Geology Reference
In-Depth Information
So
v
=-
k
dh
/
dl
(3)
Here the flow is limited to the pore space only so the average interstitial
velocity
v
=
Q
/
A
where
is porosity.
Limits of Darcy's Law
Darcy's law has both upper and lower limits of applicability; it does not hold
at very high fluid velocities. The nature of flow is quantified by the Reynolds
Number. It is expressed as,
(Re) =
vd
/
(4)
(It is a dimensionless ratio)
where,
v
is the velocity (m/s),
is the fluid density (kg/m
3
),
is the fluid
viscosity (kg/m/s), and
d
is the diameter of pipe (m).
Experimental evidence indicates that Darcy's Law is valid as long as Re
does not exceed a critical value (between 1 and 10). The law holds for low
velocity and high gradient.
EQUATIONS OF GROUNDWATER FLOW
Groundwater moves from areas of higher elevation or higher pressure/
hydraulic head (recharge areas) to areas of lower pressure or elevation/
hydraulic head. Permeable material contains interconnected cracks or spaces
that are both numerous enough and large enough to allow water to move
freely. In some permeable materials groundwater may move several metres
a day; in other places, it moves only a few centimetres in a century. The
direction of groundwater flow normally follows the general topography of
the land surface. The groundwater movement is governed by established
hydraulic principles.
Derivation of Groundwater Flow Equation
The groundwater flow equation is often derived for a small representative
elemental volume (REV)—a cube, where the properties of the medium are
assumed to be effectively constant. A mass balance is calculated on the
water flowing in and out of this small volume, the flux terms in the relationship
being expressed in terms of head by using the Darcy's law.
The volume of REV (
V
) =
X
Y
Z
(5)
Let
q
be the specific discharge, so the rate of flow of water through this
REV can be expressed in terms of three components viz.,
q
x
,
q
y
,
q
z
. According
to the Mass Balance equation outflow minus inflow is equal to the change
in storage, i.e.,
