| Preface |
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xi | |
| About the Authors |
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xiii | |
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Chapter 1 Introduction to Modelling in Hydrology, Hydraulics, and Contaminant Transport |
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1 | (4) |
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1.1 Examples of Different Types of Models in Water Systems: Deterministic, Stochastic, Data-Based, and Others |
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1 | (1) |
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1.2 Choosing a Numerical Approach for Flow and Transport Modelling |
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2 | (1) |
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1.3 Python as the Preferred Programming Platform |
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2 | (1) |
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3 | (1) |
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1.5 Types of Models Treated in the Book |
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3 | (2) |
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Chapter 2 Non-Linear and Simultaneous Equations |
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5 | (32) |
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2.1 Examples of Non-Linear Functions |
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5 | (3) |
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2.1.1 Normal Depth of Flow in a Trapezoidal Channel |
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5 | (1) |
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2.1.2 Height and Velocity of a Surge Wave |
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6 | (1) |
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2.1.3 Depth of Flow in a Constricted and Raised Channel Section |
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7 | (1) |
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8 | (6) |
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2.2.1 System of Reactors - Steady-State Analysis |
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8 | (2) |
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2.2.2 Steady-State Distribution of Flow in Pipe Networks |
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10 | (3) |
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2.2.3 Derivation of the Unit Hydrograph |
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13 | (1) |
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14 | (3) |
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2.3.1 Non-Linear Equations in One Variable |
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14 | (1) |
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2.3.2 Linear Simultaneous Equations |
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15 | (1) |
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2.3.3 Non-Linear Simultaneous Equations |
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16 | (1) |
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17 | (19) |
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2.4.1 Non-Linear Equations in One Variable: Finding Uniform Flow Depth in a Channel |
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17 | (3) |
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2.4.2 Non-Linear Equations in One Variable: Finding the Height and Velocity of a Surge Wave |
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20 | (3) |
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2.4.3 Non-Linear Equations in One Variable: Finding the Depth of flow above a Hump in a Contraction |
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23 | (2) |
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2.4.4 Solution of Linear Simultaneous Equations: Concentrations in Interconnected Reactors |
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25 | (2) |
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2.4.5 Solution of Linear Simultaneous Equations: Derivation of the Unit Hydrograph |
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27 | (3) |
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2.4.6 Solution of Non-Linear Simultaneous Equations: Flow Distribution in a Three-Pipe Network |
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30 | (3) |
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2.4.7 Solution of Non-Linear Simultaneous Equations: Flow Distribution in a General Pipe Network |
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33 | (3) |
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36 | (1) |
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Chapter 3 Ordinary Differential Equations |
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37 | (38) |
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3.1 Examples of Ordinary Differential Equations in Hydrology, Hydraulics, and Water Resources Engineering |
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37 | (9) |
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3.1.1 Emptying of a Water Tank |
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37 | (1) |
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3.1.2 Computing Flood Outflow from the Spillway of a Dam by the Level-Pool Routing Method |
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38 | (1) |
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3.1.3 Water Surface Profile for Steady-State Gradually Varied Flows |
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39 | (2) |
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3.1.4 Steady-State Concentration Profile for Dissolved Oxygen and Biochemical Oxygen Demand in One-Dimensional Flows |
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41 | (1) |
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3.1.5 Oscillations of Water Level in a Surge Tank |
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42 | (2) |
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3.1.6 Recharge of Rainwater into Ground and Steady-State Groundwater-Table Profile |
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44 | (1) |
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3.1.7 Steady-State Concentration Profile for Contaminant Injection in One-Dimensional Channel Flows |
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45 | (1) |
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46 | (5) |
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3.2.1 First-Order Ordinary Differential Equations |
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47 | (1) |
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47 | (1) |
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3.2.1.2 Fourth-Order Runge-Kutta Method |
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48 | (1) |
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3.2.1.3 Accuracy and Stability |
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49 | (1) |
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3.2.2 Second-Order Ordinary Differential Equations |
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50 | (1) |
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3.2.3 Two-Point Boundary Value Problems |
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51 | (1) |
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51 | (23) |
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3.3.1 First-Order ODE: Solving the Tank Filling and Emptying Problem Using Heun's Method |
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52 | (2) |
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3.3.2 First-Order ODE: Flood Routing through a Reservoir and Spillway Using Heun's Method |
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54 | (4) |
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3.3.3 First-Order ODE: Computation of the Backwater Gradually Varied Flow Profile Using Fourth-Order Runge-Kutta (RK4) Method |
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58 | (3) |
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3.3.4 First-Order ODE: Computing the Steady-State BOD and DO Concentration Profiles in a One-Dimensional Stream Using Heun's Method |
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61 | (3) |
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3.3.5 Second-Order ODE: Surge-Tank Oscillation Problem Solved Using Heun's Method |
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64 | (2) |
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3.3.6 Second-Order ODE: Steady-State Groundwater Table Profile for Recharge and Withdrawal |
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66 | (4) |
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3.3.7 Second-Order ODE: Computing the Steady-State Concentration Profile for Point Loadings in One-Dimensional Channel Flow |
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70 | (4) |
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74 | (1) |
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Chapter 4 Partial Differential Equations in Surface Hydrology, Free Surface Flows, and Ideal Fluid Flows |
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75 | (36) |
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4.1 Governing Equations of Free Surface Flow |
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76 | (3) |
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4.1.1 Governing Equations of Flow in a Prismatic Channel |
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76 | (2) |
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78 | (1) |
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4.1.3 Governing Equations of Two-Dimensional Depth-Averaged Flows |
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78 | (1) |
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4.2 Numerical Methods for Solving the Flow Equations |
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79 | (9) |
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4.2.1 Solving the Kinematic Wave Equation for Flow in a Prismatic Channel with Lateral Inflows |
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79 | (2) |
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4.2.2 Routing a Flood Wave by the Kinematic Wave Approximation in a Triangular Channel |
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81 | (1) |
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4.2.3 Open-Book Catchment Hydrograph with the Kinematic Wave Approximation |
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82 | (1) |
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4.2.4 Simulation of Unsteady Flows in a Channel Using the St. Venant Equations |
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82 | (2) |
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4.2.5 Ideal Fluid Flow Equation Solving |
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84 | (2) |
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4.2.6 Simulation of Two-Dimensional Depth-Averaged Flows in a Shallow Basin |
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86 | (2) |
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88 | (22) |
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4.3.1 Flow in a Rectangular Channel with Lateral Inflows Solved by the Kinematic Wave Equation |
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88 | (3) |
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4.3.2 Routing a Flood Hydrograph by the Kinematic Wave Approximation in a Triangular Channel |
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91 | (3) |
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4.3.3 Simulation of a Simplified Open-Book Catchment Hydrograph with the Kinematic Wave Approximation |
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94 | (2) |
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4.3.4 Simulation of a Surge Wave in a Trapezoidal Channel Using the St. Venant Equations |
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96 | (6) |
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4.3.5 Simulation of Streamlines in an Ideal Fluid Flow |
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102 | (2) |
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4.3.6 Two-Dimensional Depth-Averaged Flows in a Shallow Basin |
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104 | (6) |
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110 | (1) |
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Chapter 5 Partial Differential Equations in Subsurface Flows |
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111 | (22) |
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5.1 Governing Equations of Subsurface Flows |
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111 | (3) |
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5.1.1 Governing Equations of Flow in an Unconfined Aquifer |
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112 | (1) |
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5.1.2 Governing Equations of Flow in a Confined Aquifer |
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113 | (1) |
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5.1.3 Governing Equation of Steady-State Seepage in the Vertical Plane |
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114 | (1) |
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5.2 Numerical Methods for Solving the Groundwater and Seepage Flow Equations |
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114 | (5) |
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5.2.1 Solving the Unsteady One-Dimensional Groundwater Flow in an Unconfined Aquifer |
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114 | (2) |
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5.2.2 Solving the Unsteady Two-Dimensional Groundwater Flow in an Unconfined Aquifer |
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116 | (2) |
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5.2.3 Steady-State Seepage below Floors and Piles |
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118 | (1) |
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119 | (12) |
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5.3.1 Unsteady One-Dimensional Groundwater Flow in an Unconfined Aquifer |
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119 | (3) |
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5.3.2 Unsteady Two-Dimensional Groundwater Flow in an Unconfined Aquifer |
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122 | (5) |
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5.3.3 Steady Seepage below a Weir Floor and Sheet Pile |
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127 | (4) |
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131 | (2) |
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Chapter 6 Partial Differential Equations in Contaminant Transport |
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133 | (20) |
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135 | (2) |
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6.1.1 Governing Equations for Reaction-Diffusion, without Advection |
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135 | (1) |
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6.1.2 Governing Equations for Advection and Diffusion |
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136 | (1) |
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6.1.3 Governing Equations for Advection, Diffusion, and Reaction |
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137 | (1) |
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6.2 Numerical Methods for Finding the Fate of a Contaminant |
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137 | (4) |
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6.2.1 Solving the One-Dimensional Unsteady Reaction-Diffusion Problem |
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137 | (2) |
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6.2.2 Solving the One-Dimensional Unsteady Advection-Diffusion Problem |
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139 | (1) |
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6.2.3 Solving the One-Dimensional Combined Unsteady Advection, Diffusion, and Reaction Equation |
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139 | (1) |
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6.2.4 Solving the Two-Dimensional Unsteady Advection and Diffusion Equation |
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140 | (1) |
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141 | (11) |
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6.3.1 One-Dimensional Unsteady Reaction-Diffusion Problem |
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141 | (2) |
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6.3.2 One-Dimensional Unsteady Advection-Diffusion Problem |
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143 | (3) |
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6.3.3 Two-Dimensional Unsteady Advection-Diffusion Problem |
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146 | (2) |
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6.3.4 Contaminant Dispersion for Seepage below Sheet Pile and Floor |
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148 | (4) |
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152 | (1) |
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Chapter 7 Simple Data-Based Models |
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153 | (24) |
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7.1 Environmental Data and Motivation for Data Analysis |
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154 | (8) |
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7.1.1 Time-Series Data: Variations in Time |
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154 | (1) |
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7.1.1.1 Hourly Record of Temperature and Humidity |
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154 | (1) |
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7.1.1.2 Record of Daily River Stage and Discharge |
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155 | (2) |
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7.1.1.3 Variation of the Rate of Infiltration in Soil with Time |
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157 | (2) |
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7.1.2 Data Recorded in One-Dimensional Space |
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159 | (1) |
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7.1.2.1 Velocity at a Point in a Channel |
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159 | (1) |
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7.1.2.2 Elevation Versus Reservoir Capacity |
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160 | (1) |
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7.1.2.3 Variation of Sediment Concentration with Depth in a Channel |
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160 | (1) |
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7.1.3 Area of a Closed Polygon |
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161 | (1) |
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162 | (6) |
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162 | (2) |
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164 | (2) |
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7.2.3 Area-Finding and Numerical integration |
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166 | (2) |
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168 | (8) |
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169 | (1) |
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170 | (2) |
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7.3.3 Computation of Area |
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172 | (1) |
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7.3.4 Numerical Integration |
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173 | (3) |
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176 | (1) |
| Index |
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177 | |