The Groundwater Project

Introduction to Fluid Mechanics for Groundwater Scientists

Publication year: 2023
Number of pages: 130

ISBN: 978-1-77470-056-3

Author:

Harald Klammler: Federal University of Bahia, Brazil

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Released: 21 novembro 2023

Description

Starting from Newton’s laws of motion and viscosity, this book is an introduction to fundamental aspects of fluid dynamics that are most relevant to groundwater scientists. Based on a perspective of driving versus resisting forces that govern the motion of a fluid, the author derives Darcy’s law for flow through porous media by relating it to the Navier-Stokes equation for fluid flow in general. By combining the effects of gravity and pressure, the author identifies hydraulic head as a convenient numerical quantity to represent the force driving groundwater flow. In contrast to the physical derivation of hydraulic head, hydraulic conductivity emerges as a parameter related to the resisting frictional forces between the mobile fluid and the stationary porous medium. These frictional seepage forces also affect the effective stress state of the porous medium, thus establishing a link to soil stability and quicksand formation.

Combining Darcy’s law with the law of mass conservation leads the reader to the fundamental equations of saturated groundwater flow. Finally, the effects of capillary forces are included to establish the governing equations for unsaturated and multi-phase flow.

Throughout the book, the author focuses on thoroughly illustrating and deriving the equations while applying order of magnitude analyses. This approach makes it possible to extract the most information, for example in terms of the scale of response time, without requiring explicit solutions. A number of boxes and solved exercises contain further details and links to practical applications such as the water table ratio that reflects ‘fullness’ of an aquifer and the performance of slug tests for in situ measurement of hydraulic conductivity. This book makes an important contribution to groundwater science by providing a progressive introductory explanation of the physical mechanics of groundwater flow and the accompanying socioeconomic and ecological problems that may arise.

Interview with Author

Contents

1 INTRODUCTION

2 STRAIGHT MOVEMENT OF A RIGID BODY

2.1 Location, Velocity, and Acceleration

2.2 Newton’s Second Law of Motion, Momentum, and Kinetic Energy

2.3 Coulomb Friction and Drag Forces

3 VISCOUS FLOW AND STOKES EQUATION

3.1 Newtonian Fluids, Viscosity, and Stokes Drag

3.2 Flow Between Two Plates – Planar Poiseuille Flow

3.3 Flow Through a Circular Pipe – Cylindrical Poiseuille Flow

4 INVISCID FLOW AND EULER’S EQUATION

5 NAVIER STOKES EQUATION AND REYNOLDS NUMBER

6 FLOW THROUGH POROUS MEDIA AND DARCY’S LAW

6.1 Negligible Inertia and Continuum Perspective

6.2 Hydraulic Head as Driving Force Potential

6.3 Hydraulic Head as Flux Potential

6.4 Anisotropy

7 CONSERVATION OF MASS AND FLOW EQUATIONS

8 INITIAL AND BOUNDARY CONDITIONS

9 WRAP-UP

10 EXERCISES

11 BOXES

Box 1 Order of Magnitude Analysis

Box 2 A Simple Numerical Solution Method

Box 3 Effective Stress, Seepage Force and Quicksand Formation

Box 4 Anisotropy and Notational Conventions

Box 5 The Radial Flow Problem

Box 6 The Water Table Ratio

Box 7 Unsaturated Flow and Richards Equation

Box 8 Multi Phase Flow

11 EXERCISE SOLUTIONS

12 REFERENCES

13 BASIC NOTATIONS

14 ABOUT THE AUTHOR