1st Edition

Open Channel Flow Numerical Methods and Computer Applications

By Roland Jeppson Copyright 2010
    1258 Pages 447 B/W Illustrations
    by CRC Press

    A comprehensive treatment of open channel flow, Open Channel Flow: Numerical Methods and Computer Applications starts with basic principles and gradually advances to complete problems involving systems of channels with branches, controls, and outflows/ inflows that require the simultaneous solutions of systems of nonlinear algebraic equations coupled with differential equations. The book includes downloadable resources that contain a program that solves all types of simple open channel flow problems, the source programs described in the text, the executable elements of these programs, the TK-Solver and MathCad programs, and the equivalent MATLAB® scripts and functions.

    The book provides applied numerical methods in an appendix and also incorporates them as an integral component of the methodology in setting up and solving the governing equations. Packed with examples, the book includes problems at the end of each chapter that give readers experience in applying the principles and often expand upon the methodologies use in the text. The author uses Fortran as the software to supply the computer instruction but covers math software packages such as MathCad, TK-Solver, MATLAB, and spreadsheets so that readers can use the instruments with which they are the most familiar. He emphasizes the basic principles of conservation of mass, energy, and momentum, helping readers achieve true mastery of this important subject, rather than just learn routine techniques.

    With the enhanced understanding of the fundamental principles of fluid mechanics provided by this book, readers can then apply these principles to the solution of complex real-world problems. The book supplies the knowledge tools necessary to analyze and design economical and properly performing conveyance systems. Thus not only is the book useful for graduate students, but it also provides professional engineers the expertise and knowledge to design well performing and economical channel systems.

    Dimensions, Terminology, and Review of Basic Fluid Mechanics
    One-, Two-, and Three-Dimensional Flows
    Steady versus Unsteady Flow
    Uniform versus Nonuniform Flow
    Prismatic versus Non-Prismatic Channels
    Subcritical, Critical, and Supercritical Flows
    Turbulent versus Laminar Flow
    Review of Basic Fluid Mechanics Principles
    Physical Properties of Fluids and Their Effects on Open-Channel Flows
    Conservation of Mass, or Continuity Equations
    Energy Principle

    Energy and Its Dissipation in Open Channels
    Approaches to Frictional Resistance
    Combining the Chezy and the Chezy C Equations
    Empirical Formula: Use of Manning’s Equation
    Channels with Varying Wall Roughness, but Q = Constant
    Specific Energy, Subcritical and Supercritical Flows
    Delivery Diagrams
    Graphical Aids to Solving Critical Flow Problems
    Upstream Depth When Critical Conditions Occur at Reduced Downstream Section
    Dimensionless Treatment of Upstream Trapezoidal Channel to Downstream Rectangular Channel
    Hydraulically Most Efficient Section

    The Momentum Principle Applied to Open Channel Flows
    The Momentum Function
    Characteristics of the Momentum Function
    Rectangular Channels and Momentum Function per Unit Width
    Polynomial Form for Momentum Function
    Dimensionless Momentum Functions
    Celerity of Small Amplitude Gravity Waves
    Constant Height Waves
    Open Channel to Pipe Flow
    Multiple Roughness Coefficient for Channel Section— Compound Sections Problems
    Problems to Solve Using Program CHANNEL

    Nonuniform Flows
    Types of Nonuniform Flows
    Ordinary Differential Equation for Gradually Varied Flow
    Gradually Varied Flow in Prismatic Channels without Lateral Inflow or Outflow
    Numerical Methods for Solving ODEs
    Canal Systems
    Simultaneous Solution of Algebraic and Ordinary Differential Equations
    Flow into a Mild Channel with a Downstream Control
    Different Modes of Gate Operation
    Hydraulic Jump Downstream from a Gate in a Finite Length Channel
    Nonprismatic Channels
    GVF Profiles in Nonprismatic Channels
    GVF Profiles in Branched Channel Systems
    GVF Profiles in Parallel Channels
    Solutions to Spatially Varied Flows
    Spatially Varied Inflows
    Spatially Varied Flow in Nonprismatic Channels
    Tile Drainage
    Downstream Controls in Nonprismatic Channels
    Gutter Flow and Outflow through Grates
    Multiple Branched Channel Systems
    Other Dependent Variables in GVF Computations
    Varied Flow Function
    Moving Waves
    Moving Hydraulic Jump

    Common Techniques Used in Practice and Controls
    Resistance to Flow in Natural Streams and Rivers
    Techniques Used for Solving Steady Flows in Irregular Channels
    Water Measurement in Channels
    Design of Transitions
    Submerged Flow Downstream from Vertical Gates
    Series of Submerged Gates
    Design of Side Weirs
    Optimal Design of Trapezoidal Channels Considering Total Costs

    Unsteady Flows
    When Should Flow Be Handled as Unsteady?
    Basic One-Dimensional Equations for Unsteady Channel Flows (The St. Venant Equations)Determination of Mathematical Type of St. Venant Equations
    Taking Advantage of the Equation Characteristics
    Solution to Unsteady Flows That Deviate Only Slightly from Uniform Conditions
    Boundary Conditions
    Maximum Possible Flow Rates
    Extending the Methods to Non-Rectangular Channels
    Maximum Flow Rates in Non-Rectangular Channels
    Positive Waves
    Control Structures
    Partial Instant Opening of Gates in Rectangular Channels
    Partial Instant Closing of Gates in Trapezoidal Channels
    Partial Instant Closure Followed by Slow Movement Thereafter
    Dam Break Problem

    Numerical Solution of the St. Venant Equations
    Method of Characteristics
    Boundary Conditions
    Using Characteristics with Specified Time Increments
    Iterative Solution Technique
    Explicit Evaluation of Variables at Points L and R
    Accuracy of Numerical Solutions
    Implicit Methods
    Gauss–Seidel or Successive-Over-Relaxation (SOR) Iterative Solution Techniques
    Crank–Nicolson Newton Iterative Implicit Method
    Weighting Current and Advanced Time Steps Differently
    The Preissmann Implicit Method
    Solving Preissmann Difference Equations Using the Newton Method
    Two-Dimensional Free Surface Flows

    Appendix A: Open Channel Geometry and Properties
    Appendix B: Numerical Methods
    Appendix C: ODESOL: Subroutine to Solve ODEs


    Roland Jeppson is Professor Emeritus of civil and environmental engineering in the Utah Water Research Laboratory (UWRL) at Utah State University in Logan.