Principles of Ground Water Flow

Instructional Objectives
On completion of the lesson, the student shall be learn
1. The description of steady state of gr
ound water flow in the form of Laplace
equation derived from continuity
equation and Darcy’s law for ground
water movement.
2. The quantitative description of
unsteady state ground water flow.
3. The definition of the
terms Specific Yield and
Specific Storage and their
relationship with Storativit
y of a confined aquifer.
4. The expressions for ground wate
r flow in unconfined and confined
aquifers, written in terms of Transmissivity.
5. Expression for two – dimensional
flow in unconfined and confined
aquifers; Boussinesq equation.
6. Expression for two – dim
ensional seepage flow below dams.
7. Analytical solution of steady one di
mensional flow in simple cases of
confined and unconfined aquifers.
2.6.0 Introduction
In the earlier lesson, qualitat
ive assessment of subsurface water whether in the
unsaturated or in the saturated ground was
made. Movement of water stored in
the saturated soil or fractured bed rock,
also called aquifer, was seen to depend
upon the hydraulic gradient. Other relationships between the water storage and
the portion of that which
can be withdrawn from an aqui
fer were also discussed.
In this lesson, we derive the mathematic
al description of saturated ground water
flow and its exact and approximate relations to the hydraulic gradient.
2.6.1 Continuity equation and Darcy’s law under steady state
conditions
Consider the flow of ground water taking place within a small cube (of lengths
?
x,
?
y and
?
z respectively the direction of the
three areas which may also be called
the elementary control volume) of a sa
turated aquifer as shown in Figure 1.