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Entropy Theory in Hydraulic Engineering - An Introduction, 2014
- Cover
- Contents
- Preface
- Chapter 1 Entropy Theory [Go to Page]
- 1.1 Overview of This Volume
- 1.2 Entropy Concept
- 1.3 Entropy Theory
- 1.4 Types of Entropy
- 1.5 Application of Entropy Theory to Hydraulic Engineering Problems
- 1.6 Hypothesis on the Cumulative Distribution Function
- 1.7 Methodology for Application of Entropy Theory
- Appendix 1.1
- Questions
- References
- Additional Reading
- Part 1: Velocity Distributions [Go to Page]
- Chapter 2 One-Dimensional Velocity Distributions [Go to Page]
- 2.1 Preliminaries
- 2.2 Derivation of One-Dimensional Velocity Distributions
- 2.3 One-Dimensional Velocity Distribution with No Physical Constraint
- 2.4 One-Dimensional Velocity Distribution with One Physical Constraint
- 2.5 Testing of One-Physical-Constraint Velocity Distribution
- 2.6 One-Dimensional Velocity Distribution with Two Physical Constraints
- 2.7 One-Dimensional Velocity Distribution with Three Physical Constraints
- Appendix 2.1: Method of Lagrange Multipliers
- Questions
- References
- Additional Reading
- Chapter 3 Two-Dimensional Velocity Distributions [Go to Page]
- 3.1 Derivation of Velocity Distributions
- 3.2 Construction of Isovels and Relation between (x, y) Coordinates and (r, s) Coordinates
- 3.3 Estimation of Parameters of Velocity Distribution
- 3.4 Maximum and Mean Velocities
- 3.5 Comparison of Mean Velocity Estimates
- 3.6 Alternative Method for Estimation of the Cross-Sectional Area Mean Velocity for New River Sites
- 3.7 Derivation of 2-D Velocity Distribution Using a Mathematically Sound Coordinate System
- 3.8 Trapezoidal Domain
- Appendix 3.1
- Appendix 3.2
- Questions
- References
- Additional Reading
- Chapter 4 Power Law and Logarithmic Velocity Distributions [Go to Page]
- 4.1 Preliminaries
- 4.2 One-Dimensional Power Law Velocity Distribution
- 4.3 One-Dimensional Prandtl–von Karman Universal Velocity Distribution
- 4.4 Two-Dimensional Power Law Velocity Distribution
- 4.5 Two-Dimensional Prandtl–von Karman Velocity Distribution
- 4.6 Two-Dimensional Representation of Velocity Using a General Framework
- Questions
- References
- Additional Reading
- Chapter 5 Applications of Velocity Distributions [Go to Page]
- 5.1 Sampling Velocity Measurements
- 5.2 Use of k[sub(1)]–Entropy Relation for Characterizing Open-Channel Flows
- 5.3 Energy and Momentum Coefficients
- 5.4 Shear Stress Distribution
- 5.5 Relation between Maximum Velocity, Darcy’s Friction Factor, and Entropy Number
- 5.6 Discharge Measurements
- 5.7 Determination of Discharge at Remote Locations
- 5.8 Determination of Flow Depth Distribution
- 5.9 Determination of Entropy Parameter from Hydraulic and Geometric Characteristics
- Questions
- References
- Additional Reading
- Chapter 6 Velocity Distribution in Pipe Flow [Go to Page]
- 6.1 Derivation of Velocity Distribution
- 6.2 Comparison with Prandtl–von Karman Velocity Distribution
- 6.3 Darcy–Weisbach Equation
- 6.4 Head Loss and Friction Factor
- 6.5 Relation of Mean Velocity, Maximum Velocity, and Friction Coefficient to M
- 6.6 Relation of Friction Coefficient, Manning’s n, and M
- 6.7 Uncertainty in M, fl, n, and Velocity Distribution
- Questions
- References
- Additional Reading
- Part 2: Sediment Concentration and Discharge [Go to Page]
- Chapter 7 Grain Size Analysis and Distribution [Go to Page]
- 7.1 Grain Size Distribution
- 7.2 Soil Characteristics Using Grading Entropy
- Questions
- References
- Additional Reading
- Chapter 8 Suspended Sediment Concentration and Discharge [Go to Page]
- 8.1 Preliminaries
- 8.2 Sediment Concentration
- 8.3 Entropy-Based Derivation of Sediment Concentration Distribution
- 8.4 Suspended Sediment Discharge
- Questions
- References
- Additional Reading
- Chapter 9 Sediment Concentration In Debris Flow [Go to Page]
- 9.1 Notation and Definition
- 9.2 Entropy Theory
- Questions
- References
- Additional Reading
- Part 3: Hydraulic Geometry [Go to Page]
- Chapter 10 Downstream Hydraulic Geometry [Go to Page]
- 10.1 Hydraulic Geometry Relations
- 10.2 Preliminaries
- 10.3 Derivation of Hydraulic Geometry Relations
- 10.4 Downstream Hydraulic Geometry Equations for a Given Discharge
- Questions
- References
- Additional Reading
- Chapter 11 At-a-Station Hydraulic Geometry [Go to Page]
- 11.1 Hydraulic Geometry Relations
- 11.2 Preliminaries
- 11.3 Derivation of At-a-Station Hydraulic Geometry Relations
- 11.4 Possibilities II to XI
- Questions
- References
- Additional Reading
- Part 4: Channel Design [Go to Page]
- Chapter 12 Longitudinal River Profile [Go to Page]
- 12.1 Longitudinal Profiles
- 12.2 Energy Gradient
- 12.3 Derivation of Longitudinal Profiles
- 12.4 Longitudinal Channel Profile from Fall Entropy
- Questions
- References
- Additional Reading
- Chapter 13 Design of Alluvial Channels [Go to Page]
- 13.1 Channel Cross Section
- 13.2 Notation
- 13.3 Shannon Entropy
- 13.4 Entropy Method, Case 1: No Constraint
- 13.5 Entropy Method, Case 2: One Constraint
- 13.6 Comparison with Two Bank Profiles
- 13.7 Evaluation of Entropy-Based Bank Profiles of Threshold Channels
- 13.8 Local Boundary Stress by Different Methods
- 13.9 Channel Shape
- 13.10 Design of Threshold Channels
- 13.11 Evaluation Using Laboratory Data
- 13.12 Determination of Friction Factor
- 13.13 Type I Channels
- Questions
- References
- Additional Reading
- Part 5: Water Flow and Level Monitoring [Go to Page]
- Chapter 14 Water-Level Monitoring Networks [Go to Page]
- 14.1 Design Considerations
- 14.2 Information-Related Approaches
- 14.3 Method of Application
- 14.4 Informational Correlation Coefficient
- Questions
- References
- Additional Reading
- Chapter 15 Rating Curves [Go to Page]
- 15.1 Stage–Discharge Relation
- 15.2 Forms of Stage–Discharge Relations
- 15.3 Derivation of Rating Curves Using Entropy
- Questions
- References
- Additional Reading
- Part 6: Water Distribution Systems [Go to Page]
- Chapter 16 Reliability of Water Distribution Systems [Go to Page]
- 16.1 Preliminary Considerations
- 16.2 Entropy-Based Redundancy Measures
- 16.3 Transmission of Redundancy through Network
- 16.4 Extension of Entropy-Based Redundancy Measures
- 16.5 Modified Redundancy Measure with Path Parameter
- 16.6 Modified Redundancy Measure with Age Factor
- 16.7 Modified Overall Network Redundancy
- 16.8 Flow Reversal and Dual Flow Directions
- 16.9 Other Considerations
- 16.10 Optimization for Design of Networks Incorporating Redundancy
- Questions
- References
- Additional Reading
- Chapter 17 Evaluation of Water Quality and Wastewater Treatment Systems [Go to Page]
- 17.1 Diversity Index
- 17.2 Evaluation of Water Quality Using the Diversity Index
- 17.3 Evaluation of Water Treatment Systems
- 17.4 Relation to Shannon Entropy
- 17.5 Environmental Performance of Waste Treatment Systems
- Questions
- References
- Additional Reading
- Index [Go to Page]
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- X
- Y
- Z
- About the Author [Go to Page]