Open Channel Flow by M.Hanif Chaudhry - BY Civildatas.blogspot.in.pdf

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Unformatted text preview: Civ ild ata s.b log spo t.in Visit : Civildatas.blogspot.in Visit : Civildatas.blogspot.in Visit : Civildatas.blogspot.in Open-Channel Flow Ci vil da tas .bl og sp ot. in Second Edition Visit : Civildatas.blogspot.in Visit : Civildatas.blogspot.in Ci vil da tas .bl Second Edition og sp Open-Channel Flow ot. in M. Hanif Chaudhry Visit : Civildatas.blogspot.in Visit : Civildatas.blogspot.in tas .bl og sp ot. in Dr. M. Hanif Chaudhry University of South Carolina Department of Civil and Environmental Engineering 300 Main Street Columbia, SC 29208 Library of Congress Control Number: 2007936602 e-ISBN 978-0-387-68648-6 da ISBN 978-0-387-30174-7 Printed on acid-free paper. Ci vil 2008 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com Visit : Civildatas.blogspot.in Ci vil da tas .bl og sp ot. in Visit : Civildatas.blogspot.in Visit : Civildatas.blogspot.in Ci vil da tas .bl To Shamim og sp ot. in Visit : Civildatas.blogspot.in Visit : Civildatas.blogspot.in Ci vil da tas .bl og sp ot. in Visit : Civildatas.blogspot.in Visit : Civildatas.blogspot.in in Visit : Civildatas.blogspot.in og sp ot. Preface Ci vil da tas .bl This book covers the introduction and analysis of flows in open channels for use as a text or as a reference book. Strong emphasis is given to the application of efficient solution techniques, computational procedures and numerical methods suitable for computer analyses. In addition, the coverage of unsteady flow is as detailed as that of steady flow and extensive up-to-date references are included. To facilitate learning, short computer programs in FORTRAN related to different chapters, the input data for sample problems, and the computer output are included as Appendices on a CD. These may be used as a guide for the development of software in other advanced languages, such as C, C++ , etc. Visual Basic, Mathcad, or Excel are suitable for the majority of these applications. The original text was based on the lecture notes for a course on openchannel flow for senior-level undergraduate and graduate students and an advanced graduate course on unsteady flow at Old Dominion University and at Washington State University. This is a revised version of the material, parts of which were used at the University of South Carolina in recent years. Suggestions and comments of students, instructors, and several reviewers are incorporated, as appropriate. References are updated throughout the book and additional problems are included. A chapter on sediment transport replaces the chapter on finite-element method and chapters 4 and 15 are supplemented with recent contributions on the topic. Photographs are used extensively to facilitate and enhance the learning of the subject matter. In recent years, the author has used Chapters 1 through 6, 9 and 10 and parts of chapter 7 in a 3-semester-hour course for senior-level undergraduate and graduate students in water resources and chapters 11 through 15 and part of chapter 17 in an advanced graduate class. Other instructors may prefer to a reduced coverage of chapters 6 and 7 and instead utilize chapters 7 and/or 11 and 16. Parts of different chapters may be used in a course on computational hydraulics or on hydraulic structures. Visit : Civildatas.blogspot.in Visit : Civildatas.blogspot.in Preface viii ot. in Thanks are extended to anonymous reviewers for their suggestions for the clarity of presentation. For the preparation of this edition, the assistance of Drs. Ahmed Sattar and Pranab Mohapatra for updating and Ken Young for converting the figures and illustrations for inclusion in Latex files is thankfully acknowledged. Ci vil da tas .bl og sp M. Hanif Chaudhry Visit : Civildatas.blogspot.in in Visit : Civildatas.blogspot.in og sp ot. Contents PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii BASIC CONCEPTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3 Classification of Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Steady and Unsteady Flows . . . . . . . . . . . . . . . . . . . . . . . . Uniform and Nonuniform flows . . . . . . . . . . . . . . . . . . . . . . Laminar and Turbulent Flows . . . . . . . . . . . . . . . . . . . . . . . Subcritical, Supercritical, and Critical Flows . . . . . . . . . . 1-4 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5 Velocity Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Momentum Cefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 1-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6 Pressure Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Static Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Horizontal, Parallel Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . Parallel Flow in Sloping Channels . . . . . . . . . . . . . . . . . . . Curvilinear Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7 Reynolds Transport Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8 Computer Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 2 4 5 7 7 8 8 9 11 13 15 16 16 16 17 18 20 21 21 26 CONSERVATION LAWS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 Conservation of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4 Equation of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Steady Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 28 28 29 31 33 Ci vil da tas .bl 1 2 Visit : Civildatas.blogspot.in Visit : Civildatas.blogspot.in x Contents 55 56 56 56 58 59 60 63 63 64 65 66 67 67 69 70 70 71 71 72 74 75 77 79 80 84 UNIFORM FLOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2 Flow Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3 Flow Resistance Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chezy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 88 88 89 89 tas da Ci vil 4 33 34 34 37 38 42 43 45 47 48 50 54 CRITICAL FLOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2 Rectangular Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specific Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specific force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wave Celerity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3 Non-Rectangular Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specific Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specific Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4 Application of Critical Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Constant-width Channel with Bottom Step . . . . . . . . . . . Horizontal, Variable-width Channel . . . . . . . . . . . . . . . . . . Example 3-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5 Location of Critical Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6 Computation of Critical Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trial-and-Error Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 3-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7 Critical Depths in Compound Channels . . . . . . . . . . . . . . . . . . . . General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 3-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Algorithm for Computing the Critical Depths . . . . . . . . . 3-8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .bl 3 og sp ot. in Steady, Uniform Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unsteady, Nonuniform Flow . . . . . . . . . . . . . . . . . . . . . . . . 2-5 Specific Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6 Application of Momentum and Energy Equations . . . . . . . . . . . . 2-7 Channel Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 2-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8 Hydraulic Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 2-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9 Hydraulic Jump at Sluice Gate Outlet . . . . . . . . . . . . . . . . . . . . . Example 2-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Visit : Civildatas.blogspot.in Visit : Civildatas.blogspot.in Contents xi ot. in Manning Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Other Resistance Equations . . . . . . . . . . . . . . . . . . . . . . . . . 100 4-4 Computation of Normal Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Example 4-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4-5 Equivalent Manning Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4-6 Compound Channel Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . 107 4-7 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 GRADUALLY VARIED FLOW . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5-2 Governing Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5-3 Classification of Water-Surface Profiles . . . . . . . . . . . . . . . . . . . . . 122 5-4 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5-5 Sketching of Water-Surface Profiles . . . . . . . . . . . . . . . . . . . . . . . . 127 Example 5-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Example 5-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5-6 Discharge From a Reservoir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Example 5-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5-7 Profiles in Compound Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Example 5-4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Example 5-5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 5-8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 6 COMPUTATION OF GRADUALLY VARIED FLOW . . . . . 151 6-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 6-2 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 6-3 Direct-Step Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Example 6-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 6-4 Standard Step Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Example 6-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 6-5 Integration of Differential Equation . . . . . . . . . . . . . . . . . . . . . . . . 166 6-6 Single-step Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 Euler method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Improved Euler method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Modified Euler Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Fourth-order Runge-Kutta Method . . . . . . . . . . . . . . . . . . 171 6-7 Predictor-Corrector Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 6-8 Simultaneous Solution Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Single and Series Channels . . . . . . . . . . . . . . . . . . . . . . . . . 175 Channel Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Example 6-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 Practical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Ci vil da tas .bl og sp 5 Visit : Civildatas.blogspot.in Visit : Civildatas.blogspot.in xii Contents in 6-9 Computer Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 6-10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 RAPIDLY VARIED FLOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 7-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 7-2 Application of Conservation Laws . . . . . . . . . . . . . . . . . . . . . . . . . 201 7-3 Channel Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Subcritical Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 7-4 Supercritical Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 Oblique Hydraulic Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 7-5 Weirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 Sharp-Crested Weirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 Broad-Crested Weirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 7-6 Hydraulic Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Ratio of Sequent Depths . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Length of Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Jump Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Jump types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Energy loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Jump Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Control of Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 7-7 Spillways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 Overflow Spillway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 7-8 Energy Dissipators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 Stilling Basins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Flip Buckets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 Roller Buckets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 7-9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 8 COMPUTATION OF RAPIDLY VARIED FLOW . . . . . . . . . 247 8-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 8-2 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 Characteristic directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 Coordinate Transformations . . . . . . . . . . . . . . . . . . . . . . . . 252 8-3 Computation of Supercritical Flow . . . . . . . . . . . . . . . . . . . . . . . . . 254 Finite-difference methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 8-4 Computation of Sub- and Supercritical Flows . . . . . . . . . . . . . . . 261 Numerical Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 8-5 Simulation of Hydraulic Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 Ci vil da tas .bl og sp ot. 7 Visit : Civildatas.blogspot.in Visit : Civildatas.blogspot.in Contents xiii ot. CHANNEL DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 9-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 9-2 Rigid-Boundary Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 Example 9-1 . . . . . . . . . . . . . . . . . . . . . . . . ...
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