URBAN HYDROLOGY, HYDRAULICS, AND STORMWATER QUALITY Engineering Applications and Computer Modeling 0471431583

Table of contents :
Preface
Acknowledgments
CONTENTS
Introduction
1.1 Urbanization and Stormwater Runoff / 1
1.2
1.3
Problems / 4
Urban Hydrology, Hydraulics, and Stormwater Quality / 2
Organization of the Book / 2
Rainfall for Designing Urban Drainage Systems
2.1
2.2
Hydrologic Description of Rainfall / 5
Probabilistic Description of Rainfall I 8
2.2.1
2.2.2 Frequency Analysis I 10
2.2.3
2.2.4
Return Period and Hydrologic Risk I 8
Intensity-Duration-Return Period Curves I 13
Mathematical Intensity-Duration Relationships I 14
2.3 Design Rainfall I 15
2.3.1 Continuous Simulation and Single-Event Methods I 16
xiii
xv
1
5
vi i
Viii CONTENTS
2.3.2
2.3.3
2.3.4
Construction of Design-Storm Hyetographs I 18
2.4.1 Soil Conservation Service Method I 18
2.4.2 Yen and Chow Method I 20
2.4.3 Huff Method I 21
2.4.4
2.4.5 Chicago Method I 27
Design Return Period I 17
Design-Storm Duration and Depth I 18
Spatial and Temporal Distribution of Design Rainfall I 18
2.4
Synthetic Block Hyetograph Method I 25
Problems I 29
References I 32
3 Rainfall Excess Calculations
3.1 Calculation of Rainfall Abstractions I 34
3.1.1 Interception Storage I 35
3.1.2 Infiltration I 36
3.1.3 Depression Storage I 52
3.2 Combined Loss Models I 53
3.2.1 Soil Conservation Service Method I 53
3.2.2 Other Combined Loss Models I 59
Problems I 60
References I 63
34
4 Rainfall Excess and Open-Channel Flow in Urban Watersheds 65
4.1 Open-Channel Hydraulics I 65
4.1.1 Basic Definitions I 65
4.1.2
4.1.3
4.1.4
4.1.5 Normal Flow I 70
4.1.6
States of Open-Channel Flow I 67
Open-Channel Flow Equations I 68
Steady Gradually Varied Flow I 69
Open-Channel Rating Curve I 70
4.2 Overland Flow / 71
4.2.1 Kinematic-Wave Model I 72
4.2.2 Overland Flow on Impervious Surfaces / 73
4.2.3 Overland Flow on Pervious Surfaces I 77
4.3 ChannelFlow I 79
4.3.1 Muskingum Method I 80
CONTENTS iX
4.3.2 Muskingum-Cunge Method I 83
4.3.3
4.3.4 Modified Att-Kin Method I 88
Muskingum-Cunge Method for Routing with Lateral Inflow I 85
Problems I 90
References I 93
5 Calculation of Runoff Rates From Urban Watersheds 94
5.1 Basic Concepts I 95
5.1.1 Elements of Urban Runoff Hydrographs I 95
5.1.2 Definition of Time of Concentration I 97
5.2 Calculation of Time of Concentration I 97
5.2.1 SCS Time-of-Concentration Method I 98
5.2.2 Kinematic Time-of-Concentration Formulas I 100
5.2.3 KirpichFormula I 103
Unit Hydrograph Method I 104
5.3.1 Unit Hydrograph Development I 104
5.3.2 Application of the Unit Hydrograph Method / 117
Soil Conservation Service Methods for Runoff Rate Calculations / 119
5.4.1 TR-55 Graphical Peak Discharge Method I 119
5.4.2 TR-55 Tabular Hydrograph Method I 121
5.5 The Santa Barbara Urban Hydrograph Method I 125
5.6 USGS Regression Equations / 129
5.7 The Rational Method I 132
5.8 The Kinematic-Rational Methods I 136
Problems I 141
References I 145
5.3
5.4
6 Stormwater Drainage Structures
6.1 Drainage of Street Pavements I 147
6.1.1 General Design Considerations I 147
6.1.2 Flow in Gutters I 148
6.1.3 Pavement Drainage Inlets / 155
6.1.4 Pavement Drainage Inlet Locations I 164
6.2 Storm Sewer Systems I 166
6.2.1 Storm Sewer Hydraulics I 168
6.2.2 Design Discharge for Storm Sewers I 174
147
X CONTENTS
6.2.3
6.2.4
6.2.5
Sizing Storm Sewers I 176
Hydraulic Grade Line Considerations I 176
Storm Sewer System Design Calculations I 177
6.3 Culverts I 184
6.3.1 Inlet Control Flow I 185
6.3.2 Outlet Control Flow I 194
6.3.3 Sizing of Culverts I 199
6.4 Design of Surface Drainage Channels I 200
6.4.1 Design of Unlined Channels I 201
6.4.2 Design of Grass-Lined Channels I 208
Problems I 213
References I 217
Suggested Reading I 2 17
7 Stormwater Detention for Quantity Management
7.1 Detention Basins I 218
7.1.1 Stage-Storage Relationship I 219
7.1.2 Stage-Discharge Relationship I 222
7.1.3 Pond Routing I 227
7.1.4 Pond-Routing Charts I 23 1
7.1.5 Design of Detention Basins I 239
7.2 Infiltration Practices I 249
7.2.1 Capture Volume I 249
7.2.2 Soil Textures I 253
7.2.3 Infiltration Basins I 253
7.2.4 Infiltration Trenches I 257
7.2.5 Dry Wells I 259
7.2.6 Porous Pavements I 262
Problems I 262
References I 266
Suggested Reading I 267
21 8
8 Urban Stormwater Pollution 268
8.1 Modeling Urban Stormwater Quality I 269
8.1.1
8.1.2
8.1.3
Solids Buildup and Wash-off from Impervious Areas I 269
Solids Wash-off from Pervious Surfaces I 273
Wash-off of Pollutants Other than Solids I 277
CONTENTS Xi
8.1.4 Pollutographs and Loadographs I 277
8.2 Annual Pollutant Load Estimates I 279
8.2.1 EPA Model for Annual Pollutant Loading Estimation I 279
8.2.2 U.S. Geological Survey Model for Mean Annual Loads I 283
8.2.3 Metropolitan Washington Council of Governments
Method I 285
Problems I 287
References I 290
9 Best Management Practices for Urban Stormwater
Quality Control 291
9.1
9.2
9.3
9.4
9.5
9.6
9.7
Extended Detention Basins I 293
9.1.1
9.1.2
9.1.3
Retention Basins I 299
9.2.1 Permanent Pool Volume / 300
9.2.2 Retention Basin Design Considerations I 303
9.2.3 EPA Methodology for Analysis of Wet Pond Detention
Basins I 304
Water Quality Trenches I 3 13
SandFilters I 314
Stormwater Wetlands I 316
Other Vegetative BMPs I 320
9.6.1 Grass Swales I 320
9.6.2 Filter Strips I 321
The National Stormwater BMP Database I 321
Sizing Extended Detention Basins I 294
Sizing Water Quality Outlet Devices I 296
Additional Extended Detention Basin Design
Considerations I 298
Problems I 322
References I 324
10 Urban Stormwater Computer Models:
HEC-HMS and EPA-SWMM 326
10.1 Hydrologic Modeling Overview and Watershed Delineation I 327
10.2 Model Structure and Features of HEC-HMS I 331
10.3 Technical Capabilities of HEC-HMS I 334
10.4 HEC-HMS Example Problem / 337
xii CONTENTS
10.5 Structure and Features of EPA-SWMM / 344
10.6 Technical Capabilities of EPA-SWMM / 345
10.7 EPA-SWMM Example Problem / 347
10.8 Model Calibration and Verification / 347
Problems / 348
References / 350
Suggested Reading / 350
Append i x Tabu I a r Hydro g ra p h U n it Discharges
for SCS Type II Rainfall Distribution 351
Index 367

Citation preview

URBAN HYDROLOGY, HYDRAULICS, AND STORMWATER QUALITY Engineering Applications and Computer Modeling

A. Osman Akan Old Dominion University

Robert J. Houghtalen Rose-Hulman Institute of Technology

fB WILEY

JOHN WILEY & SONS, INC.

This book is printed on acid-free paper.

@

Copyright @ 2003 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc.. Hoboken. New Jersey Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4744, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-601 1, fax (201) 748-6008, e-mail: [email protected]. Limit of LiabilityDisclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our web site at www.wiley.com.

Library of Congress Cataloging-in-Publication Data Akan, A. Osman. Urban hydrology, hydraulics, and stormwater quality : engineering applications and computer modeling / A. Osman Akan, Robert J. Houghtalen. p. cm. Includes bibliographical references and index. ISBN 0-471-43158-3 (cloth) 1. Urban hydrology. 2. Urban runoff-Management. 3. Water quality management. I. Houghtalen, Robert J. 11. Title. TC409 .A39 2003 628’.215-dc21 2003001377 Printed in the United States of America 1 0 9 8 7 6

To my family A. Osman Akan

To my dear friend and mentor, the late Jerry Normann Robert J. Houghtalen

ACKNOWLEDGMENTS

Writing a book requires much dedication, but it is also an extremely fulfilling experience. I am grateful to John Wiley & Sons for this opportunity. I missed having a co-author during my first authoring experience. Therefore, I was very pleased when Robert Houghtalen accepted my offer to join me in writing this book. Working with Robert has been a gratifying experience. Besides his immense knowledge, Robert is a very pleasant and patient individual. I had excellent professors at Middle East Technical University in Ankara, Turkey, as an undergraduate student and at the University of Illinois at Urbana as a graduate student. I also had excellent students and colleagues at Middle East Technical University and at Old Dominion University. In addition, I have read numerous papers, books, and reports authored by colleagues from all over the world. I am certain that the material in this book has been influenced by many of my teachers, students, and colleagues. I am grateful to all of them. Of course, the late Ben C. Yen, my doctoral advisor, still occupies a special place in my heart. I am most grateful to my wife, Guzin, a doctor of engineering herself, and my son Doruk, an engineering student. They have given me all the happiness, inspiration, support, and peace of mind I needed to write this book. I also would like to thank Old Dominion University for providing me with the opportunity and the institutional support in the preparation of the book.

A. OSMANAKAN

It was an honor to be approached by Osman Akan to participate in the writing of this textbook and desk reference. I had the opportunity to sit in on a few classes offered by Osman at Old Dominion University in the early 1980s. His explanation of difficult xv

xvi

ACKNOWLEDGMENTS

concepts was extraordinarily clear. He is a gifted teacher and an exemplary scholar. It is my hope that others can benefit from his gifts through this book. I teach an urban hydrology and modeling class to advanced undergraduates and master’s students at Rose-Hulman. I have been using the draft version of this book for years, and my students have been a big help in the revision process. I have also been honored to teach a continuing education course for the American Society of Civil Engineers on the Corps of Engineers HEC-HMS model and the Environmental Protection Agency SWMM model. The attendees have helped to formulate the information presented in this book, particularly the modeling chapter. I would like to sincerely thank all of my students for their contributions and for putting up with me. I certainly don’t want to forget to thank my wife, Judy, and my children (Jesse, Jamin, and Jared) for their patience with me as I was spending long hours on this project. They bring a smile to my face and keep me humble. I continue to be grateful to the late Jerome Normann, whose professional coattails I have ridden for over two decades. I also want to thank Rose-Hulman for giving faculty members the encouragement and opportunity to concentrate on teaching and scholarly endeavors like this one. It is truly a wonderful place to work. I am grateful to John Wiley & Sons for agreeing to publish the book. In particular, Liz Roles and Jim Harper have been very helpful. And lastly, I want to thank Ned Hwang who asked me to be his co-author on my first book. Ned was a great help in getting me started in this “second career” that I find so fulfilling. And now I praise God that it is done.

ROBERTJ . HOUGHTALEN

PREFACE

Urban hydrology, hydraulics, and stormwater quality are important topics for civil engineers, urban planners, hydrologists, and environmental engineers. Over the last decade, many articles have been written on the decay of our urban infrastructure. To be sure, stormwater collection, transport, and treatment systems are important components of this urban infrastructure. In that same period of time we have learned that the water quality of our rivers and lakes cannot be improved dramatically unless we focus on nonpoint source pollution. Again, proper attention to advances in stormwater collection and treatment is critical. And, finally, the problem of urban sprawl has received a lot of attention recently. Rehabilitation of decaying stormwater systems in the inner city is critical to slowing urban sprawl through redevelopment, particularly in the case of brownfields. Innovative design of new stormwater management techniques is likewise critical to minimizing the adverse impacts of any urban sprawl that does occur. In response to these critical problems, engineers and scientists have developed many innovative techniques to analyze urban hydrology. They have also designed many innovative structures to control urban flooding and improve stormwater quality. These analysis techniques and designed structures rely heavily on numerical methods and computer models. Thus, desktop methods and empirical models are giving way to new, physically based techniques that are embedded in modern computer software. This book is intended to catalog these advances in urban hydrology and stormwater management. Background information is supplied, but applications are emphasized. Most of the methods introduced represent the algorithms found in hydrologic and hydraulic computer models. In fact, the last chapter of the book introduces two popular (nonproprietary) computer models, the U.S. Army Corps of Engineers HECHMS (Hydrologic Engineering Center’s-Hydrologic Modeling System) model and the Environmental Protection Agency SWMM model (or stormwater management xiii

xiv

PREFACE

model). Both models are widely used and accepted for urban stormwater management, and both rely heavily on the numerical techniques (finite difference methods) that are covered throughout the book. In essence, this book provides a practical introduction of urban hydrology, hydraulics, and stormwater quality. It is primarily intended to serve as a textbook for an undergraduate course in hydrology for civil and environmental engineers in lieu of a traditional hydrology book. There are three reasons to adopt this book: (1) most hydrologic analysis and design performed by practicing engineers is done in the urban environment, (2) hydrologic analysis is more apt to be performed with computer models that rely on physically based methods than desk-top, empirical techniques, and (3) stormwater quality has become as big a concern as stormwater quantity. The book could be used for an advanced undergraduate or master’s level class in urban stormwater management. It would also serve as a good desk reference for practicing civil engineers, hydrologists, planners, and environmental engineers. Problems are provided at the end of each chapter for the benefit of students. Typically, three problems are presented for each topic introduced. The first problem is qualitative and focuses on a broad understanding of the topic. The second problem is fundamental and quantitative, a straightforward application of an analysis technique or an engineering design method. The third problem is an extended application that pushes the students to extrapolate their basic knowledge beyond what is covered in the book. These problems emphasize logic and could be used for classroom discussion. Since many of the techniques presented rely on finite difference methods, the student is encouraged to employ spreadsheet solutions. A solutions manual is available to faculty members. We hope you will enjoy our humble effort to advance the education of urban hydrology, hydraulics, and stormwater management. We have done our best to make this edition error free. Any who have engaged in this effort know that this is virtually impossible. Thus, you are encouraged to email your suggestions and corrections to the junior author at roberthoughtalen @rose-hulman.edu.

CONTENTS

Preface

xiii

Acknowledgments

xv

Introduction

1

1.1 Urbanization and Stormwater Runoff / 1

1.2 Urban Hydrology, Hydraulics, and Stormwater Quality / 2 1.3 Organization of the Book / 2 Problems / 4

Rainfall for Designing Urban Drainage Systems

5

2.1 Hydrologic Description of Rainfall / 5 2.2 Probabilistic Description of Rainfall I 8 2.2.1 Return Period and Hydrologic Risk I 8 2.2.2 Frequency Analysis I 10 2.2.3 Intensity-Duration-Return Period Curves I 13 2.2.4 Mathematical Intensity-Duration Relationships I 14 2.3 Design Rainfall I 15 2.3.1 Continuous Simulation and Single-Event Methods I 16 vi i

Viii

CONTENTS

2.3.2 2.3.3 2.3.4 2.4

Design Return Period I 17 Design-Storm Duration and Depth I 18 Spatial and Temporal Distribution of Design Rainfall I 18

Construction of Design-Storm Hyetographs I 18 2.4.1 Soil Conservation Service Method I 18 2.4.2 Yen and Chow Method I 20 2.4.3 Huff Method I 21 2.4.4 Synthetic Block Hyetograph Method I 25 2.4.5 Chicago Method I 27

Problems I 29 References I 32 3

Rainfall Excess Calculations 3.1

34

Calculation of Rainfall Abstractions I 34 3.1.1 Interception Storage I 35 3.1.2 Infiltration I 36 3.1.3 Depression Storage I 52

3.2 Combined Loss Models I 53 3.2.1 Soil Conservation Service Method I 53 3.2.2 Other Combined Loss Models I 59 Problems I 60 References I 63 4

Rainfall Excess and Open-Channel Flow in Urban Watersheds 4.1

Open-Channel Hydraulics I 65 4.1.1 Basic Definitions I 65 4.1.2 States of Open-Channel Flow I 67 4.1.3 Open-Channel Flow Equations I 68 4.1.4 Steady Gradually Varied Flow I 69 4.1.5 Normal Flow I 70 4.1.6 Open-Channel Rating Curve I 70

4.2

Overland Flow / 71 4.2.1 Kinematic-Wave Model I 72 4.2.2 Overland Flow on Impervious Surfaces / 73 4.2.3 Overland Flow on Pervious Surfaces I 77

4.3 ChannelFlow I 79 4.3.1 Muskingum Method I 80

65

CONTENTS

iX

4.3.2 Muskingum-Cunge Method I 83 4.3.3 Muskingum-Cunge Method for Routing with Lateral Inflow I 85 4.3.4 Modified Att-Kin Method I 88 Problems I 90 References I 93

5 Calculation of Runoff Rates From Urban Watersheds

94

5.1 Basic Concepts I 95 5.1.1 Elements of Urban Runoff Hydrographs I 95 5.1.2 Definition of Time of Concentration I 97 5.2 Calculation of Time of Concentration I 97 5.2.1 SCS Time-of-Concentration Method I 98 5.2.2 Kinematic Time-of-Concentration Formulas I 100 5.2.3 KirpichFormula I 103 5.3 Unit Hydrograph Method I 104 5.3.1 Unit Hydrograph Development I 104 5.3.2 Application of the Unit Hydrograph Method / 117 5.4 Soil Conservation Service Methods for Runoff Rate Calculations / 119 5.4.1 TR-55 Graphical Peak Discharge Method I 119 5.4.2 TR-55 Tabular Hydrograph Method I 121 5.5 The Santa Barbara Urban Hydrograph Method I 125 5.6 USGS Regression Equations / 129 5.7 The Rational Method I 132 5.8 The Kinematic-Rational Methods I 136 Problems I 141 References I 145 6 Stormwater Drainage Structures

6.1 Drainage of Street Pavements I 147 6.1.1 General Design Considerations I 147 6.1.2 Flow in Gutters I 148 6.1.3 Pavement Drainage Inlets / 155 6.1.4 Pavement Drainage Inlet Locations I 164 6.2 Storm Sewer Systems I 166 6.2.1 Storm Sewer Hydraulics I 168 6.2.2 Design Discharge for Storm Sewers I 174

147

CONTENTS

X

6.2.3 Sizing Storm Sewers I 176 6.2.4 Hydraulic Grade Line Considerations I 176 6.2.5 Storm Sewer System Design Calculations I 177 6.3 Culverts I 184 6.3.1 Inlet Control Flow I 185 6.3.2 Outlet Control Flow I 194 6.3.3 Sizing of Culverts I 199 6.4 Design of Surface Drainage Channels I 200 6.4.1 Design of Unlined Channels I 201 6.4.2 Design of Grass-Lined Channels I 208 Problems I 213 References I 217 Suggested Reading I 2 17 7 Stormwater Detention for Quantity Management

218

7.1 Detention Basins I 218 7.1.1 Stage-Storage Relationship I 219 7.1.2 Stage-Discharge Relationship I 222 7.1.3 Pond Routing I 227 7.1.4 Pond-Routing Charts I 23 1 7.1.5 Design of Detention Basins I 239 7.2 Infiltration Practices I 249 7.2.1 Capture Volume I 249 7.2.2 Soil Textures I 253 7.2.3 Infiltration Basins I 253 7.2.4 Infiltration Trenches I 257 7.2.5 Dry Wells I 259 7.2.6 Porous Pavements I 262 Problems I 262 References I 266 Suggested Reading I 267

8

Urban Stormwater Pollution 8.1 Modeling Urban Stormwater Quality I 269 8.1.1 Solids Buildup and Wash-off from Impervious Areas I 269 8.1.2 Solids Wash-off from Pervious Surfaces I 273 8.1.3 Wash-off of Pollutants Other than Solids I 277

268

CONTENTS

Xi

8.1.4 Pollutographs and Loadographs I 277 8.2 Annual Pollutant Load Estimates I 279 8.2.1 EPA Model for Annual Pollutant Loading Estimation I 279 8.2.2 U.S. Geological Survey Model for Mean Annual Loads I 283 8.2.3 Metropolitan Washington Council of Governments Method I 285 Problems I 287 References I 290

9 Best Management Practices for Urban Stormwater Quality Control

291

9.1 Extended Detention Basins I 293 9.1.1 Sizing Extended Detention Basins I 294 9.1.2 Sizing Water Quality Outlet Devices I 296 9.1.3 Additional Extended Detention Basin Design Considerations I 298 9.2 Retention Basins I 299 9.2.1 Permanent Pool Volume / 300 9.2.2 Retention Basin Design Considerations I 303 9.2.3 EPA Methodology for Analysis of Wet Pond Detention Basins I 304 9.3 Water Quality Trenches I 3 13 9.4 SandFilters I 314 9.5 Stormwater Wetlands I 316 9.6 Other Vegetative BMPs I 320 9.6.1 Grass Swales I 320 9.6.2 Filter Strips I 321 9.7 The National Stormwater BMP Database I 321 Problems I 322 References I 324 10 Urban Stormwater Computer Models: HEC-HMS and EPA-SWMM 10.1 Hydrologic Modeling Overview and Watershed Delineation I 327 10.2 Model Structure and Features of HEC-HMS I 331 10.3 Technical Capabilities of HEC-HMS I 334 10.4 HEC-HMS Example Problem / 337

326

xii

CONTENTS

10.5 Structure and Features of EPA-SWMM / 344

10.6 Technical Capabilities of EPA-SWMM / 345 10.7 EPA-SWMM Example Problem / 347

10.8 Model Calibration and Verification / 347 Problems / 348 References / 350 Suggested Reading / 350

Append ix TabuI a r Hydrograph Unit Discharges for SCS Type II Rainfall Distribution

351

Index

367

CHAPTER

INTRODUCTION

1.1

URBANIZATION AND STORMWATER RUNOFF

The rainfall-runoff process is extremely complex, making it difficult to model accurately. In undeveloped areas, the quantity and rate of stormwater runoff are affected by natural surface detention, soil infiltration characteristics, and the drainage pattern formed by natural flow paths. The soil type, vegetative cover, and topography play key roles. Urbanization impacts the rainfall-runoff process in a variety of ways. Infiltration is reduced due to the addition of impervious surfaces, resulting in increasing quantities of runoff. Tree removal, surface leveling, soil flipping, and surface compaction are also likely to boost the quantity of runoff. In addition, the rate of stormwater runoff is intensified due to the extensive network of pipes and channels that are designed into the urban environment. The long surface travel times from undeveloped land are shortened, and gutters and pipes quickly convey stormwater to receiving streams. Unfortunately, the increase in runoff quantities and rates can produce downstream flooding and accelerate channel erosion. Stormwater quantity isn’t the only problem associated with urbanization. Stormwater quality is impaired as well. Urban land surfaces are subject to the buildup of pollutants during dry weather, many of which are associated with human activity. When it rains, these pollutants are washed off the land surface and contribute to diminished receiving water quality. In fact, this nonpoint source pollution is the primary source of water quality impairment in the United States and many other countries of the world, Nonpoint source pollution includes eroded soil from construction sites, oil and grease from cars, nitrogen and phosphorus from fertilizers, pesticides from lawn and shrub care products, fecal droppings from pets and other animals, dust and dirt from dry fall, and various pollutants from illegal dumping and spills. 1

2

INTRODUCTION

1.2

URBAN HYDROLOGY, HYDRAULICS, AND STORMWATER QUALITY

An understanding of urban hydrology, hydraulics, and stormwater quality is necessary to address the previously documented problems. In fact, many innovative practices have been developed over the last two decades to mitigate the detrimental effects of urbanization on stormwater runoff. These practices are often referred to as stomwater management. This book goes beyond the scope of stormwater management. It investigates the occurrence of stormwater in urban watersheds, its movement through the different elements of the drainage system, its collection and transport of various nonpoint source pollutants, its response to various stormwater management practices, and the incorporation of all of these elements into modem computer software. Simply stated, this book provides the reader with pertinent information on the quantity and quality of stormwater runoff that is essential to proper planning, design, and operation of stormwater management practices. The field of urban hydrology, hydraulics, and stormwater quality is not an exact science. Certainly the principles of hydraulics are well developed and understood. The principles of hydrology are less advanced and still rely occasionally on empirical or semiempirical coefficients. On the other hand, the science of stormwater quality is in its infancy and relies heavily on empirical techniques and good field data to calibrate the appropriate models. Nonetheless, the science of the latter two has advanced over the last few decades, and physically based mathematical models are rapidly replacing empirical techniques. In addition, the use of desktop hydrologic techniques is being replaced with hydrologic computer models. These models incorporate many of the physically based techniques in a user-friendly environment. Unfortunately, more and more software users understand less and less about the underlying algorithms. This book provides the reader with a working knowledge of modern hydrologic models and the algorithms on which they rely. This knowledge will help the reader pick the most appropriate algorithms (since most computer models allow the user to choose from a variety of hydrologic algorithms) and verify the model results. The book also provides a number of desktop methods for small projects that do not justify computer modeling. These methods may also be used to check the results from computer models.

1.3 ORGANIZATION OF THE BOOK

Modern hydrologic computer models follow the path of a drop of water through the hydrologic cycle. Thus, these computer models start with a design or historic rainfall event, remove the losses (rainfall abstractions), route the excess over the land surface and through the conveyance system (pipes, channels, and ponds), and finally account for any stormwater management devices that are placed in the system. Therefore, the chapters have been arranged in a similar sequence. The first and probably the most important task in designing a stormwater project is the selection of a storm on which the design will be based. Both the hydrologic

ORGANIZATION OF THE BOOK

3

and probabilistic characteristics of the historical, local rainfall data are considered in selecting a design storm. Chapter 2 of this book describes various methods to determine the elements of a design-storm hyetograph. Part of the design rainfall, collectively referred to as losses from rainfall, is diverted from becoming runoff due to several processes, such as interception by trees and infiltration into the soil. Reasonably accurate determination of the rainfall losses is important, because the quantity of design runoff (or rainfall excess) results from the removal of these losses from the design rainfall. Chapter 3 describes the types of rainfall losses and presents several methods to calculate the quantity of rainfall excess. The rainfall excess is transported to the design point through various flow processes. The flow in most elements of an urban watershed has a free surface at atmospheric pressure and is generally classified as open-channel flow. Chapter 4 presents the basic concepts of open-channel flow relevant to urban watersheds. It also discusses the two basic types of open-channel flow occurring in an urban watershed, overland flow and channel flow. The methods described in this chapter are critical to understanding the key components of a complex urban drainage system. Chapter 5 describes a variety of lumped urban rainfall-runoff models to calculate the design flows resulting from specified rainfall excess. These methods simulate the response of an urban watershed as a whole during design-storm conditions. The timeof-concentration concept is introduced along with unit hydrograph techniques, the U.S. Soil Conservation Service methods, U.S. Geological Survey (USGS) regression equations, and the rational method. Chapter 6 is devoted to the design of drainage structures. Typical drainage structures found in urban stormwater systems include gutters (street flow), storm sewers, culverts, and surface drainage (open) channels. Special attention is given to the design of storm sewer systems, including drainage inlet placement, drainage inlet hydraulics, storm sewer sizing, and hydraulic grade line calculations. The increased stormwater runoff due to urbanization needs to be controlled to protect the downstream areas from flooding. Detention basins are often used to control the post-development peak flow rates. Chapter 7 describes the analysis and design of flood protection detention basins. In addition, infiltration practices are covered, including infiltration basins, infiltration trenches, dry wells, and porous pavements. The quality of stormwater is also impaired due to urbanization as addressed in Chapter 8. Single-event pollutograph calculations are presented considering both the impervious and pervious areas of an urban watershed. Also, several methods, including the Environmental Protection Agency (EPA) and USGS procedures and the simple method, are presented to predict the annual pollutant loadings in urban stormwater runoff. Chapter 9 describes how the quality of urban stormwater runoff can be enhanced using various best management practices (BMPs). BMPs covered include extended detention basins, retention basins, water quality trenches, sand filters, stormwater wetlands, and grass swales. The National Stormwater BMP Database is introduced and referenced.

4

INTRODUCTION

Chapter 10 introduces two of the most frequently used hydrologic computer models, the Corps of Engineers' HEC-HMS model and the EPA's SWMM model. The chapter begins with a brief modeling overview. Then the model structure and features are covered along with the technical capabilities. A detailed example problem is provided for both computer models along with a discussion of the model results and error checking. A variety of both physically based and empirical methods developed by a number of different organizations and individuals is presented throughout the book. Physically based equations are dimensionally homogeneous, and they are valid for any consistent system of units. In a consistent unit system, we can use any units of length, time, and force we wish as long as we use them consistently. In other words, if we select meter as the length unit, second as the time unit, and newton as the force unit, all the depths involved will be in meters, areas in square meters, volumes in cubic meters, velocities in meters per second, discharges in cubic meters per second (cms), and pressures in newtons per square meter. The empirical equations, generally, are not dimensionally homogeneous. Many of these equations employ mixed units, such as acres for area and cubic feet per second (cfs) for discharge. The coefficients and the parameters involved in empirical equations are specific to the unit system used. Therefore, the applicable units are clearly indicated in the text for all the empirical equations. Where feasible, different values of the empirical coefficients and parameters are also provided in multiple unit systems.

PROBLEMS

1. Obtain some references (other than this textbook) on the topic of urban stormwater hydrology or urban stormwater management. Based on these references, identify the factors that lead to hydrologic (i.e., rainfall-runoff) changes when a watershed is urbanized. Describe the changes and comment on their importance. 2. Many governmental agencies collect and distribute hydrologic and environmental data that are useful to those of us working in the field of urban stormwater hydrology. Perform an Internet search to obtain web addresses for the following: United States Geologic Survey (USGS), National Weather Service (NWS), Environmental Protection Agency (EPA), United States Army Corps of Engineers (USACE), United States Bureau of Reclamation (USBR), and Natural Resources Conservation Service (NRCS, formerly the Soil Conservation Service, SCS). Browse the home pages of these agencies to become acquainted with the information they collect and make available to the public.

CHAPTER

2 RAINFALL FOR DESIGNING URBAN DRAINAGE SYSTEMS

Precipitation may occur in an urban watershed in various forms, including drizzle, rain, snow, and hail. Drizzle and rain consist of liquid water droplets, while snow is composed of ice crystals, and hail contains solid ice stones. The liquid water droplets reaching the earth surface are usually called drizzle if they are smaller than 0.5 mm in diameter. Otherwise, they are referred to as rain. Of these different types of precipitation, rain is the most important in urban hydrology since it drives the design of urban storm drainage structures in most parts of the world. 2.1

HYDROLOGIC DESCRIPTION OF RAINFALL

Rainfall is the amount of liquid precipitating in the form of rain. A rainfall event takes place over a period of time during which measurable rainfall occurs. The length of this period, which is preceded and followed by periods of no measurable rainfall, is called rainfall duration. In other words, rainfall duration is the time elapsed from start to end of the rainfall event (Ponce 1986).We sometimes refer to a rainfall event as a storm and rainfall duration as storm duration. The total depth or depth of rainfall is the depth to which the rainwater would accumulate if it stayed where it fell on the ground. The rainfall intensity refers to the time rate of rainfall. The average intensity is equal to the total depth of rainfall divided by the storm duration. Normally, intensity varies throughout the storm duration, and a plot of rainfall intensity versus time is called a hyetograph. A hyetograph can be a continuous curve as in Figure 2.la or in the form of a discrete histogram as shown in Figure 2.lb. In these figures i = rainfall intensity and t = time. Sometimes, the cumulative rainfall is plotted as a function of time in dimensional form as in Figure 2.2a or in 5

h

f

1.4-

h

1.2.

>

'=: 1.0.

Y

C

.-c

1.41.2. 1.0.

%

I

-

0.8.

'jj 0.8. C

- 0.4.

0.6.

0.2.

0.2.

__

__

0.6.

0.4.

0.00 0.25 0.50 0.75 1'.00 1'.25 1'.50 1'.75 2.00 2.25

000 0 2 5 0 5 0 0 7 5 1 0 0 1 2 5 1 5 0 1 7 5 2 0 0

Time (hr)

Time (hr)

FIGURE 2.1. Rainfall hyetographs. 1.2

I

1.o

c

9

0.8

0.6

0.4

0.2

0.0 0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

t (hr) 1.o

0.8

0.6

ct

c

0.4

0.2

0.0 0.00

0.25

0.50

0.75

ufd

FIGURE 2.2. Cumulative rainfall hyetographs.

6

1.oo

7

HYDROLOGIC DESCRIPTION OF RAINFALL

1

h

24-hr rainfall

.-

-

I

.-C

1-hr rainfall

30-min rainfall

1"

I

0

50

100

150

200

250

300

Area (sq mi)

FIGURE 2.3. Rainfall depth versus area relationship.

dimensionless form as in Figure 2.2b, where P = cumulative rainfall, f i = total depth, and fd = storm duration. Rainfall intensities vary spatially as well as temporally during a storm event. Generally, the rainfall depth is highest near the storm center, and it will decrease with increasing distance from the storm center. Often a spatially averaged depth over the area covered by the storm is used to characterize a storm. The spatially averaged rainfall depth decreases as the areal extent of a storm increases. Figure 2.3 presents a general relationship between the size of a watershed and the spatially averaged rainfall depth for various storm durations. This figure is adapted from the US Weather Bureau (1961), now the National Weather Service (NWS).

Example 2.1 Consider the rainfall hyetograph given in Figure 2.lb. Determine the total depth and average rainfall intensity. Also, prepare a plot of cumulative rainfall versus time in dimensional form and dimensionless form. Columns 1 and 2 in Table 2.1 are a tabular representation of the given hyetograph. For example, the intensity is 0.2 i n h r between t = 0 and 0.25 hr. During this time increment of At = (0.25 - 0) hr = 0.25 hr, an incremental rainfall of A P = (0.2 in./hr)(0.25 hr) = 0.05 in. is produced. We calculate all the entries in column 3 in the same manner. The total depth of rainfall PT is equal to the sum of all the A P ' s in column 3, and equals 1.2 in. Also, the duration fd is 2 hr. Therefore, the average intensity becomes (1.2 in.)/(2 hr) = 0.6 in./hr.

8

RAINFALL FOR DESIGNING URBAN DRAINAGE SYSTEMS

Table 2.1. Rainfall Hyetograph Example

1

(hr)

i (idhr)

A P (in.)

0.2

0.05

0.4

0.10

0.8

0.20

1.2

0.30

1.o

0.25

0.6

0.15

0.4

0.10

0.2

0.05

P (in.)

tltd

Plq.

0

0

0

0.05

0.125

0.041

0.15

0.250

0.125

0.35

0.375

0.250

0.65

0.500

0.542

0.90

0.625

0.750

1.05

0.750

0.875

1.15

0.875

0.958

1.20

1.000

1.000

0 0.25 0.50 0.75 1.oo

1.25 1.50 1.75 2.00

The cumulative rainfall P at time t is equal to the sum of the A P ’ s up to time t . For example, as shown in column 4, the cumulative depth corresponding to t = 0.50 hr is 0.05 + 0.10 = 0.15 in. All the P values in column 4 are found in the same manner. Note that the last value in column 4 is equal to PT = 1.2 in. Figure 2.2a displays a plot of column 4 versus column 1. To obtain a similar but dimensionless plot, we first calculate the entries in column 5 simply by dividing those in column 1 by td = 2 hr. Likewise, we obtain the entries in column 6 by dividing those in column 4 by PT = 1.2 in. Then, we plot column 6 versus column 5 as displayed in Figure 2.2b.

2.2

PROBABILISTIC DESCRIPTION OF RAINFALL

Rainfall events are difficult to predict accurately by deterministic models. Their occurrence is uncertain, and the rainfall depth and duration are highly variable in time and space. In hydrology, we treat rainfall events as random events, and we use probabilistic methods to determine the likelihood of their occurrence.

2.2.1

Return Period and Hydrologic Risk

Return period is defined as the average number of years between occurrences of a hydrologic event with a specified magnitude or greater. In the case of rainfall, both the rainfall duration and depth must be specified. For example, if the rainfall events

PROBABILISTIC DESCRIPTION OF RAINFALL

9

at a specified location are expected to produce a depth of 3.0 in. or more over a 24-hr period four times during the next 100 years, then the return period of a 24-hr, 3.0in. rainfall at this location is 100/4 = 25 years. We can alternatively state that the 25-year, 24-hr rainfall is 3.0 in. The exceedence probability p is defined as the probability that a rainfall event with a specified duration and depth will be equaled or exceeded in any one year. This probability is equal to the inverse of the return period Tr, that is, p = -

1 Tr

for T, > 1. (Probability is a dimensionless number that is always greater than zero and smaller than one.) If the 25-year, 24-hr rainfall is 3.0 in., then there is a 1/25 = 0.04 = 4% probability that a depth of 3.0 in. or higher will be produced over a 24-hr period in any given year. Note that we are treating the rainfall events as being purely random. In other words, if a 25-year event has already been exceeded this year, the probability that it will be exceeded again next year is still 4%. Rainfall events are often used as the basis for determining the design capacity of a stormwater structure. Because of the probabilistic nature of rainfall, however, there is always some chance that the design capacity of the structure will be exceeded. In other words, there is a hydrologic risk associated with any design. This risk is commonly defined as the probability that the design event will be exceeded one time or more during the service life of the structure. We can calculate the hydrologic risk as

$)

N

J = 1 - (1 where

J = hydrologic risk, TI = return period of the event used as a basis for design, and N = service life of the stormwater structure.

Example 2.2

A highway culvert is designed to convey a 25-year storm. Determine the hydrologic risk of this design if the expected service life of the culvert is 30 years. From Equation 2.2, J=l-

(

1--

,>,O

=0.71=71%

Example 2.3 Consider the culvert in the example above. What return period should be used as a basis for design if the allowed hydrologic risk is 0.10 (or lo%)?

10

RAINFALL FOR DESIGNING URBAN DRAINAGE SYSTEMS

Again, from Equation 2.2,

Solving for T,, we obtain Tr = 285 years. In practice, for economic reasons, we use a return period of 2-50 years in designing stormwater structures that allow hydrologic risks much higher than 10%. Therefore, flooding from a stormwater structure, such as a culvert or a street inlet, does not always mean that the structure was improperly designed. 2.2.2

Frequency Analysis

We use frequency analysis procedures in hydrology to derive meaningful information from historical data. For example, we can analyze the discharge measurements at a river location to determine the return periods associated with the different magnitudes of the discharge at that location. A rainfall event is characterized with a depth and duration. Therefore, a frequency analysis of rainfall aims to determine the return periods associated with different magnitudes of the rainfall depth for a specified duration. The first step in a frequency analysis is to reduce the historical rainfall records to an annual maximum series of rainfall depths for the duration selected. An annual maximum depth is the greatest depth of rainfall that has occurred during the year for a given duration. We should note that by “duration,” we do not necessarily mean the full duration of historic storms. For example, the actual full duration of a historic storm may be 42 min, while we are interested in the frequency analysis of 30-min storms. Suppose the rainfall depth produced during a 30-min portion of this 42-min storm is larger than that produced over any other 30-min duration during the year. Then we will use the rainfall during the 30-min portion of the 42-min storm as the annual maximum 30-min depth for this particular year. The next step is to fit a probability distribution to the annual maximum series thus obtained. Various probability distributions are available for analyzing hydrological data. Strictly speaking, we should evaluate the goodness of fit of a probability distribution to a particular data series by using a statistical test such as a chi-square test. However, these tests are beyond the scope of this text. Furthermore, experience shows that the extreme value type I distribution, also known as the Gumbel distribution, fits most rainfall data well. Therefore, this distribution is often used in practice for frequency analysis of rainfall data. For a given rainfall duration id, we can express the maximum rainfall depths as

Pr

+

= PTM K s

where

PT = rainfall depth for a specified return period ( T r ) , PTM = mean of annual maximum depths,

(2.3)

11

PROBABILISTIC DESCRIPTION OF RAINFALL

Table 2.2. Frequency Factor K for Extreme Value Type I Distribution

n

5

10

25

50

100

15 20 25 30 35 40 45 50 75 100

0.967 0.919 0.888 0.866 0.851 0.838 0.829 0.820 0.792 0.779 0.719

1.703 1.625 1.575 1.541 1.516 1.495 1.478 1.466 1.423 1.401 1.305

2.632 2.517 2.444 2.393 2.354 2.326 2.303 2.283 2.220 2.187 2.044

3.321 3.179 3.088 3.026 2.979 2.943 2.913 2.889 2.812 2.770 2.592

4.005 3.836 3.729 3.653 3.598 3.554 3.520 3.491 3.400 3.349 3.137

00

Source: Statistical Methods in Hydrology by C . T. Haan, 0 1 9 1 7 , Iowa State University Press. Used with permission.

s = standard deviation of annual maximum depths, and K = frequency factor. The frequency factor K depends on the probability distribution being used, the return period, and the length of the annual maximum series. The length of the series is equal to the number of years included in the original rainfall record, because a single rainfall depth represents each year in an annual maximum series. Kendall(l967) and Haan (1977) reported the values of the extreme value type I frequency factors K . Table 2.2 presented herein is extracted from Haan (1977), and it summarizes these values for different combinations of T' and n, where rz = length of the data series. The mean of maximum annual depths is determined by using PTM=-

C Pj n

(2.4)

while the standard deviation is calculated from

where Pj = maximum annual depth for the jth year, and j changes from 1 to n.

Example 2.4 A 25-year annual maximum series of 15-min storm depths is given in decreasing order in column 2 of Table 2.3. Determine the 15-min storm depths and average intensities associated with return periods of 5, 10, 25,50, and 100 years. Assume that the extreme value type I distribution fits the annual maximum series.

12

RAINFALL FOR DESIGNING URBAN DRAINAGE SYSTEMS

Table 2.3. Mean and Standard Deviation Example

fd

= 15 min

td =

30 min

~

Pj (in.)

Pj (in.)

p~~

P,d2 (in* j

-

rd =

min

120 min

~

Pj (in.)

pi (in.)

0.985 0.628 0.413 0.263 0.154

2.80 2.55 2.20 2.00 1.90

1.775 1.172 0.536 0.283 0.187

3.20 2.80 2.60 2.47 2.40

2.027 1.048 0.678 0.481 0.389

1.55 1.40 1.35 1.26 1.20

0.436 0.260 0.212 0.137 0.096

2.20 2.00 1.85 1.72 1.60

1.16 1.10 1.05 1.01 0.97

0.073 0.044 0.026 0.014 0.006

1.53 1.47 1.40 1.34 1.28

0.104 0.069 0.037 0.018 0.005

1.80 1.70 1.60 1.52 1.48

0.1 10 0.054 0.018 0.003 0.000

2.29 2.18 2.07 2.00 1.90

0.264 0.163 0.086 0.050 0.015

0.92 0.88 0.86 0.82 0.80

0.001 0.000 0.001 0.005 0.008

1.24 1.20 1.14 1.09 1.04

0.001 0.000 0.005 0.014 0.028

1.43 1.40 1.35 1.29 1.25

0.001 0.005 0.014 0.032 0.047

1.81 1.71 1.64 1.60 1.53

0.001 0.004 0.019 0.03 1 0.061

0.75 0.71 0.68 0.65 0.60

0.020 0.032 0.044 0.058 0.084

1 .00 0.95 0.90 0.86 0.82

0.043 0.066 0.095 0.121 0.150

1.21 1.18 1.16 1.12 1.08

0.066 0.083 0.095 0.121 0.150

I .46 1.40 1.35 I .29 1.22

0.100 0.142 0.182 0.237 0.310

0.56 0.53 0.50 0.48 0.46

0.109 0.130 0.152 0.168 0.185

0.78 0.74 0.7 1 0.68 0.65

0.183 0.2 19 0.248 0.278 0.3 11

1.05 1 .OO 0.93 0.86 0.83

0.174 0.219 0.289 0.369 0.407

1.16 1.09 1.07 1.06

0.380 0.444 0.47 1 0.499 0.5 13

22.25

2.300

'0.19

4.436

86.69

6.210

.4.41

8.594

1.20:

(in.) 0.89C

s (in.)

P,

td = 60

-

0.310

1.461 0.430

1.11

1.71t 0.509

0.598

We first calculate the mean and the standard deviation of the annual maximum depths by using Equations 2.4 and 2.5. Tabular calculations summarized in columns 2 and 3 of Table 2.3 yield PTM = 0.89 in. and s = 0.31 in. We will use Table 2.2 to pick the frequency factors. In this table, n = 25 since the annual maximum series contains 25 values. Then for the return periods of T, = 5 , 10, 25, 50, and 100 years, the frequency factors are obtained from Table 2.2 as 0.888, 1.575, 2.444, 3.088, and 3.729. respectively. Now, we can use Equation 2.3 to determine the 15-min, 5-year depth as PT = 0.89

+ (0.888)(0.31) = 1.17 in.

PROBABILISTIC DESCRIPTION OF RAINFALL

13

Likewise, for TI = 10 yr,

4. = 0.89 + (1.575)(0.31)

= 1.38 in.

We calculate the rainfall depths corresponding to return periods of 25, 50, and 100 years in the same manner as being 1.65, 1.85, and 2.04 in., respectively. To find an average intensity, we divide the rainfall depth by the duration. In this example the duration is 15 min = 0.25 hr. Then by dividing the calculated P’s by 0.25 hr, we obtain the average intensities of 4.66, 5.51,6.59,7.38, and 8.18 in./hr, respectively, for the return periods of 5, 10,25,50, and 100 years. 2.2.3 Intensity-Duration-Return Period Curves

The probabilistic relationships between the average rainfall intensity, duration, and return period are usually presented in graphical form as shown in Figure 2.4 for Norfolk, Virginia. These curves are often referred to as intensity-duration-frequency (IDF) curves. A visual inspection of the IDF curves will reveal that an infinite number of rainfall events with different average intensity and duration can have the same return period. Moreover, for a specified return period, the average intensity decreases as the duration increases. As expected, for the same duration, the average intensity is higher for longer return periods. Frequency analysis methods are used to develop the IDF curves. First, the annual maximum rainfall depths corresponding to various durations are extracted from the local historical rainfall data. Then a frequency analysis of annual maximum depths is performed for each duration as discussed in the preceding section. The results

-

i .F

20.00 15.00 10.00 8.00 6.00 4.00

2.00

2a,

a:88 0.60

a

0.40

$

0.20

.-E:

m

P

0o:a

0.06 0.04 0.02

FIGURE 2.4. IDF curves for Norfolk, Virginia. After VDOT (1980).

14

RAINFALL FOR DESIGNING URBAN DRAINAGE SYSTEMS

~~

td = 15 min

td = 30 min

f i =~0.890 in. I+M = 1.208 in. s = 0.310 in. -

TI

(years) K 5 10 25 50 100

0.888 1.575 2.444 3.088 3.729

s = 0.430 in. -

td = 60 min td = 120 min f i =~1.468 in. PTM= 1.776 in.

s = 0.509 in. -

s = 0.598 in.

-

(in.)

i (in.kr)

P (in.)

i Whr)

P (in.)

(in./hr)

1.59 1.89 2.26 2.54 2.81

3.18 3.77 4.52 5.07 5.62

1.92 2.27 2.71 3.04 3.36

1.92 2.27 2.71 3.04 3.36

2.31 2.72 3.24 3.62 4.01

1.15 1.36 1.62 1.81 2.00

P

i

P

(in.)

(in./hr)

1.17 1.38 1.65 1.85 2.04

4.66 5.51 6.59 7.38 8.18

i

are then plotted in the form of the IDF curves. Sometimes an annual exceedence series rather than an annual maximum series is employed. For example, an annual exceedence series extracted from a 25-year rainfall record contains the largest 25 values measured during this 25-year period. It is possible that more than one value in this series would come from the same year while the series may not contain any values from some of the years included in the 25-year period. IDF curves are readily available for most major cities, and they can be found in local drainage manuals and ordinances. In the absence of local IDF curves and rainfall records, the regional relationships, such as those developed by Hershfield (1961) can be used.

Example 2.5 The annual maximum rainfall depths are available for a 25-year period for 1 5 , 30-, 60-, and 120-min durations. These depths are tabulated in decreasing order of magnitude in columns 2,4, 6, and 8 of Table 2.3 for the durations shown. We are to develop the IDF curves for this location. In Example 2.4, we performed a frequency analysis of the annual maximum depths for the 15-min duration. To obtain the IDF curves, the same procedure is applied to the annual maximum data for the other durations being considered. The calculations are summarized in Tables 2.3 and 2.4, and the results are plotted in Figure 2.5.

2.2.4

Mathematical Intensity-Duration Relationships

IDF relationships can also be expressed in equation form. For a specified return period, two commonly used forms are a

-

i=td

-k b

DESIGN RAINFALL

i

and f = fp

if

fp
12,500. Between the laminar and turbulent states, a transitional flow can occur. The ratio of the inertial to gravitational forces acting on the flow is represented by the dimensionless Froude number, Fr, defined as TI

Fr=

m

(4.3)

68

RAINFALL EXCESS AND OPEN-CHANNEL FLOW IN URBAN WATERSHEDS

The flow is said to be at the critical state when Fr = 1.0. The flow is subcritical when Fr < 1.0, and it is supercritical when Fr > 1.0. The hydraulic behavior of open-channel flow varies significantly depending on whether the flow is critical, subcritical, or supercritical. 4.1.3 Open-Channel Flow Equations

Unsteady, gradually varied flow in open channels can be represented by the St. Venant equations of continuity and momentum written, respectively, as (4.4) and

-aaQ+t

a\. + gA-ax = gA(S0 - Sf)

a(Q2/A)

ax

(4.5)

where

x

= displacement in the flow direction,

t = time, qLAT= lateral inflow, and

Sf = friction slope. The friction slope represents the slope of the energy grade line, and we can evaluate it using the Darcy-Weisbach formula as

where

fd

is the friction factor. For laminar flow, C fd

(4.7)

=

in which C is the laminar flow resistance factor. Similar expressions are available for fd in the transitional and turbulent flow regimes. However, in practice, the Manning formula is commonly used for turbulent flow to evaluate the friction slope as

(=)*

Sf = n Q

3+

where

k = 1.0 m'/'/s = 1.49 ft'I3/s, and n = Manning roughness factor.

(4.8)

OPEN-CHANNEL HYDRAULICS

69

Table 4.1. Manning Roughness Factor, n

Depth range Channel material Concrete Grouted riprap Soil cement Asphalt Bare soil Rock cut

0-0.15 m (0-0.5 ft)

0.15-0.60 m (0.5-2.0 ft)

20.60 m (>2.0 ft)

0.015 0.040 0.025 0.018 0.023 0.045

0.013 0.030 0.022 0.016 0.020 0.035

0.013 0.028 0.020 0.016 0.020 0.025

Source: Adapted from Brown et al. (1996).

The values of the roughness factor are given in Table 4.1 for various channel materials. Strictly speaking, the Manning roughness factor varies with the flow depth. However, this variation is negligible for turbulent flow. Thus, if the roughness factor is to be treated as a constant for a given channel material, then the use of the Manning formula should be limited to turbulent flow. 4.1.4

Steady Gradually Varied Flow

As noted previously, Equations 4.4 and 4.5 are valid for unsteady, gradually varied flow conditions. If the flow is steady, that is, if there are no changes with respect to time, we can simplify Equations 4.4 and 4.5 by dropping all the partial differential terms with respect to time t . Also, by setting qLAT= 0, Equation 4.4 reduces to dx

(4.9)

In other words, with no lateral inflow, the discharge Q remains constant along the channel under the steady-state conditions. Likewise, Equation 4.5 reduces to (4.10) Noting that V = Q / A and referring to Figure 4.2, we can rewrite Equation 4.10 in the familiar finite difference form as (4.11) in which the subscripts U and D, respectively, denote the upstream and downstream sections, and Ax is the distance between the two sections. In Equation 4.1 1, Sf represents the average friction slope between sections U and D. Noting that (zu ZD)/AX = So, and (Ax)(&) = hf = head loss, Equation 4.11 can be rewritten as

Hu

- HD = hf

(4.12)

70

RAINFALL EXCESS AND OPEN-CHANNEL FLOW IN URBAN WATERSHEDS

4.1.5

Normal Flow

If the flow is uniform (i.e., constant flow characteristics along the channel), we can drop all the differential terms with respect to x in Equation 4.10. This simplifies the equation to Sf = So. We often refer to a steady, uniform flow as normal pow. Under this condition, the energy grade line and the water surface will be parallel to the channel bottom, and the Manning formula is appropriate for solution. It can be written as k 213 112 Q = -ARh So n

(4.13)

Strictly speaking, normal flow can occur only in long, prismatic channels in the absence of flow controls like weirs or other structures. However, in practice, channels are designed assuming that the flow is normal with the design discharge set equal to the peak discharge.

4.1 -6 Open-Channel Rating Curve A rating curve describes a relationship between the flow area A and the discharge Q at a channel section. Ideally, this relationship should be developed using field measurements. However, in the absence of field measurements, Equation 4.13 can be used to obtain a rating curve. Note that for a given channel section, n , So, and k are constant, and Rh is related to A. For certain channel section shapes, the rating relationship can be obtained analytically in the form of Q = eAm

(4.14)

in which e and m are constant. However, for most channel sections, e and m change with discharge, and we need to use the average values.

Example 4.1 This example was presented previously by Akan (1993) and is similar to an example reported earlier by Ponce (1989). The triangular channel shown schematically in Figure 4.3 has a slope SO = 0.001 and a roughness factor n = 0.05. The sides of the channel section are sloped as 5H: 1V , Determine an expression in the form of Equation 4.14 to represent the rating curve for this section.

FIGURE 4.3. Triangular channel section.

OVERLAND FLOW

71

From the geometry of the triangular section,

P = 2 y d m = 10.2y

Substituting these into Equation 4.13, we get

(E)

Q = - (5y2)(0.49y)2/3(0.001)1'2 Q =2.93~"~ Now, since A = 5y2, or y = 0.2A'I2, we obtain Q = 0.343A4l3

Therefore, e = 0.343 ft1I3/s and m = 413 for this section.

4.2

OVERLAND FLOW

Overland flow occurs in urban watersheds over impervious surfaces such as roofs, driveways, and parking lots, as well as pervious surfaces such as lawns. The rainfall excess will flow over these surfaces, under the effect of gravitational forces, in the form of sheet flow until it reaches a channel like a ditch or street gutter. Overland flow is a special type of open-channel flow with a very shallow depth. Therefore, the definitions and equations given in the preceding sections are applicable to overland flow as well. However, the definition of the state of overland flow needs additional consideration. Overland flow normally has a low Reynolds number Re as defined by Equation 4.2 since the flow depth is very small. Therefore, based on the Reynolds number alone, overland flow would be classified as laminar. However, many other factors affect the state of overland flow. For example, the rainfall impact and obstructions such as rocks, grass, and litter continuously introduce flow disturbances pulling the flow away from the laminar condition despite the low Reynolds number (Akan 1993). Therefore, it is reasonable to assume that the flow is generally turbulent. The governing equations of overland flow presented in the sections to follow are valid for both laminar and turbulent conditions. Most of the example applications, however, are for the turbulent state. The Manning formula, Equation 4.8 or 4.13, is used for turbulent overland flow. Because of the turbulent nature of the flow and its small depth, the Manning roughness factor for overland flow can be quite different from channel flow. For overland flow, all the factors affecting the flow resistance are lumped into an effective Manning

72

RAINFALL EXCESS AND OPEN-CHANNEL FLOW IN URBAN WATERSHEDS

Table 4.2. Effective Roughness Factor-Overland

Flow

n value

Surface type

0.01-0.013 0.01-0.015 0.01-0.0 16 0.012-0.3 0.012-0.033 0.008-0.01 2 0.06-0.12 0.16-0.22 0.06-0.12 0.10-0.16 0.30-0.50 0.04-0.10 0.07-0.17 0.17-0.47 0.053-0.13 0.10-0.20

Concrete Asphalt Bare sand Graveled surface Bare clay-loam (eroded) Fallow, no residue Conventional tillage, no residue Conventional tillage, with residue Chisel plow, no residue Chisel plow, with residue Fall disking, with residue No till, no residue No till (2040% residue cover) No till (60-100% residue cover) Sparse vegetation Short grass prairie Source: Akan (1985), with permission ASCE.

roughness factor. Table 4.2, compiled mainly from two sources (Woolhiser 1975; Engman 1983), presents the effective n values for different types of land surface. 4.2.1

Kinematic-Wave Model

Overland flow is normally unsteady and nonuniform. Therefore, we should apply the St. Venant equations (Equations 4.4 and 4.5) to solve overland flow problems. However, analytical solutions are not available for the St. Venant equations, and we need sophisticated mathematical models to solve them numerically. On the other hand, we can simplify the St. Venant equations for overland flow and still obtain reasonably accurate results. The kinematic-wave method is such an approximation and is adequate for most practical overland flow situations. Henderson (1966) and Eagleson (1970) reported detailed reviews of the kinematic-wave model for overland flow. The brief summary presented herein is similar to that previously reported by Akan (1993). Overland flow has a very shallow depth. Therefore, it can be viewed as flow in a wide rectangular channel with a flat bottom. For this type of flow, R h = D = y and T = W = width of the overland flow plane. It is convenient to carry out the overlandflow calculations for a unit width in terms of a discharge per unit width, 4 = Q/ W . For an overland-flow strip approximated by a rectangular plane of unit width with uniform characteristics, as shown in Figure 4.4, the St. Venant equation of continuity (Equation 4.4) is written as

-a4+ - = i aY ax

at

f

(4.15)

OVERLAND FLOW

73

FIGURE 4.4. Elements of an overland flow plane.

where i = rate of rainfall, and

f = rate of losses from rainfall. The equation of momentum, Equation 4.5, is simplified by dropping all the terms on the left-hand side. This results in Sf = SO. Thus, for a unit flow width, we can rewrite the Darcy-Weisbach equation (Equation 4.6 with 4.7) for laminar flow or the Manning formula (Equation 4.8) for turbulent flow in the form of

q = aym

(4.16)

where a and m depend on the flow resistance formula adopted. For laminar flow, m = 3 and

a = -8g so

(4.17)

(X)

(4.18)

cv

For turbulent flow, m =

and CY

=

sy2

Equations 4.15 and 4.16, combined, represent overland flow as a kinematic wave.

4.2.2

Overland Flow on Impervious Surfaces

For an impervious plane subjected to a constant rate of rain io, we can obtain an analytical solution to Equations 4.15 and 4.16 simultaneously. Such a solution would also be valid if the rate of rainfall excess i - f is constant and equal to io. The

74

RAINFALL EXCESS AND OPEN-CHANNEL FLOW IN URBAN WATERSHEDS

boundary condition is y = 0 at x = 0 (upstream end), and the initial condition is y = 0 everywhere at t = 0. Eagleson (1970) reported the details of this solution procedure based on the method of characteristics, which is beyond the scope of this text. The results are summarized herein. We assume that the overland flow plane is initially dry. At t = 0 the rainfall excess and, therefore, the flow commences. Under a constant rate of rainfall excess of infinite duration, the discharge at the downstream end of the plane would continue to increase until equilibrium is reached, and then it would remain constant. We can determine this equilibrium time or time to equilibrium by using (4.19)

where

re = time to equilibrium,

L = length of the overland flow plane, and

io = i

- f = constant rate of rainfall (or rainfall excess).

As we will see in a later chapter, the equilibrium time is sometimes referred to as time of concentration for overland flow. Under a rainfall excess of finite duration td the shape and the peak discharge of the runoff hydrograph depends on whether &J is greater than or less than te. 1. If t, 5 td (see Figure 4.5a), we calculate the rising limb for t 5 te by using

qL = Q(i0t)"'

(4.20)

where qL = discharge per unit width at x = L (downstream end). For t -= td, the flow will be in equilibrium with qL = ioL

te
t d (4.22) where yL = flow depth at the downstream end defined as

YL =

1/ i l l

($)

(4.23)

2. If t, > td (see Figure 4.5b). the rain ceases before the equilibrium is reached.

75

OVERLAND FLOW

a

0

120

240

360

480

600

720

840

960

1080 1200 1320

t (s)

FIGURE 4.5. Kinematic-wave overland flow hydrographs.

We still calculate the rising limb by using Equation 4.20 for 0 < t < td. The runoff hydrograph will be flat for td < t < tp with a discharge remaining constant at q L = a(i0tdlrn

(4.24)

where (4.25) The flow rates will decrease during the period when t > tp and we use Equations 4.22 and 4.23 to calculate the falling limb of the runoff hydrograph. The flat portion of the runoff hydrograph between td and t,, does not represent an equilibrium condition. While the flow rate at the downstream end is constant during this period, the depths and discharges will decrease at upstream sections. A thorough discussion of the method of characteristics, which is beyond the scope of this text, is needed to fully explain this phenomenon. However, it is evident that the cessation of rainfall does not decrease the flow at the downstream end until t > tp. The kinematic wave equations, Equations 4.15 and 4.16, are dimensionally homogeneous, and they are valid in any consistent unit system. However, coupling the kinematic equations with the Manning formula, Equation 4.8, will limit us to two commonly used unit systems unless we determine the values of k for other systems. The time and the length units should be second and foot, respectively, if we use k = 1.49 ft1I3/s. In that event, q will be in cfs/ft, i will be in ft/s, L and y will be in feet, etc. Likewise, if k = 1.O m1I3/s, then second and meter, respectively, should

76

RAINFALL EXCESS AND OPEN-CHANNEL FLOW IN URBAN WATERSHEDS

be used as the units of time and length with q in m3/s per m width or m3/s/m, i in ds, and L and y in meters.

Example 4.2 The length of a parking lot is L = 60 m, and it is sloped at So = 0.01. The surface of the lot is bare clay with a Manning roughness factor of n = 0.020. A rainstorm produces a constant rainfall excess at the rate of io = 20 mm/hr = 5.555 x lop6 mJs. We are to determine the runoff hydrograph at the downstream end of the parking lot if (a) td = 12 min, and (b) td = 6 min. We first calculate and re from Equations 4.18 and 4.19, respectively, using m = = 1.667, l / m = 0.6, and (m - l ) / m = 0.4, ( 1.O) (0.01 ) O . j cY=

te =

0.020

= 5.00 n ~ ' / ~ / s

60°.6

(5.00)o.6(5.555x 10-6)o.4

= 562 s = 9.36 min

1. For td = 12 min = 720 s, t, < td. Thus, the flow will increase between time zero and 562 s, and we calculate the rising limb using Equation 4.20 for 0 < t < 562 s. Part a of Table 4.3 summarizes these calculations with the resulting qL values tabulated in column 2. The discharge will reach the equilibrium value of 33.33 x 10-5 m3/s/m at t = t, = 562 s, and it will remain constant until the rain stops at t = fd = 720 s. To calculate the falling limb, the qL values in column 3 of Table 4.3 are arbitrarily chosen from the peak flow to zero. Then, column 4 is calculated using Equation 4.23, and column 5 is calculated using Equation 4.22. 2. For td = 6 min = 360 s, te > td. In other words, the rainfall excess will cease before the flow reaches equilibrium. The peak discharge will be smaller than the equilibrium discharge, and it will occur at t = 360 s. We calculate the rising limb using Equation 4.20 for 0 < t < 360 s. The maximum discharge is 15.87 x 10-5 m3/s/m as shown in column 2 of Table 4.3, part b. Next, we calculate the intermediate parameter t p , using Equation 4.25 as 360

60 + = 598 s 1.667 (1.667)(5.00)(5.555 x 10-6)o.667(360)0.667

tp = 360 - -

The discharge will remain constant at 15.87 x 10-5 m3/s/m between 360 and 598 s. Flow rates will fall after 598 s for t > t p . The falling limb is calculated using Equations 4.22 and 4.23, and the results are tabulated in part b of Table 4.3. To calculate the falling limb, the qL values in column 3 are chosen. Then, column 4 is calculated using Equation 4.23, and column 5 is calculated using Equation 4.22. Figure 4.5 displays the runoff hydrographs calculated in this example.

OVERLAND FLOW

77

Table 4.3. Kinematic Wave Model Example

(a)

(1)

(2)

4.2.3

0 120 240 360 480 562

0.00 2.54 8.08 15.87 25.64 33.33

0 120 240 360

0.00 2.54 8.08 15.87

(4)

(3)

Rising limb

(5)

Falling limb

33.33 24.00 15.00 10.00 5.00

3.12 2.56 1.93 1.52 1.00

720 828 915 1102 1332

15.87 12.00 8.00 4.00 2.00

2.00 1.69 1.33 0.87 0.58

598 685 813 1053 1336

Overland Flow on Pervious Surfaces

The analytical kinematic-wave solutions given in the preceding section are primarily for impervious surfaces under a constant rate of rainfall. These solutions can also be used for pervious surfaces if the rate of rainfall excess is assumed constant. If the rate of rainfall excess varies, as in most real life situations, an analytical solution is not available. In that event, we would need to solve Equations 4.15 and 4.16 numerically combined with an infiltration model by using a computer program. By generalizing the results of a computer model solving the kinematic-wave and the Green and Ampt infiltration equations simultaneously, Akan (1985) developed a chart, shown in Figure 4.6, to determine the peak overland flow discharge over pervious surfaces. The parameters of this chart are dimensionless and are evaluated as qP q; = iL I

(4.26) 0.6

(4.27)

Next Page 78

RAINFALL EXCESS AND OPEN-CHANNEL FLOW IN URBAN WATERSHEDS

0

0.5 a* 1.0

0

1.0

'

I

I

P

"

2.0

1.5

'

I

I

0.5 a* 1.0

0 1.0

I

0.8

I

I

p*

(

1.5 I

,

2.0 I

K*=0.3

FIGURE 4.6. Overland flow from pervious surfaces. From Akan (1985), with permission ASCE.

(4.28) (4.29) where qp = peak discharge per unit width,

i = rate of rainfall assumed to be constant, L = length of overland flow plane,

K = hydraulic conductivity of soil,

Pf = soil suction head, q5 = effective soil porosity,

Si = initial degree of saturation, td

= duration of rainfall, and

(4.30) with k = 1.0 m'I3/s = 1.49 ft1j3/s.

CHAPTER

5 CALCULATION OF RUNOFF RATES FROM URBAN WATERSHEDS

The land area that contributes flow (runoff) to a stormwater structure is usually called the watershed, catchment, or drainage basin of that structure. In other words, if the rainfall excess produced at some point in an urban area eventually contributes to the flow at a stormwater structure; this point is included in the watershed of that structure. The location of the structure is usually referred as the design point, the watershed outlet, or the basin outlet. As mentioned in the earlier chapters, stormwater projects are designed to accommodate a design runoff event. If historical runoff has not been measured at or near the design point, the first step in formulating the design runoff event is the selection of a design storm as discussed in Chapter 2. The second step is to determine the quantity of runoff (or rainfall excess) resulting from the design rainfall. Chapter 3 presented several methods to separate the losses from rainfall and to calculate the rainfall excess. The objective of this chapter is to calculate the flow rates at the design point resulting from the transport of the rainfall excess to the watershed outlet. The rainfall excess is transported to the design point by flowing over or through various elements, such as roofs, driveways, street gutters, and storm sewers. The overland and channel flow models discussed in Chapter 4 are useful in determining the flow through individual elements of an urban watershed. However, a typical urban watershed may include hundreds of overland flow and channel flow elements. Therefore, it is not feasible to consider each of these elements separately, as in a distributed model, when we are interested in the rates of runoff from the whole watershed. Instead, we use lumped models in which the hydrologic characteristics of the entire watershed are combined and typified by one or more parameters, simple mathematical expressions, or graphs. This chapter discusses the most commonly used lumped urban watershed models. Various sections of this chapter are adapted from Akan (1993). 94

BASIC CONCEPTS

5.1

95

BASIC CONCEPTS

The volume of runoff passing through a flow section is called its discharge, runoff rate, orflow rate. The runoff reaches the watershed outlet (or the design point) from different parts of the watershed at different times and rates. Therefore, the discharge at the watershed outlet during and after a storm event varies with time. A plot of the discharge versus time is called a hydrograph. A runoff hydrograph is generally bellshaped, although multipeaked hydrographs can result from variable rainfall rates. Theoretically, a runoff hydrograph can have a flat top if the rainfall excess occurs at a constant rate over a long duration.

5.1.1

Elements of Urban Runoff Hydrographs

The total runoff from a watershed consists of base flow and direct runoff components. The baseflow or dry-weatherflow results from the exchange of water between a stream and the connected groundwater aquifer. The direct runoff component is due to the rainfall excess that flows over the ground surface and possibly in storm sewers to reach the watershed outlet. The base flow is often negligible in small urban watersheds. Therefore, in this chapter, the term runoff hydrograph will refer to the direct runoff hydrograph. If present, the base flow rates need to be added to the runoff rates calculated here to find the total discharge. Let us adopt a simple conceptual rainfall-runoff model to construct a runoff hydrograph (Hjelmfelt and Cassidy 1975; Akan 1993) for the drainage basin shown in Figure 5.1. In the figure, point B represents the lowest point of the basin, the basin outlet. The flow timelines depicted indicate the time it takes the stormwater to reach

Equal flow time lines

A

l h

0.5 h

B, Outlet FIGURE 5.1. Sample conceptual basin.

96

CALCULATION OF RUNOFF RATES FROM URBAN WATERSHEDS

the basin outlet from that location. For instance, the rainfall excess produced at a point on the 1-hr timeline will take 1 hr to reach point B. The timelines have divided the drainage basin into four subareas marked 1, 2, 3, and 4, each having a drainage area of A1, A2, A3, and A4, respectively. The average flow times from subareas 1, 2, 3, and 4 to the basin outlet are 0.25, 0.75, 1.25, and 1.75 hr, respectively. Suppose some rainfall excess is generated in this drainage basin at a constant rate I and it lasts 2.5 hr. We will now construct the runoff hydrograph resulting from this rainfall excess. Let us assume that the flow time from anywhere within a subarea is equal to the average flow time of the subarea. Thus, no runoff will reach point B before t = 0.25 hr, and only subarea 1 will contribute to the discharge at B between 0.25 and 0.75 hr. This contribution will be at a rate equal to the product IA1. Subarea 1 will continue to contribute at this rate until 0.25 hr after the rainfall excess stops, that is, until t = 2.75 hr. Likewise, subarea 2 will contribute to runoff at B at a rate equal to IA2 between 0.75 and 3.25 hr. Table 5.1 shows the contributions from all the subareas during all the time intervals considered. The sum of contributions from each subarea will equal the total discharge at the design point. A plot of the discharge values thus obtained versus time will result in an approximate hydrograph in the form of a block diagram as represented by the solid lines in Figure 5.2. If we used a large number of subareas instead of just four, the resulting runoff hydrograph would be a smooth curve, displayed as a dotted line in Figure 5.2. The runoff hydrograph shown in Figure 5.2 has a rising limb between t = 0 and 2 hr, a flat portion between t = 2 and 2.5 hr, and a falling (recession)limb after the rainfall excess ceases at t = 2.5 hr. The flat portion represents an equilibrium state. The discharge between t = 2 and 2.5 hr, I (A1 A2 A3 A4) = ZA, is equal to the volumetric flow rate of the rainfall excess over the entire basin. For t < 2 hr (before equilibrium), the discharge is less than the incoming rainfall excess, and part of the water is being stored over the basin. The amount in storage will not change during the equilibrium state. The runoff will continue after the effective rain stops at t = 2.5 hr due to the release of water from storage. The rising limb of an actual

+ + +

Table 5.1. Sample Hydrograph Development

Time (hr) 0.25-0.75 0.75-1.25 1.25-1.75 1.75-2.25 2.25-2.75 2.75-3.25 3.25-3.75 3.754.25 4.254.75

From subarea 1

From subarea 3

From subarea 4

CALCULATION OF TIME OF CONCENTRATION

97

Q

0

0.5

1

1.5 2

2.5

3

3.5

4

4.5

t (hr)

FIGURE 5.2. Conceptual hydrograph construction.

hydrograph would be steeper than that of Figure 5.2, and the duration of the falling limb would be longer.

5.1.2 Definition of Time of Concentration

Time of concentration is often defined as the time required for stormwater to flow from the hydrologically most remote point in the basin to the basin outlet. It is also defined as the time required for all parts of a basin to contribute to discharge at the outlet simultaneously. It is interesting to note that t = 2 hr in our example (Table 5.1 and Figure 5.2) fits both definitions of the time of concentration. Figure 5.2 also shows that the flow will reach equilibrium at a time equal to the time of concentration. The runoff rate will remain constant after the time of concentration until the rainfall excess ceases. In other words, the maximum possible discharge under a constant rate of effective rainfall will be reached if the effective rain duration is equal to the time of concentration of the basin. This is one of the concepts underlying the well-known rational method discussed later in this chapter. 5.2 CALCULATION OF TIME OF CONCENTRATION Time of concentration represents the hydrologic response time of an urban watershed. It is an important parameter in many desktop hydrologic design methods, such as the rational method. It is also a required watershed characteristic in more comprehensive rainfall-runoff models. The time of concentration for a watershed is calculated using the longest flow path (with respect to travel time) within the watershed. We sometimes refer to the longest flow path as the hydraulic length of a watershed. The longest flow path is not always obvious. We may need to calculate the flow time along several possible paths before we can identify the one resulting in the largest travel time as the longest path.

98

CALCULATION OF RUNOFF RATES FROM URBAN WATERSHEDS

Different flow types, such as overland and channel flows, can occur along a flow path. When this occurs, we determine the travel times for the different flow segments separately and sum them up to determine the time of concentration. A number of time-of-concentration equations have been proposed for urban watersheds (Kibler 1982). Most of these equations are empirical and site-specific, and they may produce significantly different results when applied to the same problem. More commonly used empirical time-of-concentration equations are presented herein. Also presented are the kinematic time-of-concentration formulas, which are physically and theoretically based.

5.2.1 SCS Time-of-Concentration Method The Soil Conservation Service (SCS 1985) method is well documented and is used widely in engineering practice. The method presumes that water moves through a watershed as sheet flow, shallow concentrated flow, channel flow, or some combination of these. The time of concentration Tc is the sum of the travel (flow) times, Tf, calculated separately for the consecutive flow segments along the longest flow path. Sheetjow occurs on the land surface. For sheet flow, travel time Tf is calculated using (5.1) where n = effective Manning roughness factor (Table 4.2), L = flow length, P2 = 2-year,

24-hr rainfall, and

SO = land slope.

In Equation 5.1, Tf is in hours, L in ft, P2 in inches, and Cf = 0.007 for the customary US.units. If the metric system is used, then L is in meters, P2 in centimeters, and Cf = 0.029. After some distance (SCS suggests a maximum of 300 ft), sheet flow usually becomes a shallow concentrutedjow. The travel time for shallow concentrated flow is determined as L Tf = 3600V

where

Tf = travel time (hr),

L = flow length (ft or m), and V = average flow velocity (fps or d s ) .

CALCULATION OF TIME OF CONCENTRATION

99

The Manning formula is used to determine the average flow velocity, 213 112

V = kRh

0'

(5.3)

n

where k = 1.0 m'I3/s = 1.49 ft1l3/s, R h = A / P = hydraulic radius

(ft or m),

A = cross-sectional flow area (ft2 or m2>,

P = wetted perimeter (ft or m), So = slope (ft/ft or d m ) , and

n = Manning roughness factor. The SCS procedure assumes that Rh = 0.4 ft and n = 0.05 for unpaved areas, and Rh = 0.2 ft and n = 0.025 for paved areas. Substituting these values into Equation 5.3, we obtain

v = wso112

(5.4)

where w = 16.1 fps = 4.91 m / s for unpaved surfaces and w = 20.3 fps = 6.19 m/s for paved surfaces. Figure 5.3 is a graphical representation of Equation 5.4 in customary U.S. units. Channel flow is assumed to begin where surveyed cross sections have been obtained, where channels are visible on aerial photographs, or where blue lines (indicating streams) appear on the U S . Geological Survey quadrangle maps. Equations 5.3 and 5.2 are also used to determine the average velocity and the travel time for channel flow. In Equation 5.3, the flow area A and the wetted perimeter P are generally evaluated at bank full flow conditions.

Example 5.1 All three types of flow occur in an urban recreation park. Along the longest flow path, the length of the sheet flow segment is estimated as L = 120 ft with n = 0.20 and So = 0.01. The shallow concentrated flow occurs over unpaved land where L = 1800 ft and So = 0.015. The main channel has a length L = 5100 ft and a slope So = 0.005, and it can be approximately represented by a trapezoidal section having n = 0.025, A = 27 ft2, and P = 13 ft. The 2-year, 24-hr rainfall is 3.6 in. Determine the time of concentration Tc for this park. For the sheet flow segment, from Equation 5.1 with Cf = 0.007,

Tf= 0.007

(0.20)( 120)]03 = 0.30 hr (3.6)0.5(0.01)0.4

100

CALCULATION OF RUNOFF RATES FROM URBAN WATERSHEDS

Water course slope (%)

FIGURE 5.3. Shallow concentrated flow velocity. After SCS 1986).

For the shallow concentrated flow, from Figure 5.3 (or Equ :ion 5.4 with w = 16.1 fps), we obtain V = 2.0 fps. Then, by using Equation 5.2, we get 1800 = 0.25 hr 3600(2.0)

Tf =

For the channel flow segment, we first calculate the hydraulic radius as Rh = A / P = 27/13 = 2.08 ft. Then from Equations 5.3 and 5.2, respectively, we find

V = 1.49

(2.08)2/3(0.005)'/* = 6.87 fps 0.025

and Tf =

5100 = 0.21 hr 3600(6.87)

Therefore,

Tc = 0.30 5.2.2

+ 0.25 + 0.21 = 0.76 hr

Kinematic Time-of-Concentration Formulas

Morgali and Linsley (1965) reported an equation to calculate the time of concentration for overland flow in a rectangular catchment as

CALCULATION OF TIME OF CONCENTRATION

101

where Tc = time of concentration,

L = flow length, n = Manning roughness factor. k = 1.0 rn'l3/s = 1.49 ft113/s,

S = average slope of the catchment in the flow direction, and

i = rate of rainfall excess (assumed constant). Equation 5.5 is based on the kinematic-wave theory and is valid with a consistent set of units. Note that for overland flow under a constant rate of rainfall excess, the time of concentration is equal to the time to equilibrium, and therefore this equation is essentially the same as Equation 4.19. In terms of the working units, Equation 5.5 becomes

Tc =

0.94L0.6n0.6 i0.4~0.3

where Tc is in minutes, L is in feet, and i is in inches per hour. Time-of-concentration formulas, based on kinematic-wave theory, are available for a variety of geometrically simple basin configurations (Akan 1985, 1993). These configurations, shown in Figure 5.4, can be used to idealize various segments of urban watersheds. Type I is simply a rectangular plane, and we can use Equation 5.5 to calculate the time of concentration. Basin type I1 is a converging surface. As previously reported by Overton and Meadows (1976), the time of concentration for the converging surface, expressed in consistent units, is

(5.7) where (1 - r ) is the convergence factor, and r is defined in Figure 5.4. Basin type I11 consists of a cascade of planes. The time of concentration for this configuration, in consistent units, is (Overton and Meadows 1976)

where j = index representing a plane in the cascade,

102

CALCULATION OF RUNOFF RATES FROM URBAN WATERSHEDS

Type I I

Type Ill

Type v

Type IV

FIGURE 5.4. Various basin configurations. From Akan (1985), with permission ASCE.

N = total number of planes in the cascade, and

zj =

c j

Lm

(5.9)

m=l

Basin type IV includes a rectangular channel receiving runoff from overland flow planes on both sides. Assuming that the channel is wide, the time of concentration formula in consistent units becomes (Akan 1985)

'

1 =

io.4

[(m) Lono

0.6

~ 0 . 4 +

(B

+ L1 + L2)0,4

(%,"I

(5.10)

where B is the channel width, and W is the channel length (width of the overland flow planes). The subscripts 1 and 2 refer to the two overland flow planes, and c stands for the channel. Subscript 0 refers to the overland plane that has the larger equilibrium time. Basin type V is a generalization of type IV in which the channel receives overland flow from two composite catchments made of cascades of M and N rectangular planes. As reported by Akan (1985), the expression for the time of concentration, in consistent units, is

CALCULATION OF TIME OF CONCENTRATION

103

(5.11) where N refers to the number of planes in the cascade that has the greater equilibrium time. We should note that Equations 5.7-5.11 were derived assuming that the time of concentration is the same as the time to equilibrium. Where both overland and channel flows are involved, the sum of the equilibrium times of the two components is set equal to the time of concentration. Based on the simultaneous solutions of the kinematic-wave overland flow and Green and Ampt infiltration equations, Akan (1989) developed a time of concentration formula for infiltrating basins. For a consistent unit system,

(Ln>0,6 Tc =

+

k0.6~0.3(j ~)0.4

3.10K1.33Pf@(1- Si) i2.33

(5.12)

in which the terms are defined the same way as in Equation 5.5 and

K = hydraulic conductivity of the soil,

Pf = soil suction head, @ = effective soil porosity, and Si = antecedent degree of

saturation of the soil.

Equation 5.12 is valid for the parameter range K i0.4i. The Green and Ampt method was discussed in Chapter 3. As noted by Akan (1989, 1993), for an impervious surface ( K = 0), Equation 5.12 reduces to Equation 5.5. Also, for an initially saturated soil (Si = l.O), Equation 5.12 reduces to Equation 5.5 with a constant rate of rainfall excess i - K , replacing the rainfall rate i . In terms of the working units, Equation 5.12 becomes

0.94L0%0,6

+

Tc = ~ 0 . 3 ( i ~)0.4

186K'.33Pf@(l- Si) j2.33

(5.13)

where Tc is in minutes, i and K are in inches per hour, L is in feet, and Pf is in inches. The terms S, Si, and @ are dimensionless.

5.2.3

Kirpich Formula

A number of empirical, time of concentration formulas have been reported in the literature. Kibler (1982) presented a review and comparison of many of these formulas. One of the most popular is the Kirpich (1940) formula. It was originally developed from the SCS data for rural basins in Tennessee with well-defined channels and steep slopes. Since it was easy to use (but not necessarily appropriate), it found widespread

104

CALCULATION OF RUNOFF RATES FROM URBAN WATERSHEDS

use in urban applications. The Kirpich formula is employed to estimate both overland flow and channel flow times separately. If more than one flow segment is present along the flow path, the watershed time of concentration is set equal to the sum of the values calculated for the individual segments. The Kirpich formula is (5.14) where T, is in minutes, L is in feet (m), slope S is dimensionless, and C K = 0.0078 m i r ~ / f t O .= ~ ~0.0195 For overland flow on concrete and asphalt surfaces, T, is multiplied by 0.4, and for concrete channels by 0.2. No adjustment is needed for overland flow on bare soils or flow in roadside ditches. For overland flow on grass surfaces, multiply by 2.0 (Kibler 1982).

5.3 UNIT HYDROGRAPH METHOD The unit hydrograph method is employed to calculate the direct runoff hydrograph at the watershed outlet given the rainfall excess produced by a storm event. This method is categorized as a lumped method, since the physical characteristics of the watershed are not taken into account directly in the runoff calculations. Instead, these characteristics are combined into a mathematical procedure called a unit hydrograph. The unit hydrograph method is widely used. It is incorporated into many computer models, including the HEC-HMS model discussed in Chapter 10. 5.3.1

Unit Hydrograph Development

A conceptual direct runoff hydrograph resulting from a rainfall excess of unit depth and constant intensity for a particular watershed is called a unit hydrograph. The unit depth is 1 cm in the SI unit system and 1 in. in the customary U.S. system. We usually abbreviate a unit hydrograph as UH and use a subscript indicating the duration of the rainfall excess. For instance, the direct runoff hydrograph produced by a rainfall excess that has a duration of 3 hr and constant intensity of i n h r is denoted by UH3. Note that the depth of the rainfall excess is in./hr)(3 hr) = 1 in. Likewise, in the SI unit system, a rainfall excess of constant intensity of c d h r and a duration of 2 hr would produce a UH2. We can develop a unit hydrograph for a gaged watershed by analyzing the simultaneous rainfall and runoff records. Unfortunately, most small, urban watersheds are ungaged. However, there are several synthetic unit hydrograph methods available to develop a unit hydrograph for ungaged watersheds. Various physical characteristics of the watershed are taken into account in developing a unit hydrograph.

(4

3

5.3.1.1 Espey Ten-Minute Unit Hydrograph Espey and Altman (1978) proposed an empirical method to obtain a synthetic 10-min unit hydrograph for urban watersheds. This method was developed after analyzing the runoff records from 41

UNIT HYDROGRAPH METHOD

105

urban watersheds located in eight different states. The discussion of the Espey 10min unit hydrograph in this section is adapted from Akan (1993). As shown in Figure 5.5, we describe a 10-min unit hydrograph in terms of Qup = peak discharge of the unit hydrograph per in. of rainfall excess (cfshn.),

Tp = time of occurrence of the peak discharge (rnin),

TB = time base of the unit hydrograph (min), W50 = width W75

of the unit hydrograph at O S O Q , , (rnin),

= width for the unit hydrograph at 0.75QU, (rnin),

t A = time

at which the discharge is 0.50QUpon the rising limb (min),

tB = time

at which the discharge is 0.75QUpon the rising limb (rnin),

tE = time

at which the discharge is 0.75 Qup during recession (min), and

tF = time

at which the discharge is 0.50Qup during recession (rnin).

The basin characteristics considered in the empirical method are the following: L = main channel length from the upstream watershed boundary to the design point (ft), S = average slope of the main channel,

H = elevation difference in the channel bottom at design point and 0.8 L upstream (ft),

QUP

0.75 Q,

0.50 Q,

0 0

fA

fB

Tp

fE

fF

TB

FIGURE 5.5. Elements of Espey unit hydrograph. After Espey and Altman (1978).

106

CALCULATION OF RUNOFF RATES FROM URBAN WATERSHEDS

A = basin drainage area (sq mi),

I = percentage of impervious areas in the basin (%), n = Manning roughness factor of the main channel, and

4

= dimensionless conveyance factor which is determined from Figure 5.6.

We use the following equations to determine the 10-min unit hydrograph:

s=- H

0.8L 3.1~0.2341.57

Tp =

Qup

=

~ 0 . 2 10.18 5

3 1,620A0.96

(5.15)

(5.16) (5.17)

TP1.O’

TB =

w50 =

w75

=

125,890A

Q!f5 16,220A0,93

Q!f2 3,240A0.79

Q!p

(5.18) (5.19) (5.20)

Weighted Main Channel Manning “n“ Value FIGURE 5.6. Values of @ for Espey unit hydrograph. After Espey and Altman (1978).

UNIT HYDROGRAPH METHOD

107

(5.21) tg =

w75

Tp - 3

fE = Tp

2 w75 +3

(5.22) (5.23) (5.24)

With these equations we will be able to determine seven points on the unit hydrograph. We can then construct a graph passing through these points. However, a final check is needed to verify the area enclosed by the hydrograph represents 1 in. of direct runoff.

Example 5.2 Develop a 10-min unit hydrograph for a basin with the following characteristics: L = 9700 ft, H = 67 ft, I = 43.8%, n = 0.015, and A = 0.355 sq mi. First we obtain 4 = 0.62 from Figure 5.6 using n = 0.015 and I = 43.8%. Then using Equations 5.15-5.24 67 = 0.00863 (0.8)(9700) 3.1(9700)0.23(0.62)1.57 = 20 min (0.00863)0.25(43 .8)0.18 31,620(0.355)0,96 = 474 cfs (20) 1.07 125,890(0.355) = 128 min (474)0.95 16,220(0.355)0,93 = 21.4 min (474)0.92 3240(0.355)0.79 = 11.7min (474)0.7* 21.4 20.0 - - = 12.9 rnin 3 11.7 20.0 - - = 16.1 rnin 3

108

CALCULATIONOF RUNOFF RATES FROM URBAN WATERSHEDS

500 450 h

3

400

Zalculated points

350

2.300 a,

$250 c

8 200

a

150 100 50 0

0

20

40

80 Time (min)

60

100

120

140

FIGURE 5.7. Example Espey unit hydrograph. After Akan (1993).

Also, at t = t A and t = t F , the discharge is O S O Q , , = 237 cfs/in. Likewise, at t = t B and t = tE, the discharge is 0.75Qu, = 356 cfslin. A plot of the calculated points (the unit hydrograph) is shown in Figure 5.7. We now need to check if the unit hydrograph represents 1 in. of direct runoff. To do this, we read the discharges from the unit hydrograph at equal time intervals and tabulate them as shown in Table 5.2. The area enclosed by the hydrograph is equal to the volume of runoff. Therefore, Runoff volume = (2741 cfs)(5 min)(60 s/min) = 822,300 ft3 Dividing this volume by the basin area, the depth of rainfall excess is obtained as, Depth =

822,300 ft3 = 0.083 ft = 1 in. (0.355 sq mi)(2.788 x lo7 ft2/ sq mi)

Therefore, the hydrograph we have sketched is indeed a unit hydrograph. If the depth turned out to be different from 1 in., we would need to sketch another hydrograph through the seven calculated points to either increase or decrease the area under the curve. 5.3.7.2 SCS Unit Hydrograph The U.S. Natural Resources Conservation Service (formerly the Soil Conservation Service or SCS) recommends the use of a curvilinear dimensionless unit hydrograph that was developed by Victor Mockus (SCS 1985). This hydrograph is shown in Figure 5.8, and the ordinates are tabulated in columns 1 and 2 of Table 5.3, where

UNIT HYDROGRAPH METHOD

109

Table 5.2. Espey 10-Minute Unit Hydrograph Example

QU(cfdin.)

t (min)

0 60 160 320 474 395 310 230 180 135 105 80 60 47 38 30 25 20 17 14 10 9 8 I 5 2 0

0

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130

C Qu = 2741 CfS ~

Source: After Akan (1993)

Qu = discharge per in. of rainfall excess (cfdin.), Qup = peak discharge per in. of rainfall excess (cfshn.), t = time (hr), and tp = time of occurrence of the peak discharge (hr).

It should be noted that this dimensionless hydrograph specifies neither the peak discharge nor the timing of the peak discharge of a unit hydrograph. However, it specifies the shape of the unit hydrograph relative to the peak discharge and the time to peak. This shape represents the average shape of a large number of unit hydrographs from watersheds of different characteristics. We can convert the dimensionless hydrograph to a unit hydrograph of the desired duration if Qup and tp are known. The equations provided to determine Qup and tp

110

CALCULATION OF RUNOFF RATES FROM URBAN WATERSHEDS

1

0.9

0.8 0.7

$

0.6 0.5 0.4 0.3

0.2 0.1 0 0

0.5

1

1.5

2.5

2

3

4

3.5

t/t, FIGURE 5.8. DimensionlessSCS unit hydrograph,

Table 5.3. SCS Unit Hydrograph Example

(1)

(2)

tltp

QuIQup

0.0 0.2 0.4 0.6 0.8 1.o 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.4 3.8 4.2 4.6 5.0

0.000 0.100 0.310 0.660 0.930 1.000 0.930 0.780 0.560 0.390 0.280 0.207 0.147 0.107 0.077 0.055 0.029 0.015 0.010 0.003 0.000

(3)

(4)

~~

t

(min)

Qu (cfdin.)

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 170 190 210 230 250

0 36 113 240 338 363 338 283 203 142 102 75 53 39 28 20 11 5 4 1 0

4.5

5

Next Page UNIT HYDROGRAPH METHOD

111

from the watershed characteristics are 484A

Qup

=-

(5.25a)

tP

and tR

(5.26)

t --+tL p2

where A = watershed area (sq mi), tR = duration of tL = basin

rainfall excess (hr), and

lag time (hr).

The equation provided to determine the basin lag time t L is t L = 0.6Tc

(5.27)

where T, is the time of concentration. If we want to develop the 10-min unit hydrograph, UH1/6, we would use t~ = hr and the watershed’s time of concentration T,, to compute tp (Equations 5.27 and 5.26). With the time to peak, we would then be able to compute the peak discharge Qupfrom Equation 5.25a. We can convert the dimensionless hydrograph to a unit hydrograph of the desired duration after Qup and tp are found. We simply multiply the values on the vertical axis of Figure 5.8 by Qup and those on the horizontal axis by tp. Likewise, we can obtain a unit hydrograph in tabular form by multiplying the entries in column 1 of Table 5.3 by tp and those in column 2 by Qup. For the SI unit system, Equation 5.25a becomes 2.08A

Qup = -

(5.25b)

tP

where A is in square kilometers, Qup is in cubic meter per second per centimeter, and tp is in hours. Equations 5.26 and 5.27 are also valid for the SI unit system. It is important to note that, strictly speaking, the SCS dimensionless unit hydrograph method should be used only for tR = 0.2tp or tR = 0.133Tc. In practice, however, some latitude is allowed in the choice of tR, provided that t R 5 0.25tp or t~ 5 0.17Tc (US. Army Corps of Engineers 1987). A curvilinear unit hydrograph may be approximated by a triangular unit hydrograph for simplicity. The peak discharge Qup and the time of occurrence tp of the peak discharge can still be determined by Equations 5.25 and 5.26, respectively. However, the time base TB of a triangular unit hydrograph is usually computed using TB = 2.67tp

where tp and TB are in consistent units of time.

(5.28)

CHAPTER

6 STORMWATER DRAINAGE STRUCTURES

Stormwater drainage systems represent a significant portion of our urban infrastruture. They are made up of many structures that require proper design, installation, and maintenance. These drainage structures include street gutters, drainage inlets (grate, curb-opening, and slotted), storm sewers, manholes, junctions, culverts, and surface drainage channels.

6.1

DRAINAGE OF STREET PAVEMENTS

Stormwater on a street pavement can interrupt traffic. It can also contribute to accidents due to reduction in skid resistance, hydroplaning, and reduced visibility from splash (Johnson and Chang 1984). Therefore, effective removal of stormwater from street pavements is an important part of an urban stormwater management plan. Detailed procedures and charts for pavement drainage design are available in various publications (Johnson and Chang 1984; Brown et al. 1996). The information presented herein covers the basic and important concepts related to the design of curbs, gutters, and inlets and a summary of the design criteria reported previously by the Federal Highway Administration (Johnson and Chang 1984; Brown et al. 1996). 6.1.I

General Design Considerations

The design objective of pavement drainage systems is to keep the spread of water over the pavement below an allowable value for a specified return period. Large return periods are used for streets with high traffic volumes. Small return periods are used for lightly traveled roads. Table 6.1, which has been adapted from the Federal 147

148

STORMWATER DRAINAGE STRUCTURES

Table 6.1. Suggested Minimum Design Frequency and Spread

Road Classification

Design Frequency

Design Spread

High volume. divided, or directional < 70 km/hr (45 mph) > 70 km/hr (45 mph) Sag point

10-year 10-year SO-year

Shoulder 1 m (3 ft) Shoulder Shoulder 1 m (3 ft)

Collector < 70 km/hr (45 mph) > 70 km/hr (45 mph) Sag point

10-year 10-year 10-year

Local streets Low ADT"

5-year

High ADT

10-year

Sag point

10-year

+ +

driving lane Shoulder driving lane

i driving lane i driving lane

4 driving lane

Nore: ADT, average daily traffic. Source: After Brown et al. (1996).

Highway Administration (Brown et al. 1996), presents the suggested design return periods and allowable spreads for various types of roads. Roadway geometry plays an important role in pavement drainage. Longitudinal slopes higher than 0.5% are recommended for curbed pavements with an absolute minimum of 0.3%. Cross-slopes of 2% are recommended for most situations, since this slope provides adequate drainage without a significant effect on driver comfort and safety. It may be possible to increase the cross-slope for multilane streets, but slopes beyond 4% should not be used.

6.1.2

Flow in Gutters

Gutter flow calculations are performed to determine the flow depth and spread of water on the shoulder, parking lane. or pavement section under design flow conditions. The design discharge is often calculated using the rational method. Although, strictly speaking, the flow in a gutter is unsteady and nonuniform, in practice, we perform gutter flow calculations as if the flow is steady and uniform at the peak design discharge. Generally, this approach yields conservative results.

6.7.2.7 Triangular Gutters The Manning formula is slightly modified for gutter flow to account for the effects of the very small hydraulic radius of the flow. For a triangular gutter shown in Figure 6.1, the modified Manning formula is written as

'

513 l j 2

k,,T8'3SX = 2.64n

s,

DRAINAGE OF STREET PAVEMENTS

Triangular Section

Composite Section

149

V- Section

FIGURE 6.1. Various gutter and swale sections.

or

where Q = gutter flow, k, = conversion constant (1.O m'/3/s in metric units and 1.49 ft'l3/s in customary U.S. units), T = top width,

n = Manning's roughness,

Sx = cross slope, and SL = longitudinal bottom slope.

Obviously, the top width T also represents the water spread. Noting that y = SxT

(6.3)

Equation 6.1 can be written in terms of the flow depth y as

Also, note that the flow area A is expressed as

Example 6.1 A triangular gutter has a longitudinal slope of SL = 0.01, cross-slope of S, = 0.02, and Manning roughness of n = 0.016. Determine the flow depth and spread at a discharge of 2.0 cfs.

150

STORMWATER DRAINAGE STRUCTURES

Using Equation 6.2 with k,, = 1.49 ft'13/s, we find

T = [

(2.64)(2.0)(0.016)

I

3'8

= 9.33 ft

(1.49)(0.02)5/3(0.01)t~2

Then by using Equation 6.3, we get = (0.02)(9.33) = 0.19 ft

6.1.2.2 Composite Gutter Sections For a composite gutter section such as shown in Figure 6.1. Q=Qw+Qs

(6.6)

where Qw = discharge in the depressed section, and Qs = discharge in the section that is not depressed.

It can be shown that Q=-

Qs

1 - Eo

in which 1

EO

s wIsx

and (6.9) All geometric variables are depicted in Figure 6.1, A graphical solution to Equations 6.7 and 6.8 is given in Figure 6.2 (Akan 2000). Also, note that from the geometry y=a+TS,

(6.10)

and A = ;S,T*

+ iaw

where y = flow depth at the curb and A = flow area.

(6.1 1)

DRAINAGE OF STREET PAVEMENTS

151

225 200 175 150 125

. e

100

8

75 50

25 0 1.5

2

2.5

3

3.5

(a)

4.5

4

5

5.5

6

T/W

850 800 750

s

3

Q

(I)

P

m x

Y

700 650 600 550 500 450 400

350 300 250 200

150 100 6 (b)

6.5

7

7.5

8

8.5

9

9.5

10

10.5

11

11.5

12

TIW

FIGURE 6.2. (a) Spread calculations for T / W > 6.0. From Akan (2000), with permission ASCE. (b) Spread calculations for T / W z 6.0. From Akan (2000), with permission ASCE.

152

STORMWATER DRAINAGE STRUCTURES

Example 6.2 A composite gutter section has the dimensions W = 0.5 m,SL = 0.008, S, = 0.02, and a = 0.05 m. The Manning roughness factor is n = 0.016. Determine the discharge in the gutter at a spread T of 2.0 m. We first calculate the cross-slope of the depressed gutter S, by using Equation 6.9 as

s,. = 0.02 + 0.05 - = 0.12 0.50 Also, with reference to Figure 6.1, T, = T - W = 2.0 - 0.5 = 1.5 m. To find QS, Equation 6.1 can be rewritten for the triangular portion of the composite gutter having top a width Tj and evaluated as Qs

=

k,Tj

813 513 I f 2

S, S, 2.64n

-

(l.0)(1.5)8/3(0.02)5~3(0.008)1/2 = 0.0091 m3/s (2.64) (0.016)

Note that k , = 1.0 m1/3/s is used for the metric system. Now with S,/S, = 0.12/0.02 = 6, T / W = 2.0/0.5 = 4, and ( T / W - 1) = 4.0 - 1.0 = 3.0, by using Equation 6.8, we find Eo =

1

1

+ {6.0/ [ ( l + 6.0/3.0)8/3

-

1.01)

= 0.75

Finally, by using Equation 6.7 we get Q=-

0.0091 = 0.036 m3/s 1 - 0.75

Alternatively, we can obtain a solution to this problem by using Figure 6.2. With T / W = 4.0 and S,/S, = 6.0, the figure yields 2.64n Q 513

k,,S,

s, w813

= 74

Solving this expression for Q yields

Q=

74( 1.O) (0 . 0 2 p 3(0.008) '1' (0.50) 8/3 = 0.036 m3/s (2.64) (0.016)

Example 6.3 A composite gutter section has S, = 0.02, SL = 0.01, a = 2 in. = 0.167 ft, n = 0.016, and W = 2 ft. Determine the spread T at Q = 2.5 cfs. Solving this problem by using Equations 6.7 and 6.8 requires a trial-and-error procedure since the equations are implicit in T . In the trial-and-error procedure, we first guess the value of T and calculate the value of Q by using Equations 6.8

DRAINAGE OF STREET PAVEMENTS

153

and 6.7. If the calculated Q is the same as the given Q, then the guessed value of T is correct. Otherwise, we repeat the same procedure using another guess for T . We can eliminate the trial and error procedure by using Figure 6.2. Here we first calculate S, by using Equation 6.9:

s,

= 0.02

+ 0.167 = 0.104 2.0 ~

Then S,/S, = 0.104/0.02 = 5.2. Now we evaluate the dimensionless discharge parameter: 2.64n Q (2.64) (0.O 16) (2.5) = 76 (1.49)(0.02)5/3(0.01)1/2(2.0)8/3 knSx5 / 3 s,V 2W 813 Using this value along with Sw/Sx = 5.2, we obtain T / W = 4.25 from Figure 6.2. Therefore, T = 4.25 (2.0) = 8.5 ft. 6.1.2.3 Swale Sections V-shaped (Figure 6.1) and circular swale sections are used to convey runoff from pavements where curbs are not used. The flow within a V-section can be calculated using Equations 6.1 and 6.2 with

s, = sx, sx, sx, + s x 2

(6.12)

The flow in a circular swale or gutter can be calculated using (Brown et al. 1996) -Y= k c ( D

0.488 ~2Q . 6 n1 L ~ 0) . 5

(6.13)

where y = flow depth (m or ft),

D = diameter of circular gutter (m or ft), SL = longitudinal slope, and

k, = 1.179 in metric units and 0.972 in customary U.S. units. The top width of the flow within the circular section is expressed as (6.14)

Example 6.4 A V-section swale has S1, = 0.04, Sx2 = 0.06, n = 0.016, SL = 0.01, and T = 8 ft. Determine the maximum discharge this swale can convey without water spreading over the pavement surface. Also determine the depth of flow.

154

STORMWATER DRAINAGE STRUCTURES

For the flow not to spread over the pavement, the top width should not exceed 8 ft. Using Equation 6.12, we find (0.06) s, = (0.04) 0.04 + 0.06

= 0.024

Now, by using Equation 6.1, we obtain

Q=

( 1.49)(8.0)8/3(0.024)5~3(0.01)1/2 = 1.8 cfs

(2.64) (0.016)

Also, by using Equation 6.3, we get y = (0.024)(8.0) = 0.19 ft

Example 6.5 A V-section swale will be used in an 8-ft shoulder to convey 2.0 cfs. The longitudinal slope is SL = 0.008 and the Manning roughness factor is n = 0.016. Determine the cross-slopes and the depth of the swale. Solving Equation 6.1 for S, yields

sx

[

(2.64) (0.016) (2.0)

3/5

1

= 0.027

= (1.49)(8.0)s/3(0.008)1/2

Now, let us assume that Sxl = Sx2.Then, from Equation 6.12 we have

and Sxl = 2(0.027) = 0.054. Also, from Equation 6.3, y = (0.027)(8.0) = 0.22 ft.

Example 6.6 A circular swale with a diameter of D = 5 ft is to carry Q = 1.5 cfs. The Manning roughness factor is n = 0.016, and the longitudinal slope is SL = 0.01. Determine the required depth and the top width of the swale. Equations 6.13 and 6.14, respectively, yield

y = (5.0)(0.972)

[

(1.5)(0.016) (5.0)2.67(0.01)'/2

= 0.30 ft

and

The circular swale is required to have a top width of 2.38 ft and a depth of 0.30 ft.

DRAINAGE OF STREET PAVEMENTS

155

6.1.3 Pavement Drainage Inlets Inlets are used to collect stormwater runoff from pavements and discharge it into an underground conveyance system. The four major categories of inlets are grate inlets, curb opening inlets, combination inlets, and slotted inlets. Perspective views of these four different types of inlets are shown in Figure 6.3. The inlets can be installed with or without a depression of the gutter. The efficiency of an inlet is defined as

E = - Qi

(6.15)

Q

where E = efficiency, Q = total gutter flow rate, and Qi = intercepted flow rate.

The flow that is not intercepted by an inlet is called carryover or bypass. By definition, Qb

where

Qb

(6.16)

= Q - Qi

= carryover (bypass) flow rate.

Grate inlet

Curb opening inlet

Combination inlet

Slotted drain inlet

FIGURE 6.3. Inlet types. After Johnson and Chang (1984).

156

STORMWATER DRAINAGE STRUCTURES

6.1.3.7 Grate W e t s Grate inlets are effective where clogging with debris is not a problem. The efficiency of a grate inlet depends on the inlet and gutter characteristics and the flow in the gutter. To determine the efficiency of a grate inlet, the total gutter flow is treated as having two parts: frontal flow and side flow. The frontal flow is the portion of the total gutter flow within the width of the inlet. It is expressed as (6.17) where Qw = frontal discharge,

W = width of the depressed gutter or inlet, and

T = total spread of water in the gutter. Also. QS

=

Q - Qw

(6.18)

where Qs = side discharge corresponding to the flow outside the width of the inlet ( T - W). The ratio Rfof frontal intercepted flow to total frontal flow is expressed as (6.19a) and Rf = 1.0

for V I Vo

(6.19b)

where

Kf = conversion (0.295 s/m in metric units and 0.09 s/ft in customary U S . units), Qm, = frontal flow intercepted,

V = velocity of flow in the gutter, and

Vo = splashover velocity. Splashover velocity is the minimum velocity that will cause some water to shoot over the inlet. This velocity depends on the gutter length and type. Figure 6.4 displays the splashover velocities for several standard grates tested by the Federal Highway Administration. The ratio R, of intercepted side flow to total side flow is expressed as (6.20)

157

DRAINAGE OF STREET PAVEMENTS 13 12 -

,, -

h

p-1-7/8: Parallel " x 4"bars with 1-7/8"spacing p-1-118:Parallel 318x4" bars with 1-1/8 spacing Curved Vane: 4-112"vane spacing, " x 2 flat longitudinal bars,3-7/32 bar spacing on center 45OTil Bar: 4" vane spacing, "x4"flat longitudinal &' bar spacing on center

v)

P 9v

'8

.2; 0

s5

7-

c

5 -

[I (0

4-

-0

6-

6 -3

3Reticuline: "x4" flat longitudinal bars, 2-9/16 spacing on center, 3116x2 reticuline bars -Same as P-l-7/8 with added transverse bars spaced 4 on center

21 -

0 0

where Qsi

= side flow intercepted,

K , = conversion factor (0.0828 m0.5/s1.8for metric and 0.15 fto,5/s',8for U.S.), and L = length of grate.

The efficiency E of a grate inlet is evaluated by using

E = Rf-e w

Q

+ R,-

QS

Q

(6.21)

Example 6.7

A triangular gutter with S, = 0.02, SL = 0.01, and T = 8.5 ft carries Q = 2.5 cfs. A curved vane grate placed in this gutter has W = 2 ft and L = 2 ft. Determine the efficiency of this grate. We first determine the flow area by using Equation 6.5 as A = i(0.02)(S.5)2 = 0.72 ft2

158

STORMWATER DRAINAGE STRUCTURES

The average cross-sectional velocity becomes V = Q/A = 2.5/0.72 = 3.47 fps. Also, by using Equation 6.17 we have

[

Qw = 2.5 1.0 - (1.0 -

gy7]

= 1.28 cfs

and Qs = Q - Qw = 2.50 - 1.28 = 1.22 cfs. For the curved vane grate with L = 2 ft, the splashover velocity is obtained from Figure 6.4 as being VO= 5.95 fps. Because Vo > V in this case, by using Equation 6.19b, we obtain Rf = 1.0. Also by using Equation 6.20 we find R, =

"1

+

1 = 0.065 (0.15)(3.47)~~*]/[(0.02)(2.0)~~~]}

Finally, Equation 6.21 yields 1.28 E = 1.02.50

1.22 + 0.065-2.50 = 0.54

Thus, the intercepted flow is Qi = (0.54)(2.5) = 1.35 cfs, and the bypass is Qb = 2.5 - 1.35 = 1.15 CfS.

6.1.3.2 Curb-Opening Inlets Curb-opening inlets have certain advantages over grate inlets. They are less susceptible to clogging, and they do not interfere with traffic operations. However, the flow depth at the curb needs to be sufficiently large for effective performance of a curb-opening inlet. The efficiency of a curb-opening inlet is calculated as (6.22a)

E = 1.0

for L 2 LT

(6.22b)

where L = curb-opening length, LT = curb-opening length required to capture 100% of gutter flow,

and

(&)

0.6

LT = KcQ0.42St3

(6.23)

where K, = 0.817 s0.42/m0.26= 0.6 so.42/fto.26. For a depressed curb-opening inlet as shown in Figure 6.5, (6.24)

159

DRAINAGE OF STREET PAVEMENTS

A

Flow

W h d

L

a

A

In,

Section AA FIGURE 6.5. Depressed curb opening. After Johnson and Chang (1984).

with

s,

= s,

+ -Eo W U

(6.25)

where a = gutter depression as shown in Figure 6.5. The ratio of the flow in the depressed section to total gutter flow Eo can be calculated as discussed in Section 6.1.2.2.

Example 6.8 A curb-opening inlet is placed in a triangular gutter that has a longitudinal slope of SL = 0.01, cross-slope of S, = 0.02, and Manning roughness factor of n = 0.016. The curb-opening inlet has a length of L = 10 ft. Determine the flow intercepted by the curb-opening inlet when the gutter discharge is Q = 2 cfs. Equations 6.23 and 6.22a, respectively, yield LT = (0.6) (2.0)0.42(0.01)0.3

E)

= 25 ft

1.8

E = 1 - (1 -

= 0.60

Therefore, the intercepted flow is Qi = (E)(Q) = (0.6)(2.0) = 1.2 cfs, and the bypass flow is Q b = Q - Qi = 2.0 - 1.2 = 0.8 CfS.

Example 6.9 The composite gutter section considered in Example 6.2 has the dimensions W = 0.5 m, SL = 0.008, u = 0.05 m, and S, = 0.02 and a Manning roughness factor of n = 0.016. It was determined in the example that at a spread of T = 2.0 m, the total gutter discharge was Q = 0.036 m3/s and the frontal to total flow ratio was Eo = 0.75. Determine the efficiency of a curb-opening inlet placed in the composite gutter if the length of the inlet is L = 1.75 m.

160

STORMWATER DRAINAGE STRUCTURES

By using Equations 6.25 and 6.24, respectively, we find S, = 0.02

+ 0.05 -(0.75) 0.50

= 0.095

LT = 0.8 17(0.036)0~42(0.008)0.3

= 2.3 m

Then, Equation 6.22a gives

Therefore, Qi = ( E ) ( Q )= (0.92)(0.036) = 0.033 m3/s will be intercepted by the curb-opening inlet. 6.1.3.3 Slotted Inlets Slotted inlets can be used on both curbed and uncurbed sections. They offer little interference with traffic operations. Debris through the slotted inlets can accumulate in the pipes underneath. However, they can be accessed for cleaning with a high-pressure water jet. The flow interception capabilities of slotted inlets are similar to those of curbopening inlets provided that the slot width is greater than 4.5 cm or 1.75 in. Equations 6.22-6.25 are used to calculate the efficiency of slotted inlets. 6.7.3.4 Combination lnlets Combination inlets usually consist of a curb opening and a grate. The flow interception capacity of a combination inlet is about the same as the grate alone if the curb opening and the grate are placed side by side with nearly equal lengths. If this is the case, the curb inlet is neglected in efficiency calculations. Often, a combination inlet is used with part of the curb opening placed upstream of the grate. That part of the curb opening placed upstream will intercept part of the gutter flow as well as the debris in such installations. In this case, the curb-opening length upstream of the grate is considered in efficiency calculations.

Example 6.10 A combination inlet is installed in a triangular gutter carrying a discharge of 7 cfs. The gutter is characterized by SL = 0.01, S, = 0.025, and II = 0.016. The curb opening is 10 ft long and the grate is a 2-ft by 2-ft reticuline grate. An 8ft-long portion of the curb opening is upstream of the grate. Determine the flow intercepted by this combination inlet. We will first consider the upstream portion of the combination inlet. By using Equations 6.23 and 6.22a, respectively. we obtain LT = (0.6) (7 .0)0.42(0.O 1)o.3 E = 1.0-

[

1.0 - -

= 37 ft = 0.36

DRAINAGE OF STREET PAVEMENTS

161

Thus, the 8-ft-long portion of the curb opening intercepts (0.36)(7.0) = 2.5 cfs. The remaining flow is 7.0 - 2.5 = 4.5 cfs. The spread corresponding to this discharge is calculated using Equation 6.2 as (2.64)(4.5)(0.016)

I

8'3

T = [ (1.49) (0.025)'.67(0.01)0.5

= llft

Now, we will calculate the flow intercepted by the grate. By using Equation 6.17. we have

and Qs = Q - Q , = 4.5 - 1.9 = 2.6 cfs. The splashover velocity for the grate is Vo = 4.2 from Figure 6.4. Also, from Equation 6.5, the flow area just upstream from the grate is A = (0.5)(0.025)(11)2 = 1.5 ft2. Likewise V = Q / A = 4.511.5 = 3.0 fps. Because V < Vo, we have Rf = 1.0 from Equation 6.19b. Next, by using Equation 6.20 we get 1I

R -

= 0.10

- {[l + (0.15)(3.0)~~~]/[(0.025)(2.0)~~~]}

Then, from Equation 6.21, the efficiency of the grate is 1.9 E = 1.04.5

2.6 + 0.10-4.5 = 0.48

The flow intercepted by the grate becomes (0.48)(4.5) = 2.2 cfs. The total flow intercepted by the combination inlet is then 2.5 2.2 = 4.7 cfs. The overall efficiency is 4.717.0 = 0.67 and the bypass flow is 7.0 - 4.7 = 2.3 cfs.

+

6.7.3.5 Inlets in Sag Locations Inlets in sag locations are susceptible to clogging by debris since all the runoff entering the sag must pass through the inlet. The efficiency calculations should take clogging into account, especially for grate inlets. Curb-opening inlets are recommended for sag locations since they have the least tendency to clog. Hydraulic behavior of inlets in sag locations is similar to that of weirs at low flow depths and orifices at high flow depths. Between these depth ranges, flow will be in a transitional state. The capacity of grate, curb-opening, and slotted inlets operating as weirs is expressed as Qi = k,L,J2gd'.5

where

k , = weir discharge coefficient,

(6.26)

162

STORMWATER DRAINAGE STRUCTURES

Table 6.2. Sag Inlets Weir equation valid for

Inlet type

kw

Lwa

Grate Inlet

0.314

L+2W

d < koA0 kwLw

Curb-opening inlet

0.374

L

d s h

Depressed curbopening inletC

0.286

Slotted inlets

0.309

L

+ 1.8W L

~

d 5 (h

+ a)

d 5 0.06 m d I 0.2 ft

Definitions of terms

L = length of grate W = width of grate AO = clear opening areab L = length of curb opening h = height of curb opening

W = lateral width of depression d = TSx L = length of slot d = depth at curb

The weir length should be reduced where clogging is expected Ratio of clear opening area to total area is 0.8 for P-1-i-4 and reticuline grates, 0.9 for P-1-i and 0.6 for P-1-4 grates. Curved vane and tilt bar grates are not recommended at sag locations. See Figure 6.4 for additional information. If L > 3.6 m (12 ft), use the expressions for curb opening inlets without depression Source: After Brown et al. (1996). a

k0

AOU

Orifice equation valid for

Grate inlet

0.67

Clear opening areab

d > koAo kwLw

d = depth of water over grate

Curb-opening inlet (depressed or, undepressed horizontal orifice throat)c

0.67

(h)(L)

di > 1.4h

d = di - ( h / 2 ) di = depth of water at lip of curve

Slotted inlet

0.80

a

Definition of terms

opening h = height of curb opening (L)(W)

d ? 0.12 m d = 0.40 ft

L = length of slot W = width of slot d = deuth of water over slot

The orifice area should be reduced where clogging is expected. The ratio of clear opening area to total area is 0.8 for P-1-i-4 and reticuline grates, 0.9 for P-1-i and

0.6 for P-1-$ grates. Curved vane and tilt bar grates are not recommended at sag locations. See Figure 6.4 for additional information. See Figure 6.6 for other types of throats. Source: After Brown et al. (1996)

DRAINAGE OF STREET PAVEMENTS

163

L , = weir length, g = gravitational acceleration, and

d = flow depth.

The values and expressions for k , and L , for different types of inlets are presented in Table 6.2. In Table 6.2, the expressions given for curb-opening inlets without depression should be used for depressed curb-opening inlets if L > 3.6 m or L > 12 ft. Figure 6.6 defines ponding depths for various throat types in curb-opening inlets. The capacity of grate, curb-opening, and slotted inlets operating as orifices is expressed as (6.27)

Qi = k o A o J 2 g d

Horizontal throat

Inclined throat

d r < r ........ - - - -

d= 0:

Vertical throat

FIGURE 6.6. Various curb-opening inlets. After Johnson and Chang (1984).

164

STORMWATER DRAINAGE STRUCTURES

where k , = orifice discharge coefficient,

A , = orifice area, and d = characteristic depth as defined in Table 6.2 and Figure 6.6.

Values and expressions for k, and A , are also presented in Table 6.2 for different types of inlets. Combination inlets consisting of a curb opening and a grate are often used in sag locations. If the curb opening and the grate length are equal, the interception capacity of the combination inlet is equal to that of the grate under weir flow conditions. Under orifice flow conditions, the combination inlet has a capacity equal to the sum of the capacity of the curb opening and the grate. If the curb-opening inlet extends upstream of the grate, the upstream portion of the curb-opening inlet is considered separately.

Example 6.11 A curb-opening inlet with L = 4 ft, h = 0.3 ft, and S, = 0.03 is constructed in a sag location to intercept a design discharge of Qj = 5.5 cfs. Assuming there is no clogging, determine the flow depth at the curb and the spread. We will first assume that the curb-opening functions like an orifice under the design storm condition. This assumption will then be verified. From Table 6.2 we obtain k , = 0.67, A , = ( h ) ( L ) ,and d = di - h / 2 . Then, Equation 6.27 is rewritten as Qi = 0.67 ( h )( L )

(

di - -

,)O.,

Using the known values of Qi, h , L , and g, we solve this expression for di as 5.5

= 0.88 ft

Note that di > 1.4 h and therefore the assumption of orifice flow is verified. Finally, by using Equation 6.3, T = 0.88/0.03 = 29.3 ft. 6.1.4 Pavement Drainage Inlet Locations In general, highway pavement drainage inlets are designed to intercept stormwater runoff from the pavement only. Roadside channels and inlets are built to intercept runoff from large areas draining toward highways before reaching the pavement. However, stormwater inlets in urban areas often intercept runoff from pavement and off-pavement areas (see Sections 6.2.2-6.2.5). Roadway geometrical features often determine the locations of pavement drainage inlets. In general, inlets are placed at all low points in the gutter grade, median

DRAINAGE OF STREET PAVEMENTS

165

brakes, intersections, crosswalks, and entrance and exit ramp gores. The spacing of inlets placed between those required by geometric controls is governed by the design spread. In other words, the drainage inlets are spaced so that the spread under the design-storm conditions will not exceed the allowable spread. The rational method discussed in Chapter 5 is often used to determine the design discharge. As the reader will recall, the time of concentration is a key element in the rational method. Because pavement areas contributing flow to inlets are small, detailed time of concentrations calculations often result in values smaller than 5 min. At most sites rainfall data for durations less than 5 min are unavailable. Thus, a time of concentration of 5 min is often recommended in state and municipal drainage manuals. This leads to equal spacing of similar inlets. The gutter discharge used for inlet spacing consists of the carryover from the upstream inlet plus the stormwater runoff generated over the pavement section between the two inlets. We simply add the carryover from the upstream inlet to the peak flow rate obtained using the rational method for the pavement section between the inlets. This is an approximation, since the process is actually unsteady, and the timings of the peak pavement runoff and the carryover from upstream do not necessarily coincide. The procedure can be best explained by an example.

Example 6.12 Curb-opening inlets that have a length of 3 ft will be placed on a continuous grade in Norfolk, Virginia. The width of the pavement is 26 ft. The gutter is triangular with S, = 0.03. The longitudinal slope SL is 0.01 and the Manning roughness factor n is 0.016. The design return period TI is 10 years, and the runoff coefficient is 0.90. Determine the inlet locations by using a constant time of concentration of 5 min and an allowable spread of 6.5 ft. First consider the most upstream inlet. The drainage area for this gutter is A d = WpLd, where Wp = pavement width, and Ld = distance from the roadway crest (basin divide) to the inlet. We will use the Norfolk intensity-duration-return period curves (Figure 2.4) to determine the design-storm intensity. The rational method uses storm duration equal to the time of concentration. Thus, using a duration of 5 min and a return period of 10 years we obtain i = 7.3 i n h r = 1.69 x ft/s. There is no carryover discharge from upstream for this inlet. Therefore, by adapting the rational formula (Equation 5.44) for this situation we have

or Q = (0.90)(1.69 x 10-4)(26)Ld = 0.0039Ld

Now, substituting this in Equation 6.1 and using k, = 1.49 ft'/3/s, S, = 0.03, SL = 0.01, n = 0.016, and T = 6.5 ft, we find 0.0039Ld =

( 1.49)(6.5)s~3(0.03)5~3(0.01)1~2

(2.64) (0.016)

= 1.5 cfs

166

STORMWATER DRAINAGE STRUCTURES

We then obtain Ld = 1.5/(0.0039) = 385 ft. Therefore, the initial inlet can be placed 385 ft from the crest, and the discharge just upstream of the inlet will be Q = (0.0039)(385) = 1.5 cfs. In other words, a spread of 6.5 ft corresponds to a discharge of 1.5 cfs in the given gutter. Next we will calculate the carryover from this inlet. By using Equations 6.23 and 6.22a, we get LT = (0.6)( 1S ) ~ . ~ * ( O . O ~ ) ~ . ~

= 17.5 ft

Therefore Qi = (0.29)(1.5) = 0.44 cfs will be intercepted, and 0.44 = 1.1 pass by. For subsequent inlets, we will have Q = 1.1

Qb

= 1.5 -

+ 0.0039Ld = 1.5

since the given design spread of 6.5 ft occurs at a discharge of 1.5 cfs. Solving this expression for Ld, we obtain L d = 103 ft. Therefore, the subsequent inlets will be located 103 ft apart.

6.2 STORM SEWER SYSTEMS Stormwater is conveyed through inlets to buried pipes, which carry it to a point where it is discharged to a stream, lake, or ocean. Besides pipes, a storm sewer system contains various appurtenant structures including inlets, manholes, junction chambers, transition structures, flow splitters, and siphons. Detailed descriptions of these structures can be found elsewhere (Brown et al. 1996). Only a brief summary is given herein. Manholes (or access chambers) provide convenient access to the storm sewer system for inspection and maintenance, and they provide ventilation. Manholes also serve as flow junctions. Most manholes are made of precast or cast-in-place concrete. Typical manhole configurations are shown in Figure 6.7. Common manhole depths range from 1.5-4.0 m (5-13 ft), and typical diameters are 1.2-1.5 m (4-5 ft). Manholes are required where two or more storm drains converge, pipe sizes change, or a change in alignment or grade occurs. Manholes are also placed every 100 m or more along straight sections of small-diameter pipes for maintenance purposes. Drop manholes are used if an incoming pipe is considerably higher than the outgoing pipe. Figure 6.8 displays typical drop manhole configurations. Junction chambers are used where the joining storm sewers are larger than what can be accommodated by standard manholes. Junction chambers are usually made of precast or cast-in-place concrete. Flow channels and benches are typically built into these chambers to streamline the joining flows. Some junction chambers are

167

STORM SEWER SYSTEMS

2

2'

4'

4'

+

slop in. wr tt or 1 in. per tt P i p O.D.

Anernrti

22"-24'' clorr oponing

2'

h

4'

4'

H

k

FIGURE 6.7. Manhole configurations. From American Society of Civil Engineers (1970), with permission ASCE.

168

STORMWATER DRAINAGE STRUCTURES

FIGURE 6.8. Drop manholes. From American Society of Civil Engineers (1970), with permission ASCE.

equipped with a riser structure that extends to the ground surface to provide surface access and intercept surface flow. Manholes are generally used to transition from one pipe size to another. Occasionally, the transition is made without a manhole. Since abrupt changes in pipe size cause a significant amount of energy loss, transition sections are used. These sections provide gradual expansion (or contraction) from one size to another. Among the less commonly used appurtenant structures, $OM: splitters are junction structures in which an incoming flow is divided and diverted into two or more downstream storm sewers. Flow deflectors are used to minimize the energy losses in these structures. Maintenance of flow splitters is difficult and costly because of the deposition of material suspended in storm water flow. Inverted siphons (or depressed sewers) are used to carry the flow under an obstruction, like a stream. It is a common practice to construct at least two-barrel siphons (AASHTO 1991). Flap gates are used near storm sewer outlets if the system can potentially be back-flooded by high tides or high stages in the receiving system. These gates may be made of wood, cast iron, or steel, and they are commercially available for most common pipe sizes.

6.2.1 Storm Sewer Hydraulics Flow in storm sewers is usually nonsteady and nonuniform. However, for practical purposes, it is assumed to be steady at the peak discharge.

6.2.1.1 Storm Sewer Flow Equation The Manning formula is used to calculate the flow Q in a storm sewer: (6.29)

STORM SEWER SYSTEMS

169

where

k, = conversion (1 .O m1l3/s for SI units and 1.49 ft1I3/s for U S . customary units),

n = Manning roughness factor, A = flow area, R = hydraulic radius, and

Sf = friction slope. Alternatively, the friction slope can be determined from nQ

2

(w)

sf=

(6.30)

For full flow in a circular storm sewer, (6.31)

Note that the flow is normally pressurized under full flow conditions, and Sf > So, where So is the longitudinal bottom slope of the storm sewer. Just full %ow is a reference condition referring to the situation when the flow is steady and uniform and the flow depth y is nearly equal to the pipe diameter D. Just full flow discharge Qf is calculated using Equation 6.29 with A = Af, R = Rf, and Sf = So, where So = bottom slope of the storm sewer. That is, (6.33) Figure 6.9 can be used to determine the hydraulic elements of partially full circular storm sewers where y = flow depth. In Figure 6.9, Vf = Qf/Af = just full flow velocity.

Example 6.13 Determine the depth of flow y , flow area, and flow velocity in a storm sewer (D = 2.75 ft, n = 0.013, and So = 0.003) for a flow rate of 26.5 cfs. We first calculate the just full flow conditions. By using Equations 6.3 1, 6.32, and 6.33, we find Af = 5.94 ft2, Rf = 0.69 ft, and Qf = 29.1 cfs. Then, Vf = 29.115.94 = 4.90 fps. Now, by using Figure 6.9 with Q/Qf = 26.5129.1 = 0.91, we obtain y / D = 0.75, A/Af = 0.80, and V/Vf = 1.13. Therefore, y = (0.75)(2.75) = 2.06 ft, A = (0.80)(5.94) = 4.75 ft2, and V = (1.13)(4.90) = 5.54 fps.

Next Page 170

STORMWATER DRAINAGE STRUCTURES

1.3 1.2

1.1

1

'2 4

0.9 0.8

0.7 0.6

6 0.5

a 0.4

0.3 0.2

0.1

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Y/D FIGURE 6.9. Hydraulic elements of partially full pipes.

6.2.1.2 Head Loss Due to Friction The friction loss hf due to flow resistance in a storm sewer is calculated as hf = LSf

(6.34)

where L is the length of the sewer pipe and Sf is the friction slope. For a known discharge, the friction slope is determined using Equation 6.30. For partially full sewers we set Sf = SOfor simplicity. Also, we should remember that

where HU = energy head at the upstream end of the pipe, and

HD = energy head at the downstream end of the pipe. In addition to the energy losses due to friction in storm sewers, losses occur at transitions, bends, junctions, and other appurtenances. The procedures used to evaluate these losses are empirical, and they may vary from one locality to another. The procedures summarized herein were presented previously by the Federal Highway Administration (Brown et al. 1996), and they can be used in the absence of required procedures in local drainage manuals or regulations.

CHAPTER

7 STORMWATER DETENTION FOR QUANTITY MANAGEMENT

Urban development results in increased runoff volumes and flow rates, which may cause more frequent flooding and severe stream erosion downstream. Many communities use flow retardation structures to minimize the adverse downstream effects of urban stormwater runoff. These structures also tend to enhance stormwater quality (see Chapter 9). Various types of flow retardation structures include detention basins, retention basins, roof top storage, infiltration basins, and dry wells. Detention basins are small water impoundments with a capacity of about 10 acre-ft or less. Retention basins are usually larger, and they release stored water at a slower rate, mostly through controlled outlets. ZnJiltrationbasins allow stored water to percolate into the ground. Dry wells are small trenches excavated in porous soil and backfilled with rock. They also allow stored stormwater to percolate into the ground.

7.1

DETENTION BASINS

Although different flow retardation structures may be used under different circumstances, detention basins (ponds) are probably the most common. A detention pond can be created by damming a channel or by excavating a pond into the existing ground. Often, ponds are constructed by a combination of cut and fill. A detention basin must have at least one service outlet (to pass the base flow through the dam) and an emergency spillway (to pass floods around or over the dam safely). Multiple outlet basins can also be used to achieve more effective control of stormwater runoff. Figure 7.1 depicts a double-outlet detention basin. This chapter addresses several methods for analyzing and sizing flood protection detention basins. All the mathematical expressions included in this chapter are dimensionally homogeneous and can be used with any consistent unit system. 218

DETENTION BASINS

219

Higher outlet

Inflow

Emergency spillway Detention pond

Lower outlet OLltflow

FIGURE 7.1. Schematic of a detention basin. After Akan (1993).

We can evaluate the effect of a detention basin on a flood by routing the flood hydrograph through the basin. In a typical routing problem, the inflow hydrograph, the pond characteristics, and the initial conditions are known (or available). The outflow hydrograph is sought. The detention basin characteristics are normally prescribed as stage-storage and stage-discharge (outflow) relationships. These relationships can be in graphical, tabular, or equation form. The stage represents the elevation or height of the water surface measured from a horizontal datum. The storage (volume of water in the pond) increases with increasing stage, and the relationship depends on the shape and the size of the pond. The stage-discharge relationship is governed by the hydraulics of the outlet structures. From the given stage-storage and stage-discharge relationships, we can develop a relationship between the storage and the outflow rate. 7.1.1 Stage-Storage Relationship

For regular-shaped basins, the stage-storage relationship can be obtained from the geometry of the basin. For trapezoidal detention basins that have a rectangular base of W by L and a side slope of z (Figure 7.2), the relationship between the volume (or storage) S and the flow depth d is S =L

w d + ( L + W)Z d 2 + 422 d3

(7.1)

Dl

For irregular-shaped detention basins, the surface areas A s at various elevations h are obtained from contour maps of the detention basin site. Then

1

.......