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Summary
Summary
A clear, up-to-date presentation of the principles of flow in open channels
A fundamental knowledge of flow in open channels is essential for the planning and design of systems to manage water resources. Open-Channel Flow conveys this knowledge through the use of practical problems that can be solved either analytically or by simple numerical methods that do not require the use of computer software.
This completely up-to-date text includes several features not found in any other book on the subject. It derives one- dimensional equations of motion using both a simplified approach and a rigorous approach, and it explains the distinction between the momentum and mechanical energy equations. The author places great emphasis on identifying the types and locations of the control sections that are essential in analyzing flow profiles, and he includes a section on recently recognized nonunique flow profiles.
Offering numerous worked examples that are helpful in understanding the basic principles and their practical applications, this book:
* Presents the latest computational methods for profiling spatially varied and unsteady flow
* Includes end-of-section exercises that measure and build understanding
* Fully explains governing equations in algebraic and differential form
* Brings sluice-gate analysis completely up to date
* Covers artificial channel controls such as weirs, spillways, and gates, and special topics such as transitions in supercritical flow and flow through culverts
Written in metric units throughout, this excellent learning tool for senior- and graduate-level students in civil and environmental engineering programs is also a useful reference for practicing civil and environmental engineers.
Author Notes
Subhash C. Jain, PhD, is Professor of Civil and Environmental Engineering at The University of Iowa in Iowa City
Table of Contents
Preface | p. xi |
1 Basic Equations | p. 1 |
1-1 Introduction | p. 1 |
Types of Channels | p. 1 |
1-2 Governing Equations | p. 2 |
1-3 Basic Hypotheses | p. 3 |
Hydrostatic Pressure Distribution | p. 4 |
1-4 Differential Continuity Equation | p. 5 |
1-5 Differential Momentum Equation | p. 9 |
1-6 Differential Mechanical-Energy Equation | p. 16 |
1-7 Momentum and Energy Coefficients | p. 20 |
1-8 Governing Equations for Specific Flows | p. 21 |
Steady Uniform Flow | p. 21 |
Steady Varied Flow | p. 23 |
Unsteady Uniform Flow | p. 26 |
Unsteady Varied Flow | p. 26 |
1-9 Algebraic Equations of Motion | p. 27 |
Continuity Equation | p. 28 |
Momentum Equation | p. 29 |
Energy Equation | p. 30 |
Application | p. 31 |
1-10 Pressure Distribution in Curvilinear Flow | p. 33 |
A Rigorous Approach | p. 36 |
A-1 Differential Continuity Equation | p. 36 |
Three-Dimensional Equation | p. 36 |
One-Dimensional Equation | p. 37 |
Kinematic Boundary Condition | p. 39 |
A-2 Differential Momentum Equations | p. 42 |
Three-Dimensional Equations | p. 42 |
One-Dimensional Equation | p. 44 |
A-3 Differential Mechanical-Energy Equation | p. 50 |
Three-Dimensional Equation | p. 50 |
One-Dimensional Equation | p. 52 |
2 Steady Uniform Flow | p. 58 |
2-1 Governing Equations | p. 58 |
2-2 Open-Channel Resistance | p. 58 |
Manning Equation | p. 61 |
2-3 Normal Depth | p. 64 |
Compound Channels | p. 66 |
2-4 Equivalent Roughness | p. 69 |
2-5 Best Hydraulic Section | p. 70 |
Trapezoidal Section | p. 71 |
2-6 Design of Channels | p. 72 |
B Design Charts For Normal Depth | p. 75 |
3 Control Sections | p. 77 |
3-1 Propagation of Disturbances | p. 77 |
Celerity of Small Disturbance | p. 81 |
Upstream Propagation of Disturbance | p. 83 |
Hydraulic Jump | p. 85 |
3-2 Channel Transitions | p. 88 |
Specific Energy | p. 90 |
Critical Depth | p. 91 |
Rectangular Channels | p. 95 |
Compound Channels | p. 96 |
Change in Bottom Elevation | p. 98 |
Change in Channel Width | p. 101 |
Control Structures | p. 105 |
3-3 Locations and Types of Control Sections | p. 107 |
3-4 Flow Profiles without Channel Resistance | p. 108 |
C Surge Propagation | p. 116 |
D Coordinates of the Dimensionless Specific-Energy Curve | p. 118 |
4 Gradually Varied Flow | p. 120 |
4-1 Governing Equations | p. 120 |
4-2 Classification of Flow Profiles | p. 122 |
Backwater and Drawdown Curves | p. 123 |
4-3 Characteristics of Flow Profiles | p. 124 |
Water-Surface Slope at Zonal Boundaries | p. 124 |
Shapes of Flow Profiles | p. 124 |
Mechanism of Specific Energy Gain | p. 125 |
4-4 Sketching Flow Profiles | p. 127 |
Prismatic Channel with Change in Slope and Roughness | p. 128 |
Interaction of Controls | p. 133 |
Profiles in Channels with Transitions | p. 137 |
4-5 Nonunique Water-Surface Profiles | p. 143 |
Mild Downstream Reach | p. 143 |
Steep Downstream Reach | p. 146 |
4-6 Profile Analysis for Given Total Head | p. 148 |
Flow in a Long Channel | p. 148 |
Effect of a Downstream Control | p. 150 |
4-7 Location of Hydraulic Jump | p. 153 |
4-8 Profiles in Compound Channels | p. 154 |
5 Computation of Gradually Varied Flow | p. 158 |
5-1 Direct Integration Method | p. 158 |
Hydraulic Exponents | p. 161 |
5-2 Direct Step Method | p. 164 |
5-3 Standard Step Method | p. 167 |
5-4 The Ezra Method | p. 171 |
5-5 Inclusion of Form Losses | p. 174 |
5-6 Flow in Parallel Channels | p. 176 |
E Table of the Varied-Flow Function | p. 177 |
6 Spatially Varied Flow | p. 180 |
6-1 Lateral Outflow | p. 180 |
Governing Equations | p. 180 |
Analytical Solutions | p. 181 |
Numerical Integration | p. 187 |
6-2 Lateral Inflow | p. 189 |
Governing Equations | p. 189 |
Analytical Solution | p. 190 |
Numerical Integration | p. 192 |
7 Unsteady Flow I | p. 196 |
7-1 Governing Equations | p. 197 |
7-2 Characteristics Equations | p. 197 |
7-3 Initial and Boundary Conditions | p. 200 |
7-4 Simple-Wave Problem | p. 201 |
Subcritical Flow | p. 202 |
Supercritical Flow | p. 210 |
7-5 Dam-Break Problem | p. 212 |
Dry Downstream Channel Bed | p. 212 |
Finite Depth in the Downstream Channel | p. 216 |
7-6 Sluice-Gate Operation | p. 219 |
Sudden Complete Opening | p. 219 |
Sudden Partial Opening | p. 220 |
Sudden Partial Closure | p. 222 |
Sudden Complete Closure | p. 223 |
F Monoclinal Wave | p. 227 |
8 Unsteady Flow II | p. 229 |
8-1 Reservoir Routing | p. 229 |
8-2 The Muskingum Method | p. 234 |
Determination of K and X | p. 236 |
8-3 Simplification of the Momentum Equation | p. 238 |
Methods of Flood Routing | p. 240 |
8-4 Kinematic-Wave Method | p. 240 |
8-5 Diffusion-Wave Method | p. 243 |
The Muskingum-Cunge Method | p. 244 |
8-6 Dynamic-Wave Method | p. 247 |
8-7 Rating Curves | p. 248 |
8-8 Overland Flow | p. 250 |
9 Artificial Channel Controls | p. 262 |
9-1 Weirs, Sills, and Overfalls | p. 262 |
Sharp-Crested Weirs | p. 262 |
Sills | p. 266 |
Broad-Crested Weirs | p. 267 |
Overfalls | p. 269 |
9-2 Ogee-Crest Spillway | p. 272 |
9-3 Underflow Gates | p. 273 |
9-4 Venturi Flumes | p. 275 |
10 Special Topics | p. 277 |
10-1 Contractions and Expansions | p. 277 |
Subcritical Flow | p. 277 |
Supercritical Flow | p. 279 |
10-2 Flow in Bends | p. 295 |
Subcritical Flow | p. 295 |
Supercritical Flow | p. 298 |
10-3 Hydraulic Jump | p. 302 |
Energy Loss in the Jump | p. 302 |
Types of Jumps | p. 303 |
Length of the Jump | p. 304 |
Surface Profile of the Jump | p. 305 |
Control of the Jump | p. 306 |
Stilling Basins | p. 306 |
10-4 Flow through Culverts | p. 309 |
Discharge Equations | p. 310 |
Coefficient of Discharge | p. 313 |
10-5 Surges in Power Canals | p. 314 |
Meeting of Two Surges | p. 314 |
Surge Due to Sudden Load Rejection | p. 316 |
10-6 Roll Waves | p. 318 |
References | p. 321 |
Index | p. 325 |