Geoscience Reference
In-Depth Information
Packed soil column
Conductivity
k
s
Volume flow
Q
Hydraulic
head
H
1
Hydraulic
head
H
2
Figure 4.16
Soil column experiment illustrating Darcy's law.
at positive hydraulic head gradients (
H
increasing with
x
), water will low in the neg-
ative
x
-direction.
Question 4.9:
A 50-cm-long column containing packed sand with a saturated hydraulic
conductivity of 100 cm d
-1
is placed vertically with the bottom open to the atmosphere.
On the top surface of the column 10 cm of water ponds continuously (
Figure 4.17
). How
large is the soil water lux
q
through the column?
Above question illustrates a fundamental difference between equilibrium problems
and low problems. If the bottom of the column was sealed, then at equilibrium the
hydrostatic pressure potential head at
z
= 0 would be 60 cm because the weight of
all the water above
z
= 0 is exerted at the bottom. However, when the bottom is open
to atmosphere, water will leave the pores at the bottom of the column as soon as
any pressure higher than atmospheric pressure (by deinition equal to zero) develops.
Thus in that case,
h
= 0 at the bottom (
Figure 4.17
). In other words, in the low situa-
tion the weight of the water in the column is in equilibrium with the viscous resistive
forces between water and the porous medium.
Most soil proiles are layered. How can we apply the equation of Darcy to these
proiles?
Figure 4.18
illustrates steady water low through a layered saturated soil
column containing
N
layers of thickness
L
j
and saturated hydraulic conductivity
k
j
(
j
= 1, …
N
). We intend to calculate the water lux and hydrostatic pressure distribu-
tion given the values of
k
j
,
L
j
and ponding water layer. We might replace the hetero-
geneous proile by a proile with the same height and a uniform, effective hydraulic
conductivity, as depicted in
Figure 4.18
. The total hydraulic head loss between top
and bottom of both soil proiles can be written as:
N
∑
L
L
k
j
∆
Hq
L
k
q
L
k
q
L
k
N
∑
j
j
=
1
N
=+++ =
1
2
....
q
=
q
(4.14)
k
j
=
1
1
2
N
j
eff
Search WWH ::
Custom Search