Modelling hydrology, hydraulics and contaminant transport systems in Python

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Cover Half Title Title Page Copyright Page Table of Contents Preface About the Authors Chapter 1: Introduction to Modelling in Hydrology, Hydraulics, and Contaminant Transport 1.1 Examples of Different Types of Models in Water Systems: Deterministic, Stochastic, Data-Based, and Others 1.2 Choosing a Numerical Approach for Flow and Transport Modelling 1.3 Python as the Preferred Programming Platform 1.4 Pedagogical Emphasis 1.5 Types of Models Treated in the Book Chapter 2: Non-Linear and Simultaneous Equations 2.1 Examples of Non-Linear Functions 2.1.1 Normal Depth of Flow in a Trapezoidal Channel 2.1.2 Height and Velocity of a Surge Wave 2.1.3 Depth of Flow in a Constricted and Raised Channel Section 2.2 System of Equations 2.2.1 System of Reactors – Steady-State Analysis 2.2.2 Steady-State Distribution of Flow in Pipe Networks 2.2.3 Derivation of the Unit Hydrograph 2.3 Solution Techniques 2.3.1 Non-Linear Equations in One Variable 2.3.2 Linear Simultaneous Equations 2.3.3 Non-Linear Simultaneous Equations 2.4 Python Programs 2.4.1 Non-Linear Equations in One Variable: Finding Uniform Flow Depth in a Channel 2.4.2 Non-Linear Equations in One Variable: Finding the Height and Velocity of a Surge Wave 2.4.3 Non-Linear Equations in One Variable: Finding the Depth of flow above a Hump in a Contraction 2.4.4 Solution of Linear Simultaneous Equations: Concentrations in Interconnected Reactors 2.4.5 Solution of Linear Simultaneous Equations: Derivation of the Unit Hydrograph 2.4.6 Solution of Non-Linear Simultaneous Equations: Flow Distribution in a Three-Pipe Network 2.4.7 Solution of Non-Linear Simultaneous Equations: Flow Distribution in a General Pipe Network References Chapter 3: Ordinary Differential Equations 3.1 Examples of Ordinary Differential Equations in Hydrology, Hydraulics, and Water Resources Engineering 3.1.1 Emptying of a Water Tank 3.1.2 Computing Flood Outflow from the Spillway of a Dam by the Level-Pool Routing Method 3.1.3 Water Surface Profile for Steady-State Gradually Varied Flows 3.1.4 Steady-State Concentration Profile for Dissolved Oxygen and Biochemical Oxygen Demand in One-Dimensional Flows 3.1.5 Oscillations of Water Level in a Surge Tank 3.1.6 Recharge of Rainwater into Ground and Steady-State Groundwater-Table Profile 3.1.7 Steady-State Concentration Profile for Contaminant Injection in One-Dimensional Channel Flows 3.2 Solution Techniques 3.2.1 First-Order Ordinary Differential Equations 3.2.1.1 Euler’s Method 3.2.1.2 Fourth-Order Runge–Kutta Method 3.2.1.3 Accuracy and Stability 3.2.2 Second-Order Ordinary Differential Equations 3.2.3 Two-Point Boundary Value Problems 3.3 Python Programs 3.3.1 First-Order ODE: Solving the Tank Filling and Emptying Problem Using Heun’s Method 3.3.2 First-Order ODE: Flood Routing through a Reservoir and Spillway Using Heun’s Method 3.3.3 First-Order ODE: Computation of the Back-Water Gradually Varied Flow Profile Using Fourth-Order Runge–Kutta (RK4) Method 3.3.4 First-Order ODE: Computing the Steady-State BOD and DO Concentration Profiles in a One-Dimensional Stream Using Heun’s Method 3.3.5 Second-Order ODE: Surge-Tank Oscillation Problem Solved Using Heun’s Method 3.3.6 Second-Order ODE: Steady-State Groundwater Table Profile for Recharge and Withdrawal 3.3.7 Second-Order ODE: Computing the Steady-State Concentration Profile for Point Loadings in One-Dimensional Channel Flow References Chapter 4: Partial Differential Equations in Surface Hydrology, Free Surface Flows, and Ideal Fluid Flows 4.1 Governing Equations of Free Surface Flow 4.1.1 Governing Equations of Flow in a Prismatic Channel 4.1.2 Ideal Fluid Flow 4.1.3 Governing Equations of Two-Dimensional Depth-Averaged Flows 4.2 Numerical Methods for Solving the Flow Equations 4.2.1 Solving the Kinematic Wave Equation for Flow in a Prismatic Channel with Lateral Inflows 4.2.2 Routing a Flood Wave by the Kinematic Wave Approximation in a Triangular Channel 4.2.3 Open-Book Catchment Hydrograph with the Kinematic Wave Approximation 4.2.4 Simulation of Unsteady Flows in a Channel Using the St. Venant Equations 4.2.5 Ideal Fluid Flow Equation Solving 4.2.6 Simulation of Two-Dimensional Depth-Averaged Flows in a Shallow Basin 4.3 Python Programs 4.3.1 Flow in a Rectangular Channel with Lateral Inflows Solved by the Kinematic Wave Equation 4.3.2 Routing a Flood Hydrograph by the Kinematic Wave Approximation in a Triangular Channel 4.3.3 Simulation of a Simplified Open-Book Catchment Hydrograph with the Kinematic Wave Approximation 4.3.4 Simulation of a Surge Wave in a Trapezoidal Channel Using the St. Venant Equations 4.3.5 Simulation of Streamlines in an Ideal Fluid Flow 4.3.6 Two-Dimensional Depth-Averaged Flows in a Shallow Basin References Chapter 5: Partial Differential Equations in Subsurface Flows 5.1 Governing Equations of Subsurface Flows 5.1.1 Governing Equations of Flow in an Unconfined Aquifer 5.1.2 Governing Equations of Flow in a Confined Aquifer 5.1.3 Governing Equation of Steady-State Seepage in the Vertical Plane 5.2 Numerical Methods for Solving the Groundwater and Seepage Flow Equations 5.2.1 Solving the Unsteady One-Dimensional Groundwater Flow in an Unconfined Aquifer 5.2.2 Solving the Unsteady Two-Dimensional Groundwater Flow in an Unconfined Aquifer 5.2.3 Steady-State Seepage below Floors and Piles 5.3 Python Programs 5.3.1 Unsteady One-Dimensional Groundwater Flow in an Unconfined Aquifer 5.3.2 Unsteady Two-Dimensional Groundwater Flow in an Unconfined Aquifer 5.3.3 Steady Seepage below a Weir Floor and Sheet Pile References Chapter 6: Partial Differential Equations in Contaminant Transport 6.1 Governing Equations 6.1.1 Governing Equations for Reaction-Diffusion, without Advection 6.1.2 Governing Equations for Advection and Diffusion 6.1.3 Governing Equations for Advection, Diffusion, and Reaction 6.2 Numerical Methods for Finding the Fate of a Contaminant 6.2.1 Solving the One-Dimensional Unsteady Reaction-Diffusion Problem 6.2.2 Solving the One-Dimensional Unsteady Advection-Diffusion Problem 6.2.3 Solving the One-Dimensional Combined Unsteady Advection, Diffusion, and Reaction Equation 6.2.4 Solving the Two-Dimensional Unsteady Advection and Diffusion Equation 6.3 Python Programs 6.3.1 One-Dimensional Unsteady Reaction-Diffusion Problem 6.3.2 One-Dimensional Unsteady Advection-Diffusion Problem 6.3.3 Two-Dimensional Unsteady Advection-Diffusion Problem 6.3.4 Contaminant Dispersion for Seepage below Sheet Pile and Floor References Chapter 7: Simple Data-Based Models 7.1 Environmental Data and Motivation for Data Analysis 7.1.1 Time-Series Data: Variations in Time 7.1.1.1 Hourly Record of Temperature and Humidity 7.1.1.2 Record of Daily River Stage and Discharge 7.1.1.3 Variation of the Rate of Infiltration in Soil with Time 7.1.2 Data Recorded in One-Dimensional Space 7.1.2.1 Velocity at a Point in a Channel 7.1.2.2 Elevation Versus Reservoir Capacity 7.1.2.3 Variation of Sediment Concentration with Depth in a Channel 7.1.3 Area of a Closed Polygon 7.2 Solution Techniques 7.2.1 Interpolation 7.2.2 Regression 7.2.3 Area-Finding and Numerical integration 7.3 Python Programs 7.3.1 Interpolation 7.3.2 Regression 7.3.3 Computation of Area 7.3.4 Numerical Integration References Index