كتاب Handbook of Hydraulic Geometry - Theories and Advances
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منتدى هندسة الإنتاج والتصميم الميكانيكى
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 كتاب Handbook of Hydraulic Geometry - Theories and Advances

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مُساهمةموضوع: كتاب Handbook of Hydraulic Geometry - Theories and Advances    كتاب Handbook of Hydraulic Geometry - Theories and Advances  Emptyالخميس 09 مارس 2023, 2:31 am

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Handbook of Hydraulic Geometry - Theories and Advances
VIJAY P. SINGH
Texas A&M University

كتاب Handbook of Hydraulic Geometry - Theories and Advances  H_b_o_21
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Contents
Preface page xvii
Acknowledgments xx
1 Introduction 1
1.1 Definition 2
1.2 Analytical Basis forHydraulic Geometry Equations 4
1.3 Types of Hydraulic Geometry 5
1.3.1 At-a-Station Hydraulic Geometry 5
1.3.2 Downstream Hydraulic Geometry 6
1.3.3 Reach-Averaged Hydraulic Geometry 8
1.3.4 At-Many-Stations Hydraulic Geometry 11
1.4 Application of Hydraulic Geometry 11
1.5 Basis of Hydraulic Geometry Relations 12
1.6 Equilibrium State 12
1.7 Equilibrium Assumption 13
1.8 Validity of Power Relations 13
1.9 Stability of Hydraulic Geometry Relations 14
1.10 Variability of Exponents 15
1.11 Variation of Channel Width 17
1.12 Variation of Channel Velocity 17
1.13 Effect of Stream Size 18
1.14 Effect of River Channel Patterns 18
1.15 Effect of Hyper-concentrated Floods on Channel
Geometry Adjustment 22
1.16 Effect of Dam Removal 22
1.17 Power Relations for Drainage Basins 23
1.18 Effect of Land Use 23
1.19 Boundary Conditions 24
viiviii Contents
1.20 Organizationof Contents 24
References 25
2 Governing Equations 30
2.1 Introduction 33
2.2 Continuity Equation 34
2.3 Flow Characterization 34
2.4 Energy Equation 35
2.5 Gradually Varied Flow Equation 37
2.6 Flow Resistance Equations 37
2.6.1 Chezy’s Equation 38
2.6.2 Manning’s Equation 38
2.6.3 Einstein-Chien Equation 41
2.6.4 Darcy-Weisbach Equation 41
2.6.5 Friction Factor Equations 43
2.6.6 Shear Stress in Alluvial Channels 47
2.7 Sediment Transport 51
2.7.1 Criteria for Incipient Motion 51
2.7.2 Transport Equations 53
2.8 Stream Power 56
2.9 Entropy 61
References 62
3 Regime Theory 65
3.1 Introduction 67
3.2 Regime Theory 69
3.2.1 Lacey’s Equations 70
3.2.2 Blench’s Equations 75
3.3 Generalized Regime Theory 77
3.4 Process-Based Regime Equations 84
3.5 Natural Channels 89
3.6 Applications 98
3.6.1 Width between Incised River Banks 98
3.6.2 Scour between Bridge Piers 99
3.6.3 Scour Downstream from Piers 99
3.6.4 Aggradation Upstream from Reservoirs 99
3.6.5 Degradation Downstream fromReservoirs 99
3.6.6 Estimation of Dredging 100
3.6.7 Model Scales 100
3.6.8 Meandering 100Contents ix
3.6.9 Channel Design 102
3.6.10 Gravel-Bed River Response to Environmental Change 105
References 106
4 Leopold-Maddock (LM) Theory 110
4.1 Introduction 112
4.2 At-a-Station Hydraulic Geometry 112
4.2.1 Geomorphologic Data and Their Measurement 113
4.2.2 Bankfull Discharge 114
4.2.3 Effective Discharge 115
4.2.4 Frequency of Discharge 116
4.2.5 Variations in Hydraulic Characteristics 119
4.2.6 Relation of Channel Shape to Frequencyof Discharge 124
4.2.7 Suspended Sediment and Discharge at a Particular
Cross-Section 125
4.2.8 Width, Depth, Velocity, and Suspended Sediment at a
Given Discharge 127
4.2.9 Role of Channel Roughness and Slope in the
Adjustment of Channel Shape to Sediment Load 127
4.3 Downstream Hydraulic Geometry 130
4.3.1 Variation of Hydraulic Characteristics 131
4.3.2 Relation of Channel Shape to Frequencyof Discharge 131
4.3.3 Relation of Suspended Sediment to Discharge in a
Downstream Direction 132
4.3.4 Width, Depth, Velocity, and Suspended Sediment at a
Given Discharge 133
4.3.5 Width, Depth, and Suspended Load at a Variable Discharge 134
4.3.6 Relations between Width, Depth, Velocity, and Bed
Load at a Given Discharge 134
4.3.7 Channel Shape Adjustment during Individual Floods 135
4.3.8 Significance of Channel Roughness and Slope in
Adjustment of Channel Shape to Sediment Load 136
4.3.9 Stable Irrigation Canal: An Analogy to a Graded River 139
4.3.10 Sediment and Longitudinal Profile 140
4.4 Variation of Exponents 141
4.5 b-f-m Diagram 142
4.6 Analytical Determination of Exponents and Coefficients 147
4.7 Comparison with Stable Irrigation Channels 152
4.8 Reconstruction of Discharges 152
References 155X Contents
5 Theory of Minimum Variance 159
5.1 Introduction 160
5.2 Minimum Sum of Variances of Independent Variables 162
5.3 Minimum Total Variance of Components of Stream Power 167
5.4 Knight’s Formulation of Minimum Variance Hypothesis 172
5.5 Minimum Variance of Stream Power 177
5.6 Influence of Choice of Variables 178
5.7 Entropy Maximizing 181
References 184
6 Dimensional Principles 186
6.1 Introduction 187
6.2 Derivation of Hydraulic Geometry 190
6.3 Derivation of Width and Depth 192
6.4 Computation of Regime Channels 195
6.5 Computational Procedure 198
6.6 Method of Synthesis 205
References 209
7 Hydrodynamic Theory 210
7.1 Introduction 212
7.2 Smith Theory 213
7.2.1 Hydrodynamic Formulation 214
7.2.2 Derivation of Hydraulic Geometry 217
7.3 Julien-Wargadalam (JW) Theory 221
7.3.1 Continuity Equation 221
7.3.2 Resistance Equation 222
7.3.3 Sediment Transport Equation 223
7.3.4 Angle between Transversal andDownstream Shear
Stress Components 223
7.3.5 Hydraulic Geometry Relations 224
7.3.6 Calculation Procedure 226
7.3.7 Further Discussion 228
7.4 Parker Theory 232
7.5 Griffiths Theory 233
7.5.1 Derivation of Downstream Hydraulic Geometry 234
7.5.2 Stable Channel Design 236
7.6 Ackers Theory 237
7.6.1 Governing Equations 237
7.6.2 Hydraulic Geometry Equations 238Contents xi
7.6.3 Significance of Width-Depth Ratio 239
7.6.4 Comparison with Regime Relations 240
References 241
8 Scaling Theory 245
8.1 Introduction 247
8.2 Scaling Theory 247
8.2.1 Immobile Boundary Channels 248
8.2.2 Effect of Roughness 251
8.2.3 Mobile Bed 253
8.3 Comparison with Stable ChannelDesign Theories 254
8.3.1 Threshold Theory 254
8.3.2 Stability Index Theory 255
8.3.3 Regime Theory 256
8.4 Application to Channel Design 257
References 259
9 Tractive Force Theory 261
9.1 Introduction 262
9.2 Threshold Condition 263
9.3 Tractive Force Theory 264
9.3.1 Assumptions 265
9.3.2 Forces Acting on Threshold ChannelShape 265
9.3.3 Channel Geometry 268
9.3.4 Hydraulic Geometry 273
9.3.5 Downstream Hydraulic Geometry 277
9.3.6 Validity of Assumptions 280
9.4 Henderson Theory 281
9.4.1 Governing Equations of Threshold Theory 283
9.4.2 Bed Eoad Equation and Eacey’s Equations 287
9.4.3 Application to Design of Artificial Channels 288
9.4.4 Application to Rivers 290
References 290
10 Thermodynamic Theory 292
10.1 Introduction 294
10.2 Hypothesis 295
10.3 Determination of A* 295
10.3.1 Variation of Flow Energy 297
10.3.2 Variation of Flow Energy with Dimensionless Time 299xii Contents
10.4 Transport Equation 302
10.5 System of Regime Equations 303
10.6 Computation of Hydraulic Geometry 305
10.6.1 Basic Equations 305
10.6.2 Determination of Friction Coefficient 306
10.6.3 Computation of Geometry 307
References 336
11 Similarity Principle 338
11.1 Introduction 339
11.2 Dominant Discharge 340
11.3 Basic Parameters 340
11.4 Similarity Principle 341
11.4.1 Flow Velocity, FrictionVelocity, and Settling Velocity 341
11.4.2 Bed Shear Stress 342
11.4.3 Energy Slope 343
11.4.4 Hydraulic Roughness 344
11.4.5 Loss of Energy 344
11.4.6 Energy Gradient 345
11.4.7 Geometric and Dynamic Similarity 347
11.5 Comparison with Regime Relations 352
References 354
12 Channel Mobility Theory 355
12.1 Introduction 356
12.2 Sediment Transport 357
12.3 Hypothesis of Channel Mobility 359
12.3.1 Index of Mobility 359
12.4 Hydromorphometric Relationships 361
12.5 Tidal Estuaries Morphology 362
12.6 Relation of Channel Width to Depth and Degree of
Widening of the Channel of Tidal Estuaries 365
12.7 Longitudinal Channel Profile 366
12.7.1 Index of Mobility 367
12.8 Another Analysis of Generalized Mobility Index 368
References 371
13 Maximum Sediment Discharge and Froude Number Hypothesis 372
13.1 Introduction 374
13.2 Hypotheses 374Contents xiii
13.2.1 Flow Resistance 375
13.2.2 Sediment Transport 375
13.2.3 Energy Equation 376
13.2.4 Coefficient Ks 377
13.2.5 Water Surface Slope 378
13.3 Case 1: Straight and Meandering Single Beds 378
13.4 Case 2: Multiple Meandering Bed 380
13.5 Case 3: Meanders 380
13.6 Maximum Sediment Efficiency 386
13.6.1 Governing Equations 386
13.6.2 At-a-Station Hydraulic Geometry 388
13.6.3 Downstream Hydraulic Geometry 389
References 391
14 Principle of Minimum Froude Number 393
14.1 Introduction 394
14.2 River Stability and Froude Number 394
14.2.1 Channel Stability 395
14.2.2 Role of Potential Energy 395
14.2.3 Role of Sediment Movement 395
14.2.4 Role of Froude Number 395
14.3 Modeling and Simulation 396
14.3.1 Assumptions 396
14.3.2 Mass Conservation 396
14.3.3 Flow Resistance 396
14.3.4 Sediment Transport 397
14.4 Minimization of Froude Number 399
14.5 Testing 399
14.6 Another Look at Froude Number Minimization 402
References 405
15 Hypothesis of Maximum Friction Factor 407
15.1 Introduction 408
15.2 Formulation of Maximum Friction FactorHypothesis 408
15.3 Maximization 410
References 418
16 Maximum Flow Efficiency Hypothesis 419
16.1 Introduction 420
16.2 Basic Relations 420xiv Contents
16.2.1 Continuity Equation 420
16.2.2 Resistance Equation 421
16.2.3 Sediment Transport 421
16.2.4 Shape Parameter 422
16.3 Derivation of Hydraulic Geometry Relations 422
16.3.1 Optimum Hydraulic Geometry Relations 425
16.3.2 Lower Threshold Geometry Relations 425
16.3.3 Upper Threshold Geometry Relations 426
16.3.4 Average Channel Geometry Relations 427
16.4 Physical Evidence for Maximum Flow Efficiency 432
References 434
17 Principle of Least Action 436
17.1 Introduction 437
17.2 Adjustment of Alluvial Cross-Sections 438
17.3 Validity 440
17.4 Comparison 443
17.5 Stable HydraulicSection Using Calculus of Variation 444
References 448
18 Theory of Minimum Energy Dissipation Rate 450
18.1 Introduction 451
18.2 Theory of Minimum Energy Dissipation Rate 452
18.2.1 Flow Resistance Equation 452
18.2.2 Energy Dissipation Rate for Water Transport 453
18.2.3 Energy Dissipation Rate for Sediment Transport 453
18.2.4 Total Rate of Energy Dissipation 453
18.3.5 Sediment Concentration 454
18.3 Derivation of Hydraulic Geometry 454
18.3.1 Trapezoidal Section 454
18.3.2 Triangular Geometry 460
18.3.3 Rectangular Geometry 460
18.4 Analysis and Application 465
References 469
19 Entropy Theory 470
19.1 Introduction 471
19.2 Formulation 472
19.3 Derivation of At-a-Station Hydraulic Geometry Using Entropy 476
19.4 Derivation of Downstream Geometry Using Entropy 482Contents xv
19.5 Cross-Sectional Shape 482
19.6 Energy Gradient or Channel Slope 487
References 490
20 Minimum Energy Dissipation and Maximum Entropy Theory 491
20.1 Introduction 492
20.2 Downstream Hydraulic Geometry Relations 493
20.2.1 Primary Morphological Equations 497
20.2.2 Downstream Hydraulic Geometry Equations for a
Given Discharge 500
20.3 At-a-Station Hydraulic Geometry Relations 501
20.3.1 Morphological Equations 505
20.3.2 Derivation of At-a-Station Hydraulic Geometry Relations 507
References 508
21 Theory of Stream Power 510
21.1 Introduction 511
21.2 Definition 512
21.3 Two Postulates 513
21.4 Constraints for Hydraulic Geometry 513
21.5 Regime River Geometry 518
21.6 Stream Power and Probability 519
21.6.1 Governing Equations 520
21.6.2 Derivation of Regime Equations 522
21.6.3 Basic Regime Coefficient 523
21.7 Variation of Stream Power 524
21.8 Computation of Variation in Stream Power 527
References 527
22 Regional Hydraulic Geometry 529
22.1 Introduction 531
22.2 Relation between Discharge, Channel Shape, and Drainage Area 531
22.3 Regional Hydraulic Geometry 534
22.4 Relation between Mean Annual Discharge and Drainage Area 535
22.5 Leopold-Miller Extension of Horton Laws 536
22.6 Gupta-Mesa Theory of Hydraulic Geometry 538
22.6.1 Physical Variables andParameters 539
22.6.2 Dimensionless Ratios 539
22.6.3 Mass Conservation 540
22.6.4 Derivation of Horton Laws 541xvi Contents
22.6.5 Determination of Width Exponent 542
22.6.6 Determination of Velocity and Depth Exponents 542
22.6.7 Manning’s Roughness Coefficient and ItsExponent 545
22.7 Channel Geometry Method 546
22.8 Variation of Channel Geometry and Drainage Area 550
References 551
Index 555
Index
Acceleration due to gravity, 34, 37-38, 51, 294, 341,
344, 409
Ackers theory, 210, 237
Aggradation, 99
Alluvial channels, 5, 12, 15, 79, 90, 103, 357
Alluvial stream hydraulics, 339
Amplitude of meanders, 374
Angle of repose, 58, 283
Annual flood series, 116
Annual sediment load, 115
Antidunes, 8
Aquatic life, 23
Arc length of meanders, 89
Area ratio, 540
Armoring, 93
Armoured surface particle distribution, 257
Aspect ratio, 302, 376, 485 4-86
At-a-station hydraulic geometry, 110, 112, 124, 142,
146, 261, 388, 476, 491, 501-502, 507-508
Average cross-sectional flow velocity, 421
Average flow velocity, 41
Average sediment size, 6
Average settling velocity, 57
Average shear stress, 21
Backwater, 99
Bank erosion, 69, 90, 258
Bank full cross-sectional area, 550
Bank roughness, 103
Bank slope, 361
Bank stability, 2, 4, 65, 70
Bank stabilization, 465
Bank threshold equation, 280
Bankfull channel width, 547
Bankfull depth, 114, 152, 233
Bankfull discharge, 6, 8, 18, 96, 98, 102, 112,
114—116, 225, 233, 236, 247, 257, 261, 263,
290, 374, 396, 471, 529, 534
Bankfull elevation, 114
Bankfull flow, 7, 69
Bankfull width, 152, 233
Bar crests, 94
Bari Doab, the Punjab, India, 70
Bars, 5, 33, 68, 89
Basin Froude number, 539
Bathurst Equation, 44
Bed, 152
Bed armoring, 407
Bed configuration, 53
Bed degradation, 102
Bed features, 48
attidunes, 48
chutes, 48
dunes, 48
pools, 48
ripples, 48
surface waves, 48
Bed form, 68, 89, 374, 396-397, 473
Bed form factor, 61
Bed form resistance, 50, 397
Bed friction, 510-511
Bed gradation, 69
Bed load, 5-6, 53, 59, 87, 135, 236, 342, 374-375, 391
Bed load discharge, 376, 378
Bed load equation, 287
Bed load transport, 44, 55, 58, 134, 254, 349, 376
Bed load transporting capacity, 374
Bed material load, 236
Bed material size, 285
Bed ripples, 48
Bed roughness, 94, 350
Bed sediment load transport, 96
Bed sediment size, 71, 245
Bed sediment transport, 79
Bed shear, 345, 349
Bed shear stress, 48, 59, 342, 348-349
Bed slope, 41, 73, 85, 95, 245, 247, 257, 266,
275-276, 421
Bed threshold equation, 280
Bedload concentration, 391
555556 Index
Bedload transport equation, 386 387
Bed-sediment size distribution, 258
Bifurcation ratio, 540, 543
Blasius equation, 75
Blench equation, 75, 241
b-m-f diagram, 143, 146
boundary composition
cohesive, 19
noncohesive, 19
Boundary conditions, 3, 12, 15, 24
Boundary shear, 6
Braiding, 93
Bray equation, 44
Carnot’s formula, 344
Cayley formula, 448
Channel
braiding, 2
meandering, 2
sinuosity, 2
straight, 19
transitional, 19
wandering, 23
Channel bank, 24
Channel bars, 258
Channel bed, 2
Channel bed slope, 248
Channel cross-section shape, 419
Channel design, 102
Channel flow depth, 409
Channel form, 2, 5-6, 8, 15
Channel geometry, 22, 374
Channel geometry method, 546, 550
Channel gradient (slope), 394
Channel mobility, 357, 359 360
Channel pattern, 6, 19, 33, 53, 247, 374
Channel resistance, 65
Channel shape, 65, 70, 127, 273
Channel slope, 391, 414, 540
Channel stability, 146, 387
Channel width, 394, 421
Channel width at the water surface, 357
Channel-forming discharge, 80
Channels in equilibrium and regime, 24
Channels with erodible beds and banks, 24
Channels with rigid boundaries, 24
Chezy’s coefficient, 38, 72, 358
Chezy’s equation, 150, 453, 495, 497, 516, 545
Chezy’s friction factor, 187
Chezy’s roughness coefficient, 453, 494, 545
Cohesive banks, 84
Competence, 145, 364
Conservation of energy, 35-36
Continuity equation, 3, 34, 71, 88, 94, 149, 167, 210,
212, 221, 233, 235, 250, 280, 409, 414, 420,
432, 464, 517, 520-521
Continuity principle, 68
Conveyance, 38
Conveyance factor, 37
Cowan method, 39
Critical discharge, 54
Critical shear power, 524
Critical shear stress, 52
Critical shear stress, 58, 421
Critical shear velocity, 294
Critical velocity, 52, 358, 360
Critical velocity ratio, 72
Cross-section, 95, 110, 112, 114, 119-120, 123
Cross-sectional area, 22, 34, 41, 71, 74, 80, 270, 375,
396-397
Cross-sectional shape, 482
Cumulative distribution function, 484, 488
Cumulative frequency, 116-117, 132
Cumulative probability distribution, 478
Current-meter measurements, 114
Dam construction, 22
Dam removal, 22
Darcy-Weisbach equation, 41, 249, 343, 386,
494 495, 497, 522-523
Darcy-Weisbach friction factor, 38, 47, 95, 143, 164,
171, 176, 222, 540
Darcy-Weisbach resistance factor, 543
Degradation, 100
Density, 3
Density ratio, 51
Deposition, 68
Depth, 2-7, 12 13, 15, 30, 65, 68-70, 89, 95-96, 100,
103, 110, 112-113, 119, 123-124, 127,
130-131, 133 135, 160, 162, 212-213, 245,
247, 340, 351, 365
Depth ratio, 275
Design discharge, 87, 103
Dimensional principles, 186
Dimensionless principles, 24
Dimensionless slope, 383
Discharge, 2, 5-7, 12, 15, 69-70, 90, 95, 100, 103,
110, 112, 119-120, 123 124, 127
Discharge frequency, 110, 124, 132
Discharge hydrograph, 101
Discharge ratio, 275, 539-540
Distribution of energy, 472, 474
Dominant discharge, 69, 94, 340, 372, 374, 385, 396
Dominant grain size, 387, 389
Dominant water discharge, 386
Downstream discharge, 7
Downstream hydraulic geometry, 110, 112, 114, 130,
212-213, 221, 225, 245, 247, 261, 277, 386,
482, 491, 493, 497, 500
Drag, 341
Drag force, 52, 265-266, 342
Drainage area, 7, 14, 23, 116, 133, 215, 280, 340
Drainage basin, 23
Drainage-basin scale, 68
Dredging, 100
DuBoys equation, 53, 420Index 557
DuBoys sediment transport equation, 440, 444
DuBoys sediment transport formula, 421
Dune height, 345, 349-350
Dune length, 347
Dunes, 8, 48, 60, 68, 89, 129, 188, 190, 344, 375
Dynamic equilibrium, 4-5, 13, 67, 103, 160
Dynamic similarity, 249, 340, 347, 349
Dynamic viscosity, 35, 253, 294
Ecoregions, 529
Effective discharge, 115
Efficiency criterion, 390
Einstein bed load function, 282, 288
Einstein-Brown equation, 56
Einstein-Chien Equation, 41
Energy, 53
Energy dissipation, 12, 372, 374, 450 453, 456,
461-462, 465, 491, 494, 502
Energy dissipation rate and entropy theory, 24
Energy equation, 35, 188, 190, 376
Energy flux, 297
Energy grade line, 131
Energy gradient, 71, 345-346, 487 4-88
Energy potential, 141
Energy slope, 37-38, 53, 56, 248, 340, 342, 421, 452,
455, 487, 491, 495
Energy transfer, 297
Engelund and Hansen Equation, 55
Entropy, 30, 61, 300, 370
Entropy theory, 24, 470, 487
Equilibrium state, 12
Erosion, 2, 21, 68
gully, 125
nil, 125
sheet, 125
Euler-Lagrange equation, 446, 478
Exponents, 3, 7, 11, 13 15, 19, 120, 123-124, 133,
142, 147, 151, 166, 169, 171, 174
Extremal hypotheses, 408
Fall diameter, 341-342, 347
Fall velocity, 52-53, 60, 85, 232, 238, 341, 464
Fill, 67, 119, 139
First law of thermodynamics, 297
Flood crest, 129
Flood frequency, 115
Flood frequency analysis, 551
Flood hydrograph, 129
Floodplain width and surface area, 7
Floods, 17
Flow
critical, 34
laminar, 35
subcritical, 38
turbulent, 38
uniform, 38
Flow cross-section, 374
Flow depth, 53, 80, 99, 253, 396
Flow duration, 23
Flow efficiency, 419
Flow energy, 297, 299
Flow equation, 248
Flow resistance, 4, 7, 37, 68, 145, 375, 396-397, 454
Flow resistance equation, 37, 280, 440, 442, 452, 521
Flow turbulence, 57
Flow uniformity, 296
Flow-duration curve, 116
Fluid density, 35, 253, 294
Fluvial processes index, 524
Force ratio, 540
Form drag, 299, 342
Form factor, 439
Frequency distribution, 116, 388
Frequency of discharge, 116, 119, 125
Frequency of flow, 5
Friction, 2-3, 6-7, 12, 15, 36-37
Friction coefficient, 52, 306, 452
Friction energy, 438
Friction equation, 210
Friction factor, 38, 41, 43, 51, 75, 193, 197, 249, 251,
295, 306, 343, 346, 386, 407-109, 413—415,
417, 471, 473
Friction force, 265
Friction slope, 37, 41, 249, 252, 278
Friction velocity, 53, 341, 343
Frictional force, 540
Frictional resistance, 160
Frictional velocity, 351
Froude number, 34, 43, 70, 73, 85, 129, 145, 187, 190,
196, 248, 302, 305, 307, 343, 347-348, 374,
393-395, 398-399, 505, 542
Fully rough flow, 43, 375
Fully turbulent flow, 253
Ganguillet-Kutter (G.-K.) formula, 72
Generalized index of channel mobility, 368
Geometric and dynamic similarity, 340, 348
Geometric standard deviation of the distribution, 257
Geomorphic thresholds, 19
Gibbs equation, 292
Governing equations, 30
Graded equilibrium, 14
Gradedrivers, 119
Gradient, 65, 70
Gradually varied flow, 37
Gradually Varied flow Equation, 37
Grain diameter, 15
Grain resistance, 48, 50
Grain roughness, 252
Grain shear velocity, 251
Grain size, 7, 51
Grain size Reynolds number, 303
Granular roughness, 306
Gravel bed rivers, 43, 45, 232-234
Gravel bed streams, 106
Gravel transport, 95558 Index
Gravitational force, 540
Griffiths Equation, 44
Griffiths theory, 210, 233
Gully erosion, 125
Head
elevation, 35
pressure, 35
total, 35
velocity, 35
Head loss, 377
Henderson Equation, 43
Henderson theory, 281
Hey equation, 44
Hillslopes, 7
Horizontal length scale ratio, 350
Horton law, 536, 540-541
Horton ratio, 542-543
Horton’s law for velocity, 546
Horton’s law of stream areas, 531
Horton’s law of stream numbers, 540
Hydraulic depth, 73, 89, 271, 274
Hydraulic energy loss, 298
Hydraulic geometry, 2-A, 7-8, 11 17, 21, 23-24, 30,
34-37, 52-53, 89, 95, 105, 112, 120, 124,
141 143, 159, 161, 166, 172, 174, 182,
186-188, 212-214, 224, 227, 232, 238,
263-264, 280-281, 292, 338, 419, 422, 427
Hydraulic geometry equations, 280
Hydraulic geometry relations, 3, 247, 277, 280
Hydraulic geometry theory, 544
Hydraulic grade, 36
Hydraulic head, 36
Hydraulic mean depth, 89
Hydraulic or most efficient section, 462
Hydraulic radius, 2, 16, 34, 38, 41 42, 72, 80-81, 85,
96-97, 127, 131, 139, 221-222, 248, 271, 275,
279, 375-376, 385-386, 421, 440, 447-448,
452, 455, 485, 487, 494
Hydraulic roughness, 37, 344
Hydraulic similitude, 256
Hydraulically rough regime, 47
Hydraulically smooth regime, 47
Hydrodynamic forces, 299
Hydrodynamic theory, 24, 210
Hydroelectric power, 512
Hydrologic regions, 529
Hydromorphometric relations, 365
Hydromorphometric relationship, 361
Hyper-concentrated floods, 22
Immobile boundary channels, 248
Index of mobility, 359, 367
Inglis-Lacey equations, 85, 87, 240
Internal distortion, 37
Internal energy, 298-299, 474 475
Internal friction, 483
Irrigation canals, 11, 78, 84
Irrigation schemes, 11
Islands, 33
Julien-Wargadalam (JW) theory, 210
Kennedy equation, 88
Kennedy formula, 73
Keulegan equation, 41, 44
Keulegan type relation, 251
Kinematic viscosity, 51 52, 75, 89, 188, 199, 206,
240, 398, 539
Kinematic wave number, 43
Kinetic energy, 3, 36, 298, 300-301, 375, 377
Kutter’s resistance formula, 71
Lacey regime theory, 85
Lacey resistance equation, 72
Lacey theory, 100, 288-289
Lacey’s equation, 74, 286-287
Lacey’s regime equations, 523
Lacey’s regime theory, 281
Lacey-Malhotra equation, 87
Lagrange multipliers, 409, 456, 477, 483, 489
Lagrangian function, 410, 461, 478, 483
Laminar flow, 47
Laminar sublayer, 47
Land use, 23
Le Chatelier’s principle, 174
Least action, 436, 438
Least mobility, 213
Least-biased probability distribution, 477
Leopold and Maddock (LM) (1953) theory, 110
Leopold-Maddock (LM) empirical theory, xviii
Lift force, 52, 68, 265
Lift-to-drag ratio, 271
Logarithmic law, 52
Longitudinal bed profile, 374
Longitudinal frictional force, 58
Longitudinal profile, 102, 140-141, 366, 487
Lower threshold, 425
Manning equation, 38, 40, 43, 72, 94, 136, 213, 464, 474
Manning’s roughness coefficient, 38, 43, 71, 279, 453,
494, 545
Manning’s roughness factor, 3, 492
Manning-Strickler coefficient, 375
Manning-Strickler equation, 39, 43, 376
Manning-Strickler expression, 250
Manning-Strickler relation, 375, 378, 381
Manning-Strickler resistance equation, 254, 375
Mass conservation, 396, 540
Mass density of water, 89
Material number, 188
Material size, 6, 8-9
Maximization of Froude number, 374
Maximum bankfull depth, 89
Maximum conveyance, 446
Maximum discharge, 100Index 559
Maximum efficiency, 213, 387
Maximum entropy theory, 491
Maximum flow, 419
Maximum flow efficiency, 420, 432, 440
Maximum Flow Efficiency Hypothesis, 419
Maximum flow efficiency theory, 24
Maximum friction factor, 407 408, 410
Maximum hydraulic radius, 420, 433
Maximum sediment discharge, 372
Maximum sediment discharge and Froude number
hypothesis, 24
Maximum sediment transporting capacity, 420
Mean annual discharge, 17, 42, 117, 131, 535
Mean annual flood, 69, 290, 547
Mean annual water discharge, 95
Mean channel bed slope, 409
Mean channel depth, 357
Mean depth, 39, 374
Mean flow velocity, 394, 409
Mean particle diameter ratio, 252
Mean sediment diameter, 378
Mean stream velocity, 357
Meander belt width, 100101
Meander bends, 408
Meander geometry, 100
Meander length, 69, 101, 351
Meander loops, 299
Meander width, 100-102
Meandering, 40, 89, 100, 147, 161
Meandering beds, 380
Meandering channels, 387, 407
Meandering pattern, 338, 340
Meanders, 378, 380
Median discharge, 117
Meyer-Peter bed load formula, 375
Meyer-Peter-Muller (MPM) Equation, 54
Minimization of energy dissipation, 372
Minimum energy dissipation and maximum entropy
theory, 491
Minimum energy dissipation rate, 450
Minimum energy principle, 439
Minimum flow requirements, 11
Minimum Froude number, 393
Minimum stream power, 213, 420, 440, 452
Minimum stream power (MSP) hypothesis, 433
Minimum variance, 159, 161, 172, 213
Minimum variance theory, 24
Mobile bed, 253
Mobility number, 51, 190
Mobility theory, 24, 355
Momentum equation, 245, 247
Morphological constants, 412
Morphological equations, 491, 493, 497, 500, 505
Morphology
channel, 4
fluvial, 4
river, 20
Multiple Meandering Bed, 380
Newton’s law of motion, 33
Newton’s law of viscosity, 47, 145
Nikuradse equivalent grain size roughness, 95
Nikuradse’s sand roughness, 48
Nontidal rivers, 362, 366
Normal depth, 38
Normal force, 266
Normal probability distribution, 162
Normal velocity, 99
Overland flow, 263
Parker theory, 210, 232
Particle diameter, 52
Particle Reynolds number. 285
Perimeter, 80, 93
Periodicity, 359
Piezometric head, 36
Plan form, 89 90
Plane bed, 60
Pool, 12, 93, 512
Porosity, 263
Potential energy, 56, 298-299, 375-376, 395, 438,
493,510
Power functions, 3, 7, 13, 17
Power law, 150, 167
Power relation, 13, 20, 23
Prigogine’s principle, 474
Principle of least action, 24, 436, 438
Principle of maximum entropy, 182, 477, 483, 491,
504, 519
Principle of maximum flow efficiency, 440
Principle of maximum friction, 24
Principle of minimum Froude number, 24, 394
Principle of minimum potential energy, 439
Principle of similarity, 350, 352
Prismatic, 34
Probability density function, 61, 478, 483, 488
Production of entropy, 470
Prototype channel, 248
Quasi-equilibrium, 136, 160, 167, 174
Rate of bed load transport, 349
Recurrence interval, 115-116, 290
Regime canal, 71
Regime channel, 5, 67, 139, 186-187, 190, 195, 198,
292, 302
Regime channel geometry, 307
Regime equations, 80-81, 84, 95, 256, 303, 383, 522
Regime formula, 464
Regime relations, 352
Regime River Geometry, 518
Regime theory, 7, 53, 65, 67, 69-70, 85, 98, 240, 256,
282 ’
Regime velocity, 72
Regional geometry, 24
Regional hydraulic geometry, 529, 533-534560 Index
Regional scale, 531
Relative flow intensity, 189
Representative grain size or diameter, 294
Reservoir sedimentation, 11
Resistance, 378
drag, 48
grain, 48
Resistance equation, 193, 197, 213, 221, 237, 420 421
Resistance factor, 394
Resistance force, 52
Resistance law, 419
Return period, 290
Reynolds number, 34-35, 47, 76, 189, 341, 540
Riffle geometry, 97
Riffles, 5, 23, 96, 538
Rigid bed channel, 44
Rigid boundary gravel bed rivers, 45
Ripple height, 238, 240
Ripples, 60, 68, 72, 89, 94, 188, 190, 341, 375
River basin, 3
River meandering, 518
River morphology, 372
River slope, 374
River stability, 394
River training, 11
Rivers
braided, 90
meandering, 90
sinuous, 90
straight, 90
Roughness, 30, 33, 103, 112, 119, 124, 127, 129, 132,
136-138, 140-141, 146, 162, 247, 249, 374,
386
bank, 2
bed, 2
form, 8
skin, 8
Roughness coefficient, 376
Roughness diameter, 386
Roughness elements, 342, 407 408
Roughness factor, 86
Runoff ratio, 539
Sand bed, 84
Sand bed channels, 72
Sand grain roughness, 57
Sand roughness, 347
Sand waves, 20
Scale
mega, 68
meso, 68
micro, 68
Scale ratios, 100
Scaling theory, 24, 245, 247
Schoklitsch equation, 54
Scour, 67, 98, 119, 136, 139
Scour holes, 5
Scouring, 20
Sediemnt transport, 221
Sediment (bed load) discharge, 421
Sediment concentration, 20, 22, 49, 73, 77, 80, 85, 87,
126, 134, 136, 140, 383, 397, 399, 431, 452,
454, 473, 494, 506
Sediment continuity equation, 263
Sediment delivery ratio, 7, 512, 526
Sediment density, 383
Sediment diameter, 71, 96, 378, 383, 386
Sediment discharge, 5, 217, 232, 263, 338, 340, 357,
375, 410
Sediment efficiency, 386
Sediment Froude number, 228
Sediment grain size, 39, 391
Sediment load, 2, 5-8, 33, 53, 68, 73, 79, 8^k87,
89-90, 105, 110, 113, 125, 128-129, 134, 213,
247, 340, 359, 374, 386, 393, 396, 399, 420,
439, 450-451, 487, 518-519, 550
Sediment movement, 395
Sediment particle size, 253, 393
Sediment particle size and gradation, 53
Sediment particles, 33, 254
Sediment rating curve, 125
Sediment routing, 13
Sediment size, 88
coarse, 6
Sediment size factor, 50
Sediment storage, 7
Sediment supply, 68, 79
Sediment transport, 4, 20, 22, 24, 30, 51, 55, 65, 68,
79, 84, 90, 105, 112, 162, 188, 213, 217, 233,
247, 253, 357, 375, 383, 385, 387, 39«97,
512
Sediment transport capacity, 12, 20, 81, 357
Sediment transport equation, 409, 420, 423, 439, 442,
521
Sediment transport equations, 53, 84, 105
Sediment transport rate, 34, 53, 81, 84-85, 116, 295,
349, 372, 374
Sediment transport rating curve, 116
Sediment transport relation, 351
Sediment weight density, 341, 376
Settlement of sediment, 99
Settling velocity, 342, 398
Shannon entropy, 476-477, 483, 488
Shape factor, 434
Shape function, 486
Shape parameter, 422
Shear force, 221, 342, 524
Shear Reynolds number, 48
Shear strength, 96
Shear stress, 2, 21, 51, 53-54, 58, 60, 141, 160-161,
164, 166, 178, 189-190, 210, 266, 340,
421-422, 441
Shear velocity, 42, 51, 53, 188-189, 254, 341
Shields criterion, 288
Shields critical stress, 524
Shields entrainment function, 54, 254 255, 287, 409Index 561
Shields equation, 54
Shields parameter, 59, 229
Shields stress, 7
Silt factor, 71, 73, 75, 85 86
Similarity principle, 24, 338, 341
Similitude, 247
Sinuosity, 40, 93, 96 97, 155
Skin friction, 299, 342
Skin resistance, 37
Slope, 38, 68-71, 80, 89-90, 94, 110, 112, 119, 129,
137, 162, 212-213, 282, 340-341, 351, 374
flat, 33
side, 2
slope, 2
steep, 33
valley, 33
Smart formula, 56
Smith theory, 210, 213
Smooth turbulent flow, 75
Specific discharge, 396
Specific energy head, 36
Specific gravity of sediment, 341
Specific sediment weight, 253
Specific weight, 3, 36
Specific weight of sediment, 54
Specific weight of sediment grains, 294
Specific weight of water, 54
Spill resistance, 38
Stability criterion, 106
Stability index, 247, 257-258
Stability index theory, 245, 255
Stable canal design, 88
Stable canals, 11, 256
Stable channel design, 236, 254
Stable channel width, 254, 258
Stable channels, 144, 256
Stable gravel-bed channel, 257
Stage-discharge rating curve, 11
Stage-discharge relation, 114
Steady uniform flow, 34
Straight channels, 93
Stream fall, 56
Stream geometry, 172
Stream order, 531
Stream pattern, 21
Stream power, 3, 6, 30, 50, 53, 57-58, 161, 164, 167,
172, 177-178, 212, 395, 398, 402, 420,
440-442, 452, 473-474, 491, 494-499, 501,
503-506, 508, 510-514, 519-520, 524
Stream Size, 18
Stream transport capacity, 357
Streamflow routing, 14
Strickler equation, 473, 538
Strickler’s formula, 279, 282, 285-286
Submerged weight, 52, 265
Suspended load, 110, 113, 125, 127, 129-130, 137,
140, 145, 236, 349
Suspended sediment, 110, 113, 133 134, 145
Suspended sediment concentration, 95, 236
Suspended sediment transport, 472
Terminal velocity, 87
Thalweg, 18, 33, 93
Theory of minimum energy dissipation rate, 24, 450,
452
Theory of minimum variance, 159, 495
Theory of stream power, 24, 510
Thermodynamic theory, 24, 292
Thermodynamics, 297
Threshold channel, 79-80, 263, 276
Threshold channel geometry, 271
Threshold channel shape, 265
Threshold condition, 256, 263, 273
Threshold discharge, 261, 263, 268-269, 280-281
Threshold theory, 245, 254, 256, 263, 282-283, 287,
289, 426
Tidal estuaries, 362-363, 367
Tidal Estuaries Morphology, 362
Tidal flow, 361
Tidal prism, 366
Top width, 265, 268, 274, 456
Top width ratio, 275
Topological fractal dimension, 543
Total energy head, 36
Tractive force, 2, 51, 76, 264, 266-267, 342, 434
Tractive force theory, 24, 261, 263, 265, 282
Transition regime, 47
Transitional channels, 19
Transport equation, 223, 302
Transport equations, 210
Trapezoidal sections, 389
Turbidity, 357-359, 364, 367
Turbulence intensity, 53
Turbulent flow, 47, 92
Turbulent fluxes, 53
Turbulent stresses, 299
UBC (University of British Columbia) regime model,
105
Uniform flow, 52
Unit stream power, 56, 72, 454
Vegetation types, 96
Velocity, 2-3, 5-7, 12-13, 15-17, 30, 34, 43, 45, 47,
52-53, 68, 71-72, 7^k75, 87, 95, 97, 103, 110,
112 113, 119, 123 125, 127, 129-132, 134,
136-137, 161-162, 164 166, 169, 210,
212-213, 229, 232, 235, 245, 247
Velocity distribution, 374
Velocity profile, 48
Velocity ratio, 543
Vertical length scale ratio, 350
Viscosity, 146, 206
Viscous shear, 341
Viscous sublayer, 344
Volumetric sediment transport, 53562 Index
Wash load. 79. 339
Water discharge. 393
Water flow depth. 394
Water slope. 395
Water surface slope. 19. 129. 257. 376. 378
Water temperature. 53
Watershed. 2. 6
Wave length. 100-102. 152. 154-155
Wave length of bed forms. 89
Wave length of meanders. 92. 374
Weight density. 36
Weight density of sediment. 44. 89. 410
Weight density of water. 44. 89. 177. 234. 340. 410.
439. 494
Wetted perimeter. 22. 34. 71. 96-97. 124. 270-271.
283. 286. 385. 421.426. 446. 448. 454. 485. 487
Wetted stream perimeter. 73
Width. 2. 4. 6-7. 11-13. 15-16. 30. 58. 67. 70-71. 74.
76-77. 79. 83. 87. 95-96. 98. 100. 102-103.
110. 112-113. 116-117. 119. 123-124.
127-128. 130. 132. 134-137. 142. 147. 155.
160-161. 164-166. 169. 171-172. 174. 176.
178. 208. 210. 212-213. 221. 225. 229.
232-233. 236. 240. 245. 247. 338. 340. 351.
359. 361. 370. 374. 396
Width to depth ratio. 18. 33. 88
Width-based Reynolds number. 75
Width-depth ratio. 74. 143. 145. 222. 238-239. 457.
505
Width-discharge exponents. 16
Width-discharge relation. 16. 26
Work. 3


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