Environmental Engineering Reference
In-Depth Information
with:
q
water flux per unit width [m
2
/s];
h
height of the water column [m];
v
velocity [m/s].
For a confined aquifer (see Chap. 12) the height remains constant:
h
is equal to
the thickness of the aquifer
H
. In porous media Darcy's Law is valid, which can be
formulated as
uðxÞ¼K
@
h
@x
(13.4)
with:
K
hydraulic conductivity [m/s]
Replacing
u
in (
13.3
) by the formula (
13.4
) delivers:
q ¼T
@h
@x
(13.5)
as transmissivity is the product of hydraulic conductivity and aquifer height:
T ¼ KH
. Equation (
13.5
) is a differential equation for the function
h
(
x
). For
constant transmissivity
T
theequationiseasytosolve:
q
T
x þ h
0
hðxÞ¼
(13.6)
For the unconfined aquifer (see Chap. 12) the starting point is not (
13.5
) but the
following:
q ¼Kh
@h
@x
(13.7)
The differential equation (
13.7
) can also be written as:
2
K
@
h
2
1
q ¼
(13.8)
@x
which has the solution:
2
q
K
x þ h
0
h
2
ðxÞ¼
(13.9)
[m
3
/s] with derivative -
q
as
defining condition. The discharge potential cannot be measured directly but is
introduced, because it fits into the theoretical framework.
'
Another relevant term is the discharge potential
plays an important
role in the following chapters. Note that the findings for the potential are valid,
'
