ogee (overfall) spillway, (ii) to study the pressure distribution along the spillway surface, and (iii) to study the effect of tail water depth on energy dissipation. INTRODUCTION AND THEORY Spillway is used for disposing of surplus flood waters from a reservoir after it has been filled to its maximum capacity. If the space between the lower surface of the nappe and sharp-crested weir is filled with masonry or concrete, the resulting structure is an ogee (overfall) spillway. A spillway can also be used to measure the discharge, Q. The expression for Q can be written as Q = C B H1.5 ...(41.1) where, C is a coefficient, B the width of spillway and, H is the head over the spillway. Spillway profiles may be designed for a particular discharge or head (known as design discharge or design head) so as to conform to the profile of the underside of a freely falling nappe over a sharpcrested weir. This ensures the atmospheric pressure at all points on the spillway surface for the design head. For head other than the design head, the pressure on the spillway surface gets modified. The energy dissipation downstream of the spillway toe depends on the type of jump formed which, in turn, depends on the spillway bucket. The magnitude of scour downstream of the spillway toe can be taken as a measure of the energy dissipation and the performance of the spillway bucket can be judged. EXPERIMENTAL SET-UP The main channel is divided symmetrically into two channels, Fig. 41.1, each of about 25 cm width, 0.8m depth, and 5 m length. In each of these channels, a spillway model, Fig. 41.2, is suitably fixed. The two spillway models are identical but have different types of buckets. One model has, roller jump bucket and the other has ski-jump bucket. Sufficient number of pressure taps are provided centrally along the profile of one of the spillways to measure pressure distribution along the spillway. The channel beds downstream of the spillway models are made of loose particles.

Ogee (Overfall) Spillway

179

Figure 41.1 The experimental set-up for overfall spillway

Figure 41.2 Overfall spillway

The discharge in the parent channel is measured and controlled with a bend meter and a valve fitted in the supply pipe. The divided channels should carry equal amount of discharges and should be identical in all respects except that the spillway buckets are of different types. PROCEDURE 1. Note the profile of one of the spillway models and the location of its pressures points. 2. Regulate the discharge. Measure the head over the spillway and the inflow discharge. The discharge flowing in the channels is half of the inflow discharge. 3. Measure the pressure distribution along the surface of the spillway (initial readings at "no flow but reservoir full" condition may be noted later by letting a very thin sheet of water flow

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over the spillway and placing a finger tip on the pressure taps one by one and noting the reading on the corresponding manometer. 4. Repeat steps (2) and (3) for different heads. 5. For two suitable values of discharges, measure scour depth Ds downstream of the spillways in both channels for different tail water depths after, say, 10 minutes of flow stabilization. These scour depths would enable comparison between the performance of the two types of buckets. The bed should be levelled before the start of these measurements. The tail water depth h must also be the same in both channels. OBSERVATIONS AND COMPUTATIONS (A)

Spillway Profile x

y

(B)

Initial readings for prossure taps Pressure tap no. Initial Reading

H = Hj –Hi

Pointer gauge reading Hj

No.

Q

Head Measurement

Run Discharge Measurement

Pressure

Reading

Pressure

Reading

Pressure

Reading

Pressure

Reading

Pressure

Reading

Pressure

Reading

Pressure

Reading

Pressure

Reading

Pointer gauge reading for head over the spillway, Hi = ……………….

(C) Measuremens for calibration and pressure variation

1

2

3

4

Pressure Measurement 5

6

Ogee (Overfall) Spillway 181

182

(D)

Laboratory Work in Hydraulic Engineering

Scour Depth Measurements Sl.No.

Roller Jump Bucket Q= h

Ski-jump Bucket

Q= Ds

Q= h

Ds

h

Q= Ds

h

Ds

h = Taitwater depth

FIGURES TO BE PREPARED 1. Plot, Q v/s H (on x-axis) on a log-log graph paper and draw a line of slope 1.5 which best fits the data points. Using Eq. (41.1) and this plot, obtain the value of C. 2. Plot the spillway profile and, on it, the pressure distribution for various heads. Plot all the pressures normal to the surface with positive pressure (i.e, above atmospheric) being plotted above the surface and negative pressures below the surface. By interpolation, obtain the value of the head corresponding to which the pressure distribution on the profile would be atmospheric. This is the design head. Corresponding design discharge can be obtained from the calibration graph or Eq. (41.1) using the value of C obtained experimentally. 3. Plot Ds v/s h for two different discharges for both buckets. RESULTS AND COMMENTS 2. 3.

Mean value of C = …………………………………………………………. Design head (as obtained from the pressure distribution) = ……………

Ogee (Overfall) Spillway

183

184

Laboratory Work in Hydraulic Engineering

Ogee (Overfall) Spillway

185

C h a p t e r

Sediment Distribution at Offtakes

42 OBJECT To study the effect of angle of the offtake on the sediment distribution at an offtake. INTRODUCTION AND THEORY When a branch canal, which gets its supplies from the main canal, is to be provided, the problem of selection of offtake angle arises. Ideally speaking, this angle should be such that the percentage of sediment drawn by the offtake is in close proximity to the percentage of water discharge that it draws from the main canal. In practice, however, the percentage of sediment in the offtake is more than the percentage share of water withdrawn. This is on account of the large concentration of sediment in the lower layers of water that goes into the offtake more readily because of smaller velocity of flow at lower levels. EXPERIMENTAL SET-UP The set-up consists of a masonry channel having two offtakes one at 90o angle and the other at about 30o as shown in Fig. 42.1. Offtakes have sluice gates to control the discharge. Small red beads (slightly heavier than water) may be used to represent the sediment load. A fine wire mesh may be placed downstream of each of the branch channels to collect the red beads. Arrangements for measuring the discharges in different channels are also provided. The discharge in the main channel can be controlled and measured by a valve and bend meter fitted in the supply pipe. The depth of flow in the main channel can be adjusted with a tail gate at the downstream end of the main channel. PROCEDURE 1. Allow some flow Qm in the main channel and open the sluice gate of one of the offtakes. 2. Measure the discharge Qb in the offtake channel by the weir placed in it. 3. A known number Gm of red beads is dropped in the main channel uniformly across its width at a section well upstream of the junction of the offtake and the main channel. 4. Count the number of red beads which went into the offtake, Gb 5. Repeat steps (2) to (4) twice after varying the discharge in the offtake using the sluice gate.

Sediment Distribution at Offtakes

6. Repeat steps (1) to (5) for two more values of Qm. 7. Repeat steps (1) to (6) for other offtake also.

Figure 42.1 The experimental set-up for offtake

FIGURE TO BE PREPARED Qb Gb Plot Q v/s G m m

for the two offtakes.

RESULTS AND COMMENTS

187

Sediment Distribution at Offtakes

189

C h a p t e r

Scour around Spurs

43 OBJECT To study the effect of angle of spur on the depth of scour and also on the length of bank protected by the spur. INTRODUCTION AND THEORY Spurs are used as river training devices. When the flow has to be diverted to a desired path (for bank protection), a spur or a series of spurs can be used for the purpose. These are built transverse to the river flow extending from a bank into the river to the required extent. Scour is invariably caused around a spur. The maximum scour would occur at the nose of the spur. The extent of scour depends on flow characteristics, channel characteristics, sediment characteristics and geometric characteristics of the spur (including the angle that the spur makes with the bank). Downstream of the spur and in the vicinity of the bank from which it projects, there exists a separation pocket the length of which is termed protected length, Fig. 43.1.

Figure 43.1 The experimental set-up for spur

EXPERIMENTAL SET-UP The set-up, Fig. 43.1, consists of a rectangular channel (about 0.6 m wide, 0.8m deep, and 5 m long) having loose coarse material which can result in sufficient scour on the bed for the available flow

Scour Around Spurs

191

conditions. A slot is suitably provided downstream of the entrance section on one of the side walls of the channel. An iron sheet simulating a spur is inserted in this slot at the desired angle. The angle of spur can be varied by using different spur sheets. Arrangements for controlling and measuring the discharge should also be provided. PROCEDURE 1. Establish uniform flow conditions with a discharge slightly less than that causing incipient condition for the movement of the bed material. 2. Insert one of the spur sheets at the desired angle. 3. Note the scour depth Ds at different times for about 30 minutes at which time equilibrium scour depth may be assumed to have reached. 4. Measure the discharge. 5. Using paper pieces or aluminium powder, find the extent of separation pocket and thus the protected length. 6. Repeat steps (1) to (5) for other spur sheets at different angles, keeping blockage of the flow due to the spur sheets the same. FIGURE TO BE PREPARED 1.

Plot scour depth Ds v/s time, t for all the spurs studied.

RESULTS AND COMMENTS

192

Laboratory Work in Hydraulic Engineering

OBSERVATIONS AND COMPUTATIONS

Date: …….

Initial pointer gauge reading : ………………………………………………………….. (for channel bed) Spur No.

1

2

3

Angle of spur

Discharge, Q Protected Length, L Sl. No.

Time

Scour Depth

4

Scour Around Spurs

193