Handbook of Hydraulic Geometry Theories and Advances 1st Edition by Vijay Singh ISBN 9781009222174 1009222171

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ISBN 10: 1009222171
ISBN 13: 9781009222174
Author: Vijay Singh

 Handbook of Hydraulic Geometry Theories and Advances 1st Edition Table of contents:

1 Introduction

1.1 Definition

1.2 Analytical Basis for Hydraulic Geometry Equations

1.3 Types of Hydraulic Geometry

1.3.1 At-a-Station Hydraulic Geometry

1.3.2 Downstream Hydraulic Geometry

1.3.3 Reach-Averaged Hydraulic Geometry

1.3.4 At-Many-Stations Hydraulic Geometry

1.4 Application of Hydraulic Geometry

1.5 Basis of Hydraulic Geometry Relations

1.6 Equilibrium State

1.7 Equilibrium Assumption

1.8 Validity of Power Relations

1.9 Stability of Hydraulic Geometry Relations

1.10 Variability of Exponents

1.11 Variation of Channel Width

1.12 Variation of Channel Velocity

1.13 Effect of Stream Size

1.14 Effect of River Channel Patterns

1.15 Effect of Hyper-concentrated Floods on Channel Geometry Adjustment

1.16 Effect of Dam Removal

1.17 Power Relations for Drainage Basins

1.18 Effect of Land Use

1.19 Boundary Conditions

1.20 Organization of Contents

References

2 Governing Equations

2.1 Introduction

2.2 Continuity Equation

2.3 Flow Characterization

2.4 Energy Equation

2.5 Gradually Varied Flow Equation

2.6 Flow Resistance Equations

2.6.1 Chezy’s Equation

2.6.2 Manning’s Equation

2.6.3 Einstein-Chien Equation

2.6.4 Darcy-Weisbach Equation

2.6.5 Friction Factor Equations

2.6.6 Shear Stress in Alluvial Channels

2.7 Sediment Transport

2.7.1 Criteria for Incipient Motion

2.7.2 Transport Equations

2.8 Stream Power

2.9 Entropy

References

3 Regime Theory

3.1 Introduction

3.2 Regime Theory

3.2.1 Lacey’s Equations

3.2.2 Blench’s Equations

3.3 Generalized Regime Theory

3.4 Process-Based Regime Equations

3.5 Natural Channels

3.6 Applications

3.6.1 Width between Incised River Banks

3.6.2 Scour between Bridge Piers

3.6.3 Scour Downstream from Piers

3.6.4 Aggradation Upstream from Reservoirs

3.6.5 Degradation Downstream from Reservoirs

3.6.6 Estimation of Dredging

3.6.7 Model Scales

3.6.8 Meandering

3.6.9 Channel Design

3.6.10 Gravel-Bed River Response to Environmental Change

References

4 Leopold-Maddock (LM) Theory

4.1 Introduction

4.2 At-a-Station Hydraulic Geometry

4.2.1 Geomorphologic Data and Their Measurement

4.2.2 Bankfull Discharge

4.2.3 Effective Discharge

4.2.4 Frequency of Discharge

4.2.5 Variations in Hydraulic Characteristics

4.2.6 Relation of Channel Shape to Frequency of Discharge

4.2.7 Suspended Sediment and Discharge at a Particular Cross-Section

4.2.8 Width, Depth, Velocity, and Suspended Sediment at a Given Discharge

4.2.9 Role of Channel Roughness and Slope in the Adjustment of Channel Shape to Sediment Load

4.3 Downstream Hydraulic Geometry

4.3.1 Variation of Hydraulic Characteristics

4.3.2 Relation of Channel Shape to Frequency of Discharge

4.3.3 Relation of Suspended Sediment to Discharge in a Downstream Direction

4.3.4 Width, Depth, Velocity, and Suspended Sediment at a Given Discharge

4.3.5 Width, Depth, and Suspended Load at a Variable Discharge

4.3.6 Relations between Width, Depth, Velocity, and Bed Load at a Given Discharge

4.3.7 Channel Shape Adjustment during Individual Floods

4.3.8 Significance of Channel Roughness and Slope in Adjustment of Channel Shape to Sediment Load

4.3.9 Stable Irrigation Canal: An Analogy to a Graded River

4.3.10 Sediment and Longitudinal Profile

4.4 Variation of Exponents

4.5 b-f-m Diagram

4.6 Analytical Determination of Exponents and Coefficients

4.7 Comparison with Stable Irrigation Channels

4.8 Reconstruction of Discharges

References

5 Theory of Minimum Variance

5.1 Introduction

5.2 Minimum Sum of Variances of Independent Variables

5.3 Minimum Total Variance of Components of Stream Power

5.4 Knight’s Formulation of Minimum Variance Hypothesis

5.5 Minimum Variance of Stream Power

5.6 Influence of Choice of Variables

5.7 Entropy Maximizing

References

6 Dimensional Principles

6.1 Introduction

6.2 Derivation of Hydraulic Geometry

6.3 Derivation of Width and Depth

6.4 Computation of Regime Channels

6.5 Computational Procedure

6.6 Method of Synthesis

References

7 Hydrodynamic Theory

7.1 Introduction

7.2 Smith Theory

7.2.1 Hydrodynamic Formulation

7.2.2 Derivation of Hydraulic Geometry

7.3 Julien-Wargadalam (JW) Theory

7.3.1 Continuity Equation

7.3.2 Resistance Equation

7.3.3 Sediment Transport Equation

7.3.4 Angle between Transversal and Downstream Shear Stress Components

7.3.5 Hydraulic Geometry Relations

7.3.6 Calculation Procedure

7.3.7 Further Discussion

7.4 Parker Theory

7.5 Griffiths Theory

7.5.1 Derivation of Downstream Hydraulic Geometry

7.5.2 Stable Channel Design

7.6 Ackers Theory

7.6.1 Governing Equations

7.6.2 Hydraulic Geometry Equations

7.6.3 Significance of Width-Depth Ratio

7.6.4 Comparison with Regime Relations

References

8 Scaling Theory

8.1 Introduction

8.2 Scaling Theory

8.2.1 Immobile Boundary Channels

8.2.2 Effect of Roughness

8.2.3 Mobile Bed

8.3 Comparison with Stable Channel Design Theories

8.3.1 Threshold Theory

8.3.2 Stability Index Theory

8.3.3 Regime Theory

8.4 Application to Channel Design

References

9 Tractive Force Theory

9.1 Introduction

9.2 Threshold Condition

9.3 Tractive Force Theory

9.3.1 Assumptions

9.3.2 Forces Acting on Threshold Channel Shape

9.3.3 Channel Geometry

9.3.3.1 Top Width

9.3.3.2 Cross-Section

9.3.3.3 Wetted Perimeter

9.3.3.4 Hydraulic Depth

9.3.3.5 Hydraulic Radius

9.3.4 Hydraulic Geometry

9.3.5 Downstream Hydraulic Geometry

9.3.6 Validity of Assumptions

9.4 Henderson Theory

9.4.1 Governing Equations of Threshold Theory

9.4.2 Bed Load Equation and Lacey’s Equations

9.4.3 Application to Design of Artificial Channels

9.4.4 Application to Rivers

References

10 Thermodynamic Theory

10.1 Introduction

10.2 Hypothesis

10.3 Determination of A*

10.3.1 Variation of Flow Energy

10.3.2 Variation of Flow Energy with Dimensionless Time

10.4 Transport Equation

10.5 System of Regime Equations

10.6 Computation of Hydraulic Geometry

10.6.1 Basic Equations

10.6.2 Determination of Friction Coefficient

10.6.3 Computation of Geometry

References

11 Similarity Principle

11.1 Introduction

11.2 Dominant Discharge

11.3 Basic Parameters

11.4 Similarity Principle

11.4.1 Flow Velocity, Friction Velocity, and Settling Velocity

11.4.2 Bed Shear Stress

11.4.3 Energy Slope

11.4.4 Hydraulic Roughness

11.4.5 Loss of Energy

11.4.6 Energy Gradient

11.4.7 Geometric and Dynamic Similarity

11.5 Comparison with Regime Relations

References

12 Channel Mobility Theory

12.1 Introduction

12.2 Sediment Transport

12.3 Hypothesis of Channel Mobility

12.3.1 Index of Mobility

12.4 Hydromorphometric Relationships

12.5 Tidal Estuaries Morphology

12.6 Relation of Channel Width to Depth and Degree of Widening of the Channel of Tidal Estuaries

12.7 Longitudinal Channel Profile

12.7.1 Index of Mobility

12.8 Another Analysis of Generalized Mobility Index

References

13 Maximum Sediment Discharge and Froude Number Hypothesis

13.1 Introduction

13.2 Hypotheses

13.2.1 Flow Resistance

13.2.2 Sediment Transport

13.2.3 Energy Equation

13.2.4 Coefficient Ks

13.2.5 Water Surface Slope

13.3 Case 1: Straight and Meandering Single Beds

13.4 Case 2: Multiple Meandering Bed

13.5 Case 3: Meanders

13.6 Maximum Sediment Efficiency

13.6.1 Governing Equations

13.6.2 At-a-Station Hydraulic Geometry

13.6.3 Downstream Hydraulic Geometry

References

14 Principle of Minimum Froude Number

14.1 Introduction

14.2 River Stability and Froude Number

14.2.1 Channel Stability

14.2.2 Role of Potential Energy

14.2.3 Role of Sediment Movement

14.2.4 Role of Froude Number

14.3 Modeling and Simulation

14.3.1 Assumptions

14.3.2 Mass Conservation

14.3.3 Flow Resistance

14.3.4 Sediment Transport

14.4 Minimization of Froude Number

14.5 Testing

14.6 Another Look at Froude Number Minimization

References

15 Hypothesis of Maximum Friction Factor

15.1 Introduction

15.2 Formulation of Maximum Friction Factor Hypothesis

15.3 Maximization

References

16 Maximum Flow Efficiency Hypothesis

16.1 Introduction

16.2 Basic Relations

16.2.1 Continuity Equation

16.2.2 Resistance Equation

16.2.3 Sediment Transport

16.2.4 Shape Parameter

16.3 Derivation of Hydraulic Geometry Relations

16.3.1 Optimum Hydraulic Geometry Relations

16.3.2 Lower Threshold Geometry Relations

16.3.3 Upper Threshold Geometry Relations

16.3.4 Average Channel Geometry Relations

16.4 Physical Evidence for Maximum Flow Efficiency

References

17 Principle of Least Action

17.1 Introduction

17.2 Adjustment of Alluvial Cross-Sections

17.3 Validity

17.4 Comparison

17.5 Stable Hydraulic Section Using Calculus of Variation

References

18 Theory of Minimum Energy Dissipation Rate

18.1 Introduction

18.2 Theory of Minimum Energy Dissipation Rate

18.2.1 Flow Resistance Equation

18.2.2 Energy Dissipation Rate for Water Transport

18.2.3 Energy Dissipation Rate for Sediment Transport

18.2.4 Total Rate of Energy Dissipation

18.3.5 Sediment Concentration

18.3 Derivation of Hydraulic Geometry

18.3.1 Trapezoidal Section

18.3.1.1 Case 1: Unrestricted Trapezoid

18.3.1.2 Case 2: Width-Constrained Trapezoid

18.3.1.3 Case 3: Side-Slope Constrained Trapezoid

18.3.2 Triangular Geometry

18.3.3 Rectangular Geometry

18.4 Analysis and Application

References

19 Entropy Theory

19.1 Introduction

19.2 Formulation

19.3 Derivation of At-a-Station Hydraulic Geometry Using Entropy

19.4 Derivation of Downstream Geometry Using Entropy

19.5 Cross-Sectional Shape

19.6 Energy Gradient or Channel Slope

References

20 Minimum Energy Dissipation and Maximum Entropy Theory

20.1 Introduction

20.2 Downstream Hydraulic Geometry Relations

20.2.1 Primary Morphological Equations

20.2.2 Downstream Hydraulic Geometry Equations for a Given Discharge

20.3 At-a-Station Hydraulic Geometry Relations

20.3.1 Morphological Equations

20.3.2 Derivation of At-a-Station Hydraulic Geometry Relations

References

21 Theory of Stream Power

21.1 Introduction

21.2 Definition

21.3 Two Postulates

21.4 Constraints for Hydraulic Geometry

21.5 Regime River Geometry

21.6 Stream Power and Probability

21.6.1 Governing Equations

21.6.2 Derivation of Regime Equations

21.6.3 Basic Regime Coefficient

21.7 Variation of Stream Power

21.8 Computation of Variation in Stream Power

References

22 Regional Hydraulic Geometry

22.1 Introduction

22.2 Relation between Discharge, Channel Shape, and Drainage Area

22.3 Regional Hydraulic Geometry

22.4 Relation between Mean Annual Discharge and Drainage Area

22.5 Leopold-Miller Extension of Horton Laws

22.6 Gupta-Mesa Theory of Hydraulic Geometry

22.6.1 Physical Variables and Parameters

22.6.2 Dimensionless Ratios

22.6.3 Mass Conservation

22.6.4 Derivation of Horton Laws

22.6.5 Determination of Width Exponent

22.6.6 Determination of Velocity and Depth Exponents

22.6.7 Manning’s Roughness Coefficient and Its Exponent

22.7 Channel Geometry Method

22.8 Variation of Channel Geometry and Drainage Area

References

Index

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