Geoscience Reference
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b) Do the same for
t
= 60 minutes.
c) Compare the results of the calculations for
t
= 30 minutes and
t
= 60 minutes.
Question 4.15:
a) Find
s
f
at
t
= 60 minutes for vertical iniltration into the soil of
Question 4.14
, using
Eq. (
4.40
). Use the following procedure:
Calculate
•
t
using the value found for
s
f
in
Question 4.14b
.
•
Calculate
t
also or a somewhat larger value of
s
f
(larger, because gravity is included
now).
Find a better guess for
•
s
f
by linear interpolation.
•
Calculate again
t
for the value of
s
f
just found.
If necessary repeat these steps.
•
b) Calculate also
I
and
I
cum
using the value found for
s
f
in a.
c) Compare the results with those for horizontal iniltration (
Question 4.14b
).
4.9 Capillary Rise
Soil water will low vertically upward if the hydraulic gradient ∂
H
/ ∂
z
< 0, as depicted
in
Figure 4.11
. Upward soil water low is called capillary rise and occurs in prolonged
dry periods. Especially if the groundwater level is within 1 m of the root zone or soil
surface and the subsoil has a loamy texture, capillary rise may be considerable. We
can calculate the amount of capillary rise straight from the Darcy equation and the
soil hydraulic functions. In prolonged dry periods, we may assume soil water low
between groundwater level and root zone bottom to be more or less stationary:
d
d
h
z
()
=
=−
()
+
qz
constant
kh
1
(4.41)
Partial derivatives have been replaced by normal derivatives because
h
depends only
on
z
, not on
t
. We may rewrite Eq. (
4.41
):
=
−
()
kh
qkh
d
z
d
h
+
()
(4.42)
If we integrate Eq. (
4.42
), we get the height
Z
, which corresponds to a certain
h
above
the groundwater level:
()
+
()
Z
= −
h
kh
qkh
∫
d
∫
Zz
d
h
(4.43)
0
0
If we know the
k
(
h
) relation, we may numerically solve Eq. (
4.43
) for various values
of
q
.
Figure 4.25
shows examples for coarse sand and light loam. If
h
= -16 000 cm
at the bottom of the root zone (wilting point), light loam will still transport 2 mm d
-1
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