Open-Channel Flow

by Chaudhry, M. Hanif

• ISBN13: 9780387301747
• ISBN10: 0387301747
• Edition: 2nd
• Format: Hardcover
• Copyright: 2007-12-01
• Publisher: SPRINGER - VERLAG

Summary

Analysis of open-channel flow is needed for the planning, design, and operation of water-resource projects. The use of computers and the availability of efficient computational procedures has simplified such analysis as well as made it possible to handle complex systems. This book presents modern computational procedures for such analyses and other necessary up-to-date information on calculating open-channel flow.

Table of Contents

Preface	p. vii
Basic Concepts	p. 1
Introduction	p. 2
Definitions	p. 2
Classification of Flows	p. 4
Steady and Unsteady Flows	p. 5
Uniform and Nonuniform flows	p. 7
Laminar and Turbulent Flows	p. 7
Subcritical, Supercritical, and Critical Flows	p. 8
Terminology	p. 8
Velocity Distribution	p. 9
Energy Coefficient	p. 11
Momentum Cefficient	p. 13
Example 1-1	p. 15
Pressure Distribution	p. 16
Static Conditions	p. 16
Horizontal, Parallel Flow	p. 16
Parallel Flow in Sloping Channels	p. 17
Curvilinear Flow	p. 18
Reynolds Transport Theorem	p. 20
Computer Program	p. 21
Summary	p. 21
References	p. 26
Conservation Laws	p. 27
Introduction	p. 28
Conservation of Mass	p. 28
Conservation of Momentum	p. 29
Equation of Motion	p. 31
Steady Flow	p. 33
Steady, Uniform Flow	p. 33
Unsteady, Nonuniform Flow	p. 34
Specific Energy	p. 34
Application of Momentum and Energy Equations	p. 37
Channel Transition	p. 38
Example 2-1	p. 42
Hydraulic Jump	p. 43
Example 2-2	p. 45
Hydraulic Jump at Sluice Gate Outlet	p. 47
Example 2-3	p. 48
Summary	p. 50
References	p. 54
Critical Flow	p. 55
Introduction	p. 56
Rectangular Channel	p. 56
Specific Energy	p. 56
Unit discharge	p. 58
Specific force	p. 59
Wave Celerity	p. 60
Non-Rectangular Channel	p. 63
Specific Energy	p. 63
Specific Force	p. 64
Application of Critical Flow	p. 65
Constant-width Channel with Bottom Step	p. 66
Horizontal Variable-width Channel	p. 67
Example 3-1	p. 67
Location of Critical Flow	p. 69
Computation of Critical Depth	p. 70
Design curves	p. 70
Trial-and-Error Procedure	p. 71
Numerical Methods	p. 71
Example 3-2	p. 72
Critical Depths in Compound Channels	p. 74
General Remarks	p. 75
Example 3-3	p. 77
Algorithm for Computing the Critical Depths	p. 79
Summary	p. 80
References	p. 84
Uniform Flow	p. 87
Introduction	p. 88
Flow Resistance	p. 88
Flow Resistance Equations	p. 89
Chezy Equation	p. 89
Manning Equation	p. 94
Other Resistance Equations	p. 100
Computation of Normal Depth	p. 102
Example 4-1	p. 104
Equivalent Manning Constant	p. 106
Compound Channel Cross Section	p. 107
Summary	p. 109
References	p. 115
Gradually Varied Flow	p. 119
Introduction	p. 120
Governing Equation	p. 120
Classification of Water-Surface Profiles	p. 122
General Remarks	p. 125
Sketching of Water-Surface Profiles	p. 127
Example 5-1	p. 129
Example 5-2	p. 131
Discharge From a Reservoir	p. 131
Example 5-3	p. 134
Profiles in Compound Channels	p. 136
Example 5-4	p. 137
Example 5-5	p. 140
Summary	p. 144
References	p. 149
Computation of Gradually Varied Flow	p. 151
Introduction	p. 152
General Remarks	p. 152
Direct-Step Method	p. 156
Example 6-1	p. 158
Standard Step Method	p. 160
Example 6-2	p. 164
Integration of Differential Equation	p. 166
Single-step Methods	p. 166
Euler method	p. 168
Improved Euler method	p. 169
Modified Euler Method	p. 170
Fourth-order Runge-Kutta Method	p. 171
Predictor-Corrector Methods	p. 172
Simultaneous Solution Procedure	p. 172
Governing Equations	p. 174
Single and Series Channels	p. 175
Channel Networks	p. 180
Example 6-3	p. 186
Practical Applications	p. 187
Computer Programs	p. 188
Summary	p. 188
References	p. 194
Rapidly Varied Flow	p. 199
Introduction	p. 200
Application of Conservation Laws	p. 201
Channel Transitions	p. 203
General Remarks	p. 203
Subcritical Flow	p. 204
Supercritical Flow	p. 208
Oblique Hydraulic Jump	p. 210
Weirs	p. 212
Sharp-Crested Weirs	p. 212
Broad-Crested Weirs	p. 214
Hydraulic Jump	p. 215
Ratio of Sequent Depths	p. 215
Length of Jump	p. 216
Jump Profile	p. 217
Jump types	p. 217
Energy loss	p. 219
Jump Location	p. 220
Control of Jump	p. 222
Spillways	p. 224
Overflow Spillway	p. 225
Energy Dissipators	p. 228
Stilling Basins	p. 231
Flip Buckets	p. 232
Roller Buckets	p. 234
Summary	p. 237
References	p. 241
Computation of Rapidly Varied Flow	p. 247
Introduction	p. 248
Governing Equations	p. 249
Characteristic directions	p. 251
Coordinate Transformations	p. 252
Computation of Supercritical Flow	p. 254
Finite-difference methods	p. 254
Boundary Conditions	p. 256
Verification	p. 258
Computation of Sub- and Supercritical Flows	p. 261
Numerical Solution	p. 261
Verification	p. 267
Simulation of Hydraulic Jump	p. 270
Governing Equations	p. 271
Numerical Solution	p. 271
Computational Procedure	p. 27
Results	p. 274
Summary	p. 276
References	p. 276
Channel Design	p. 279
Introduction	p. 280
Rigid-Boundary Channels	p. 280
Example 9-1	p. 282
Most Efficient Hydraulic Section	p. 283
Erodible Channels	p. 286
Permissible Velocity Method	p. 286
Example 9-2	p. 288
Tractive Force Method	p. 289
Example 9-3	p. 292
Alluvial Channels	p. 295
Regime Theory	p. 295
Example 9-4	p. 296
Summary	p. 297
References	p. 298
Special Topics	p. 301
Introduction	p. 302
Flow in a Channel Connecting Two Reservoirs	p. 302
Mild bottom slope	p. 302
Steep bottom slope	p. 307
Air Entrainment in High-Velocity Flow	p. 308
Flow Through Culverts	p. 312
Flow Measurement	p. 315
Velocity-area method	p. 316
Slope-area method	p. 316
Flumes	p. 317
Summary	p. 317
References	p. 319
Unsteady Flow	p. 323
Introduction	p. 324
Definitions	p. 324
Occurrence of Unsteady Flow	p. 326
Height and Celerity of a Gravity Wave	p. 326
Continuity equation	p. 327
Momentum equation	p. 328
Example 11-1	p. 330
Summary	p. 331
References	p. 332
Governing Equations for One-Dimensional Flow	p. 333
Introduction	p. 334
St. Venant Equations	p. 334
Continuity Equation	p. 335
Momentum Equation	p. 337
General Remarks	p. 340
Boussinesq Equations	p. 341
Continuity equation	p. 341
Momentum Equation in z-direction	p. 342
Momentum Equation in x-direction	p. 343
Integral Forms	p. 345
Summary	p. 346
References	p. 347
Numerical Methods	p. 349
Introduction	p. 350
Method of characteristics	p. 350
Characteristics	p. 353
Initial and Boundary Conditions	p. 356
Characteristic Grid Method	p. 359
Method of Specified Intervals	p. 361
Other Numerical Methods	p. 362
Summary	p. 363
References	p. 364
Finite-Difference Methods	p. 367
Introduction	p. 368
Terminology	p. 368
Finite-difference approximations	p. 368
Explicit Finite-Difference Schemes	p. 372
Unstable scheme	p. 372
Diffusive scheme	p. 372
MacCormack Scheme	p. 377
Lambda scheme	p. 379
Gabutti Scheme	p. 382
Implicit Finite-Difference Schemes	p. 385
Preissmann Scheme	p. 385
Beam and Warming scheme	p. 388
VasilievVasiliev, O. F. scheme	p. 390
Consistency	p. 390
Stability	p. 392
Example 14-1	p. 396
Summary	p. 397
References	p. 400
Two-Dimensional Flow	p. 407
Introduction	p. 408
Governing Equations	p. 408
Numerical Solution	p. 416
MacCormack Scheme	p. 419
General formulation	p. 420
Boundary conditions	p. 421
Gabutti Scheme	p. 423
General formulation	p. 423
Boundary conditions	p. 425
Artificial Viscosity	p. 426
Beam and Warming Schemes	p. 427
General formulation	p. 427
Factored schemes	p. 430
Implicit split-flux factoring	p. 431
Boundary conditions	p. 433
Finite-Volume Scheme	p. 434
Predictor part	p. 436
Corrector part	p. 436
Applications	p. 437
Partial breach or opening of sluice gates	p. 438
Propagation of a flood wave through channel contraction	p. 440
Comparison with other methods	p. 447
Summary	p. 447
References	p. 448
Sediment Transport	p. 453
Introduction	p. 454
Sediment property	p. 454
Sediment size	p. 455
Size distribution	p. 455
Sand-bed and gravel-bed streams	p. 457
Threshold of sediment motion	p. 458
Critical Shields stress for sediment mixture	p. 460
Condition for significant suspension	p. 460
Shields diagram	p. 461
The Exner equation of bed sediment conservation	p. 463
Exner equation for multiple size fraction	p. 464
Bed-load transport relations	p. 465
Bed load transport relations for poorly sorted sediment	p. 467
Suspended-load transport	p. 468
Entrainment Relations	p. 469
Resistance relations	p. 471
Separation of form drag	p. 472
Summary	p. 474
References	p. 475
Special Topics	p. 479
Introduction	p. 480
Rating Curve	p. 480
Flood Routing	p. 481
Reservoir Routing	p. 482
Channel Routing	p. 484
Kinematic Routing	p. 486
Diffusion Routing	p. 489
Muskingum-Cunge Routing	p. 491
Aggradation and Degradation of Channel Bottom	p. 492
Introduction	p. 492
Governing equations	p. 493
Numerical Scheme	p. 494
Applications	p. 497
Aggradation due to sediment overloading	p. 498
Knickpoint migration	p. 499
References	p. 502
Subject Index	p. 507
Author Index	p. 517
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