OPEN-CHANNEL FLOW

✍ Scribed by M HANIF CHAUDHRY

• Publisher: SPRINGER
• Year: 2022
• Tongue: English
• Leaves: 566
• Edition: 3
• Category: Library

✦ Table of Contents

Preface
Contents
1 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 Coefficient
Example 1-1
Solution:
1-6 Pressure Distribution
Static Conditions
Horizontal, Parallel Flow
Parallel Flow in Sloping Channels
Curvilinear Flow
1-7 Reynolds Transport Theorem
1-8 Hydraulic Models
1-9 Summary
References
2 STEADY FLOW CONSERVATION LAWS
2-1 Introduction
2-2 Conservation of Mass
2-3 Conservation of Momentum
2-4 Equation of Motion
Steady Flow
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
Given:
Determine:
Solution:
2-8 Hydraulic Jump
Example 2-2
Given:
Determine:
Solution:
2-9 Hydraulic Jump at Sluice Gate Outlet
Example 2-3
Given:
Determine:
Solution:
Depth Downstream of Jump
Head Loss in the Jump
Thrust on the Gate
2-10 Summary
References
3 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
Given:
Determine:
Solution:
3-5 Location of Critical Flow
3-6 Computation of Critical Depth
Design curves
Trial-and-Error Procedure
Numerical Methods
Example 3-2
Given:
Determine:
Solution:
Design Curves
Trial-and-Error Procedure
Numerical Methods
3-7 Critical Depths in Compound Channels
General Remarks
Example 3-3
Given:
Determine:
Solution:
Q = 1.7m3/s
Q = 2.5m3/s
Q = 3.5 m3/s
Algorithm for Computing the Critical Depths
3-8 Summary
References
4 UNIFORM FLOW
4-1 Introduction
4-2 Flow Resistance
4-3 Flow Resistance Equations
Chezy Equation
Smooth Flows
Rough Flows
Manning Equation
Other Resistance Equations
4-4 Computation of Normal Depth
Design Curves
Trial-and-Error Procedure
Numerical Methods
Example 4-1
Given:
Determine:
Solution:
Design curves
Trial-and-Error Procedure
Numerical Method
4-5 Equivalent Manning Constant
4-6 Compound Channel Cross Section
4-7 Summary
References
5 GRADUALLY VARIED FLOW
5-1 Introduction
5-2 Governing Equation
5-3 Classification of Water-Surface Profiles
5-4 General Remarks
Zone 1 (M1 Profile)
Zone 2 (M2 Profile)
Zone 3 (M3 Profile)
5-5 Sketching of Water-Surface Profiles
Example 5-1
Solution:
Example 5-2
Solution:
5-6 Discharge From a Reservoir
Example 5-3
Given:
Determine:
Solution:
5-7 Profiles in Compound Channels
Example 5-4
Given:
Determine:
Solution:
So= 0.0094
So= 0.0049
So= 0.0029
So= 0.001
Example 5-5
Given:
Determine:
Solution:
So>Sc1
Sc1>So>Sc2
Sc2>So>Sc3
So<Sc3
5-8 Summary
References
6 COMPUTATION OF GRADUALLY VARIED FLOW
6-1 Introduction
6-2 General Remarks
6-3 Direct-Step Method
Average friction slope
Geometric mean friction slope
Harmonic mean friction slope
Example 6-1
Given:
Determine:
Solution:
Column 1, y
Column 2, A
Column 3, R
Column 4, V
Column 5, Sf
Column 6, f
Column 7, So - f
Column 8, E
Column 9, ΔE = E2-E1
Column 10, Δx = x2 - x1
Column 11, x2
6-4 Standard Step Method
Example 6-2
Given:
Determine:
Solution:
6-5 Integration of Differential Equation
6-6 Single-step Methods
Euler method
Improved Euler method
Modified Euler Method
Fourth-order Runge-Kutta Method
6-7 Predictor-Corrector Methods
6-8 Simultaneous Solution Procedure
Governing Equations
Single and Series Channels
Channel Networks
Example 6-3
Solution
Practical Applications
6-9 Summary
References
7 RAPIDLY VARIED FLOW
7-1 Introduction
7-2 Application of Conservation Laws
7-3 Channel Transitions
General Remarks
Subcritical Flow
Expansions
Contractions
7-4 Supercritical Flow
Oblique Hydraulic Jump
7-5 Weirs
Sharp-Crested Weirs
Broad-Crested Weirs
7-6 Hydraulic Jump
Ratio of Sequent Depths
Length of Jump
Jump Profile
Jump types
Weak jump ( 1<Fr1<2.5)
Oscillating jump (2.5<Fr1<4.5)
Steady jump (4.5<Fr1<9)
Strong jump (Fr1>9)
Energy loss
Jump Location
Control of Jump
Sharp-crested weir
Abrupt rise
7-7 Spillways
Overflow Spillway
Crest of Overflow Spillway
Rating Curve
Water-Surface Profile
Downstream Face
7-8 Energy Dissipators
Stilling Basins
Flip Buckets
Scour depth
Roller Buckets
Design procedure
7-9 Summary
References
8 COMPUTATION OF RAPIDLY VARIED FLOW
8-1 Introduction
8-2 Governing Equations
Characteristic directions
Coordinate Transformations
8-3 Computation of Supercritical Flow
Finite-difference methods
MacCormack Scheme
Predictor
Corrector
Stability
Boundary Conditions
Verification
Oblique Hydraulic Jump
Circular-Arc Contraction
8-4 Computation of Sub- and Supercritical Flows
Numerical Solution
Predictor
Corrector
Initial and Boundary Conditions
Inflow and outflow boundaries
Symmetry boundary
Solid side wall boundary
Stability
Artificial Viscosity
Verification
Supercritical flow in symmetrical contraction
Hydraulic jump in a gradual expansion
8-5 Simulation of Hydraulic Jump
Governing Equations
Numerical Solution
Predictor
Corrector
Initial and Boundary Conditions
Stability Conditions
Computational Procedure
Results
8-6 Summary
References
9 CHANNEL DESIGN
9-1 Introduction
9-2 Rigid-Boundary Channels
Example 9-1
Given:
Solution:
9-3 Most Efficient Hydraulic Section
Rectangular Section
Triangular Section
Trapezoidal section
9-4 Erodible Channels
Permissible Velocity Method
Example 9-2
Given:
Determine:
Solution:
Tractive Force Method
Example 9-3
Given:
Determine:
Solution:
9-5 Alluvial Channels
Regime Theory
Example 9-4
Given:
Determine:
Solution:
9-6 Summary
References
10 STEADY FLOW SPECIAL TOPICS
10-1 Introduction
10-2 Flow in a Channel Connecting Two Reservoirs
A. Mild bottom slope
1. Upstream reservoir level constant, downstream reservoir level variable
2. Downstream reservoir level constant, upstream reservoir level variable
3. Variable upstream and downstream reservoir levels, constant rate of discharge
B. Steep bottom slope
10-3 Air Entrainment in High-Velocity Flow
Nonaerated flow region
Uniform aerated region
Friction factor
Velocity distribution
Flow calculations
10-4 Flow Through Culverts
Inlet control
Unsubmerged entrance (H<1.2D)
Submerged entrance (H>1.2D)
Outlet control
10-5 Flow Measurement
Velocity-area method
Slope-area method
Flumes
10-6 Velocity Measurement*
Current meter
Acoustic Doppler Current Profiler
Ultrasonic Velocity Profiling (UVP)
Surface-Velocity Radar (SVR)
Image-Based Approaches
Large-Scale Particle Image Velocimetry
Space Temporal Image Velocimetry
Optical Flow Algorithms
Particle Tracking Velocimetry
Satellite Observations
10-7 Summary
Extra Credit:
References
11 UNSTEADY FLOW
11-1 Introduction
11-2 Definitions
11-3 Occurrence of Unsteady Flow
11-4 Height and Celerity of a Gravity Wave
Continuity equation
Momentum equation
Example 11-1
Given:
Determine:
Solution:
11-5 Summary
References
12 GOVERNING EQUATIONS FOR ONE-DIMENSIONAL FLOW
12-1 Introduction
12-2 St. Venant Equations
Continuity Equation
Momentum Equation
12-3 General Remarks
12-4 Boussinesq Equations
Continuity equation
Momentum Equation in z-direction
Free surface
Channel bottom
Momentum Equation in x-direction
12-5 Integral Forms
12-6 Summary
References
13 NUMERICAL METHODS
13-1 Introduction
13-2 Method of characteristics
Characteristics
13-3 Initial and Boundary Conditions
13-4 Characteristic Grid Method
13-5 Method of Specified Intervals
13-6 Other Numerical Methods
13-7 Summary
References
14 FINITE-DIFFERENCE METHODS
14-1 Introduction
14-2 Terminology
Finite-difference approximations
Explicit finite differences
Implicit finite differences
14-3 Explicit Finite-Difference Schemes
Unstable scheme
Diffusive scheme
General formulation
Nonconservation form
Conservation form
Boundary Conditions
Stability
MacCormack Scheme
General formulation
Predictor
Corrector
Boundary conditions
Stability
Artificial viscosity
14-4 Implicit Finite-Difference Schemes
Preissmann Scheme
General formulation
Boundary Conditions
Stability
Solution procedure
Beam and Warming scheme
Vasiliev Scheme
14-5 Consistency
14-6 Stability
Example 14-1
Solution
14-7 Summary
References
15 TWO-DIMENSIONAL FLOW
15-1 Introduction
15-2 Governing Equations
Continuity equation
Momentum equation
Continuity equation
Momentum equations
15-3 Numerical Solution
15-4 MacCormack Scheme
General formulation
Predictor
Corrector
Boundary conditions
15-5 Gabutti Scheme
General formulation
Predictor
Predictor
Corrector
Boundary conditions
15-6 Artificial Viscosity
15-7 Beam and Warming Schemes
General formulation
Factored schemes
Implicit split-flux factoring
Boundary conditions
15-8 Finite-Volume Scheme
Predictor part
Corrector part
15-9 Applications
Partial breach or opening of sluice gates
Propagation of a flood wave through channelcontraction
Comparison with other methods
15-10 Summary
References
16 LEVEE BREACH MODELING
16-1 Introduction
16-2 Estimation of Breach Flow
16-3 Levee Breach due to Overtopping
16-4 Numerical Model
Governing Equations
Hydrodynamic equations
Sediment equations
Lateral sediment load due to slumping failure
Numerical Solution
Finite-difference Scheme
Initial and Boundary Conditions
Stability condition
Artificial viscosity
16-5 Experimental Investigations
Experimental Setup
Experimental Procedures
Experimental Results
Breach Hydrograph
Breach-shape
16-6 Model Applications
Steady Flow through a Levee Breach
Levee Failure due to Overtopping
Breach Hydrograph
Breach evolution
Transient Velocity Field
Sensitivity Analysis
16-7 Summary
References
17 SEDIMENT TRANSPORT
17-1 Introduction
17-2 Sediment Properties
Sediment Size
Size Distribution
17-3 Sand-bed and Gravel-bed Streams
17-4 Threshold of Sediment Motion
Critical Shields Stress for Sediment Mixture
17-5 Condition for Significant Suspension
17-6 Shields Diagram
17-7 The Exner Equation of Bed Sediment Conservation
Exner Equation for Multiple Size Fraction
17-8 Bed-load Transport Relations
Bed Load Transport Relations for Poorly Sorted Sediment
17-9 Suspended-load Transport
Entrainment Relations
17-10 Resistance Relations
Separation of Form Drag
17-11 Summary
References
18 UNSTEADY FLOW SPECIAL TOPICS
18-1 Introduction
18-2 Rating Curve
18-3 Flood Routing
18-4 Reservoir Routing
18-5 Channel Routing
18-6 Kinematic Routing
Applicability criterion
18-7 Diffusion Routing
Applicability
18-8 Muskingum-Cunge Routing
18-9 Aggradation and Degradation of Channel Bottom
Introduction
Governing equations
Continuity equation for water
Momentum equation for water
Continuity equation for sediment
Numerical Scheme
Predictor
Corrector
Stability
Artificial Viscosity
Computational Procedure
Applications
Aggradation due to sediment overloading
Knickpoint migration
18-10 Summary
References
Authors Index
Subject Index