Flow in Porous Media and Open Channels

  1. Open-Channel Flow
    1. Introduction to Open-Channel Flow
      1. Definition and Key Features
        1. Free Surface Characteristics
          1. Atmospheric Pressure Effects
            1. Types of Open Channels
              1. Natural Channels
                1. Rivers
                  1. Streams
                    1. Irregular Geometry
                    2. Artificial Channels
                      1. Canals
                        1. Flumes
                          1. Regular Geometry
                        2. Comparison with Pipe Flow
                          1. Free Surface vs Pressurized Flow
                            1. Energy Considerations
                              1. Momentum Considerations
                                1. Flow Resistance Differences
                                2. Geometric Properties
                                  1. Channel Cross-Section Shapes
                                    1. Rectangular
                                      1. Trapezoidal
                                        1. Triangular
                                          1. Circular
                                            1. Parabolic
                                              1. Irregular
                                              2. Flow Depth
                                                1. Top Width
                                                  1. Wetted Area
                                                    1. Wetted Perimeter
                                                      1. Hydraulic Radius
                                                        1. Hydraulic Depth
                                                      2. Classification of Open-Channel Flow
                                                        1. Based on Time Variation
                                                          1. Steady Flow
                                                            1. Constant Discharge
                                                              1. Constant Depth
                                                              2. Unsteady Flow
                                                                1. Variable Discharge
                                                                  1. Variable Depth
                                                                2. Based on Spatial Variation
                                                                  1. Uniform Flow
                                                                    1. Constant Depth
                                                                      1. Constant Velocity
                                                                      2. Varied Flow
                                                                        1. Gradually Varied Flow
                                                                          1. Rapidly Varied Flow
                                                                        2. Based on Flow Regime
                                                                          1. Laminar Flow
                                                                            1. Low Reynolds Number
                                                                              1. Viscous Effects Dominant
                                                                              2. Turbulent Flow
                                                                                1. High Reynolds Number
                                                                                  1. Inertial Effects Dominant
                                                                                  2. Subcritical Flow
                                                                                    1. Froude Number Less Than 1
                                                                                      1. Tranquil Flow
                                                                                      2. Critical Flow
                                                                                        1. Froude Number Equal to 1
                                                                                          1. Minimum Energy
                                                                                          2. Supercritical Flow
                                                                                            1. Froude Number Greater Than 1
                                                                                              1. Rapid Flow
                                                                                          3. Energy and Momentum Principles
                                                                                            1. Specific Energy
                                                                                              1. Definition and Concept
                                                                                                1. Components
                                                                                                  1. Depth
                                                                                                    1. Velocity Head
                                                                                                    2. Specific Energy Diagram
                                                                                                      1. Alternate Depths
                                                                                                        1. Critical Depth
                                                                                                          1. Minimum Specific Energy
                                                                                                          2. Critical Flow Conditions
                                                                                                            1. Critical Depth Calculation
                                                                                                              1. Critical Velocity
                                                                                                                1. Critical Slope
                                                                                                                2. Specific Force
                                                                                                                  1. Definition and Concept
                                                                                                                    1. Momentum Function
                                                                                                                      1. Specific Force Diagram
                                                                                                                        1. Sequent Depths
                                                                                                                        2. Energy Losses
                                                                                                                          1. Friction Losses
                                                                                                                            1. Distributed Losses
                                                                                                                              1. Manning's Equation
                                                                                                                              2. Local Losses
                                                                                                                                1. Contractions
                                                                                                                                  1. Expansions
                                                                                                                                    1. Bends
                                                                                                                                2. Uniform Flow
                                                                                                                                  1. Concept and Conditions
                                                                                                                                    1. Equilibrium of Forces
                                                                                                                                      1. Constant Depth and Velocity
                                                                                                                                        1. Normal Depth
                                                                                                                                        2. Flow Resistance Equations
                                                                                                                                          1. Chézy Equation
                                                                                                                                            1. Chézy Coefficient
                                                                                                                                              1. Historical Development
                                                                                                                                                1. Application and Limitations
                                                                                                                                                2. Manning's Equation
                                                                                                                                                  1. Manning's Roughness Coefficient
                                                                                                                                                    1. Selection of n Values
                                                                                                                                                      1. Composite Roughness
                                                                                                                                                      2. Darcy-Weisbach Equation
                                                                                                                                                        1. Friction Factor
                                                                                                                                                          1. Application to Open Channels
                                                                                                                                                        2. Normal Depth Computation
                                                                                                                                                          1. Analytical Methods
                                                                                                                                                            1. Trial and Error Methods
                                                                                                                                                              1. Numerical Methods
                                                                                                                                                                1. Graphical Methods
                                                                                                                                                                2. Velocity Distribution
                                                                                                                                                                  1. Logarithmic Profile
                                                                                                                                                                    1. Power Law Profile
                                                                                                                                                                      1. Average Velocity
                                                                                                                                                                      2. Channel Design
                                                                                                                                                                        1. Best Hydraulic Sections
                                                                                                                                                                          1. Maximum Discharge
                                                                                                                                                                            1. Minimum Perimeter
                                                                                                                                                                            2. Rectangular Channels
                                                                                                                                                                              1. Optimal Proportions
                                                                                                                                                                              2. Trapezoidal Channels
                                                                                                                                                                                1. Optimal Side Slopes
                                                                                                                                                                                2. Circular Channels
                                                                                                                                                                                  1. Optimal Flow Depth
                                                                                                                                                                                  2. Lining Materials
                                                                                                                                                                                    1. Concrete
                                                                                                                                                                                      1. Riprap
                                                                                                                                                                                        1. Vegetation
                                                                                                                                                                                    2. Gradually Varied Flow
                                                                                                                                                                                      1. Dynamic Equation
                                                                                                                                                                                        1. Derivation and Assumptions
                                                                                                                                                                                          1. Physical Interpretation
                                                                                                                                                                                            1. Friction Slope
                                                                                                                                                                                              1. Energy Slope
                                                                                                                                                                                              2. Channel Slope Classification
                                                                                                                                                                                                1. Mild Slope
                                                                                                                                                                                                  1. Normal Depth Greater Than Critical
                                                                                                                                                                                                  2. Steep Slope
                                                                                                                                                                                                    1. Normal Depth Less Than Critical
                                                                                                                                                                                                    2. Critical Slope
                                                                                                                                                                                                      1. Normal Depth Equal to Critical
                                                                                                                                                                                                      2. Horizontal Slope
                                                                                                                                                                                                        1. Zero Slope
                                                                                                                                                                                                        2. Adverse Slope
                                                                                                                                                                                                          1. Negative Slope
                                                                                                                                                                                                        3. Water Surface Profiles
                                                                                                                                                                                                          1. Profile Classification
                                                                                                                                                                                                            1. M Profiles
                                                                                                                                                                                                              1. S Profiles
                                                                                                                                                                                                                1. C Profiles
                                                                                                                                                                                                                  1. H Profiles
                                                                                                                                                                                                                    1. A Profiles
                                                                                                                                                                                                                    2. Profile Characteristics
                                                                                                                                                                                                                      1. Asymptotic Behavior
                                                                                                                                                                                                                        1. Control Sections
                                                                                                                                                                                                                        2. Profile Drawing
                                                                                                                                                                                                                          1. Qualitative Analysis
                                                                                                                                                                                                                            1. Quantitative Computation
                                                                                                                                                                                                                          2. Computation Methods
                                                                                                                                                                                                                            1. Direct Step Method
                                                                                                                                                                                                                              1. Step-by-Step Procedure
                                                                                                                                                                                                                                1. Distance Calculation
                                                                                                                                                                                                                                2. Standard Step Method
                                                                                                                                                                                                                                  1. Iterative Solution
                                                                                                                                                                                                                                    1. Energy Balance
                                                                                                                                                                                                                                    2. Numerical Integration
                                                                                                                                                                                                                                      1. Runge-Kutta Methods
                                                                                                                                                                                                                                        1. Finite Difference Methods
                                                                                                                                                                                                                                    3. Rapidly Varied Flow
                                                                                                                                                                                                                                      1. Hydraulic Jump
                                                                                                                                                                                                                                        1. Definition and Mechanism
                                                                                                                                                                                                                                          1. Energy Dissipation
                                                                                                                                                                                                                                            1. Momentum Conservation
                                                                                                                                                                                                                                              1. Sequent Depth Relations
                                                                                                                                                                                                                                                1. Jump Classification
                                                                                                                                                                                                                                                  1. Undular Jump
                                                                                                                                                                                                                                                    1. Weak Jump
                                                                                                                                                                                                                                                      1. Oscillating Jump
                                                                                                                                                                                                                                                        1. Steady Jump
                                                                                                                                                                                                                                                          1. Strong Jump
                                                                                                                                                                                                                                                          2. Jump Location
                                                                                                                                                                                                                                                            1. Natural Location
                                                                                                                                                                                                                                                              1. Forced Location
                                                                                                                                                                                                                                                              2. Applications
                                                                                                                                                                                                                                                                1. Energy Dissipation
                                                                                                                                                                                                                                                                  1. Flow Control
                                                                                                                                                                                                                                                                2. Flow Over Weirs
                                                                                                                                                                                                                                                                  1. Sharp-Crested Weirs
                                                                                                                                                                                                                                                                    1. Rectangular Weirs
                                                                                                                                                                                                                                                                      1. Triangular Weirs
                                                                                                                                                                                                                                                                        1. Trapezoidal Weirs
                                                                                                                                                                                                                                                                        2. Broad-Crested Weirs
                                                                                                                                                                                                                                                                          1. Critical Flow Conditions
                                                                                                                                                                                                                                                                            1. Discharge Coefficients
                                                                                                                                                                                                                                                                            2. Discharge Equations
                                                                                                                                                                                                                                                                              1. Head-Discharge Relations
                                                                                                                                                                                                                                                                                1. Coefficient Determination
                                                                                                                                                                                                                                                                              2. Flow Under Gates
                                                                                                                                                                                                                                                                                1. Sluice Gates
                                                                                                                                                                                                                                                                                  1. Free Flow
                                                                                                                                                                                                                                                                                    1. Submerged Flow
                                                                                                                                                                                                                                                                                    2. Discharge Computation
                                                                                                                                                                                                                                                                                      1. Contraction Coefficients
                                                                                                                                                                                                                                                                                        1. Velocity Coefficients
                                                                                                                                                                                                                                                                                      2. Channel Transitions
                                                                                                                                                                                                                                                                                        1. Contractions
                                                                                                                                                                                                                                                                                          1. Gradual Contractions
                                                                                                                                                                                                                                                                                            1. Sudden Contractions
                                                                                                                                                                                                                                                                                            2. Expansions
                                                                                                                                                                                                                                                                                              1. Gradual Expansions
                                                                                                                                                                                                                                                                                                1. Sudden Expansions
                                                                                                                                                                                                                                                                                                2. Channel Bends
                                                                                                                                                                                                                                                                                                  1. Superelevation
                                                                                                                                                                                                                                                                                                    1. Secondary Currents
                                                                                                                                                                                                                                                                                                3. Unsteady Flow
                                                                                                                                                                                                                                                                                                  1. Governing Equations
                                                                                                                                                                                                                                                                                                    1. Saint-Venant Equations
                                                                                                                                                                                                                                                                                                      1. Continuity Equation
                                                                                                                                                                                                                                                                                                        1. Momentum Equation
                                                                                                                                                                                                                                                                                                        2. Assumptions and Limitations
                                                                                                                                                                                                                                                                                                          1. Initial Conditions
                                                                                                                                                                                                                                                                                                            1. Boundary Conditions
                                                                                                                                                                                                                                                                                                            2. Wave Propagation
                                                                                                                                                                                                                                                                                                              1. Small Gravity Waves
                                                                                                                                                                                                                                                                                                                1. Wave Celerity
                                                                                                                                                                                                                                                                                                                  1. Shallow Water Waves
                                                                                                                                                                                                                                                                                                                  2. Wave Types
                                                                                                                                                                                                                                                                                                                    1. Kinematic Waves
                                                                                                                                                                                                                                                                                                                      1. Diffusion Waves
                                                                                                                                                                                                                                                                                                                        1. Dynamic Waves
                                                                                                                                                                                                                                                                                                                        2. Wave Attenuation
                                                                                                                                                                                                                                                                                                                          1. Wave Dispersion
                                                                                                                                                                                                                                                                                                                          2. Flood Routing
                                                                                                                                                                                                                                                                                                                            1. Purpose and Applications
                                                                                                                                                                                                                                                                                                                              1. Hydrologic Routing
                                                                                                                                                                                                                                                                                                                                1. Muskingum Method
                                                                                                                                                                                                                                                                                                                                  1. Storage-Indication Method
                                                                                                                                                                                                                                                                                                                                  2. Hydraulic Routing
                                                                                                                                                                                                                                                                                                                                    1. Method of Characteristics
                                                                                                                                                                                                                                                                                                                                      1. Finite Difference Methods
                                                                                                                                                                                                                                                                                                                                        1. Finite Element Methods
                                                                                                                                                                                                                                                                                                                                      2. Dam-Break Flows
                                                                                                                                                                                                                                                                                                                                        1. Instantaneous Dam Break
                                                                                                                                                                                                                                                                                                                                          1. Gradual Dam Break
                                                                                                                                                                                                                                                                                                                                            1. Flood Wave Propagation
                                                                                                                                                                                                                                                                                                                                          2. Sediment Transport
                                                                                                                                                                                                                                                                                                                                            1. Sediment Properties
                                                                                                                                                                                                                                                                                                                                              1. Particle Size Distribution
                                                                                                                                                                                                                                                                                                                                                1. Specific Gravity
                                                                                                                                                                                                                                                                                                                                                  1. Shape Factors
                                                                                                                                                                                                                                                                                                                                                    1. Fall Velocity
                                                                                                                                                                                                                                                                                                                                                    2. Initiation of Motion
                                                                                                                                                                                                                                                                                                                                                      1. Critical Shear Stress
                                                                                                                                                                                                                                                                                                                                                        1. Shields Diagram
                                                                                                                                                                                                                                                                                                                                                          1. Critical Velocity
                                                                                                                                                                                                                                                                                                                                                          2. Transport Modes
                                                                                                                                                                                                                                                                                                                                                            1. Bed Load
                                                                                                                                                                                                                                                                                                                                                              1. Rolling
                                                                                                                                                                                                                                                                                                                                                                1. Sliding
                                                                                                                                                                                                                                                                                                                                                                  1. Saltation
                                                                                                                                                                                                                                                                                                                                                                    1. Transport Equations
                                                                                                                                                                                                                                                                                                                                                                    2. Suspended Load
                                                                                                                                                                                                                                                                                                                                                                      1. Suspension Mechanisms
                                                                                                                                                                                                                                                                                                                                                                        1. Concentration Profiles
                                                                                                                                                                                                                                                                                                                                                                          1. Transport Equations
                                                                                                                                                                                                                                                                                                                                                                          2. Wash Load
                                                                                                                                                                                                                                                                                                                                                                            1. Fine Sediments
                                                                                                                                                                                                                                                                                                                                                                              1. Supply Limited
                                                                                                                                                                                                                                                                                                                                                                            2. Factors Affecting Transport
                                                                                                                                                                                                                                                                                                                                                                              1. Flow Velocity
                                                                                                                                                                                                                                                                                                                                                                                1. Shear Stress
                                                                                                                                                                                                                                                                                                                                                                                  1. Sediment Size
                                                                                                                                                                                                                                                                                                                                                                                    1. Channel Geometry
                                                                                                                                                                                                                                                                                                                                                                                      1. Bed Forms
                                                                                                                                                                                                                                                                                                                                                                                      2. Stable Channel Design
                                                                                                                                                                                                                                                                                                                                                                                        1. Regime Theory
                                                                                                                                                                                                                                                                                                                                                                                          1. Kennedy's Method
                                                                                                                                                                                                                                                                                                                                                                                            1. Lacey's Method
                                                                                                                                                                                                                                                                                                                                                                                            2. Tractive Force Method
                                                                                                                                                                                                                                                                                                                                                                                              1. Permissible Velocity Method
                                                                                                                                                                                                                                                                                                                                                                                                1. Channel Armoring
                                                                                                                                                                                                                                                                                                                                                                                                  1. Erosion Control Measures

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                                                                                                                                                                                                                                                                                                                                                                                              1. Fundamental Concepts in Fluid Mechanics