Groundwater - Mathematics and Statistics for the Environment - page 583

interest relative to some reference level. The energy of fluid pressure is expressed as the pressure
head ( h p ). The pressure head is equivalent to the height of the water column overlying the point of
interest. The total hydraulic head is then given by

h = z + h p (21.3)

Groundwater will move from areas of high mechanical energy to areas with low mechanical
energy (Baron, 2003). The hydraulic gradient of a flow system of interest is defined as the difference
in hydraulic head between two points of interest ( dh ) and the flow distance between these two points
( dl ), or in mathematical terms

Gradient h = dh / dl (21.4)

21.2.6 F loW l ines and F loW n ets
A flow line is an imaginary line that follows the path that a parcel of groundwater would follow as
it flows through an aquifer. Flow lines are useful tools for visualizing the flow of groundwater. Flow
lines can be constructed from equipotential lines or lines of equal hydraulic head. The combination
of equipotential lines and flow lines results in a flow net—basically, a graphical solution of the two-
dimensional Laplace's equation (Fetter, 1994).

21.3 GROUNDWATER FLOW
Groundwater flow for a steady-state condition in which the water table or piezometric head does not
change within a specified time is expressed by the following equations (Gupta, 1997):

( )

Kh − h

1 2

Pore velocity or advection, v = (21.5)

nL

where pore area of flow A v = η A .
Because Q = A v , by combining we can obtain Darcy's law:

( )

Kh − hA

1 2

Rate of groundwater flow, Q = (21.6)

L

where
Q = Rate of groundwater flow.
K = Hydraulic conductivity.
h 1 = Water head at upstream end.
h 2 = Water head at downstream end.
A = Aquifer cross-section area through which flow takes place.
L = Distance between h 1 and h 2 .
η = Porosity.

Note: The term ( h 1 - h 2 )/ L is the hydraulic gradient.

■ EXAMPLE 21.2
Problem : An irrigation ditch runs parallel to a pond. They are 2200 ft apart. A pervious formation
of 40-ft average thickness connects them. Hydraulic conductivity and porosity of the pervious for-
mation are 12 ft/day and 0.55, respectively. The water level in the ditch is at an elevation of 120 ft
and at 110 ft in the pond. Determine the rate of seepage from the ditch to the pond.