Geoscience Reference
In-Depth Information
Fig. 10.9 Scaled outflow rate
q
+
from an aquifer with
rectangular cross section and with
D
c
+
=
0
.
5
,
B
+
=
1, plotted against scaled time
t
+
. The rate of flow is scaled with (
Dk
0
) and the
time variable with [(
θ
0
− θ
r
)
D
]
/
k
0
. Curve 1
describes the outflow hydrograph for soil
properties (
aD
)
−
1
=
0
.
36,
n
=
3 and
b
=
1
.
5;
curve 2 for (
aD
)
−
1
=
0
.
1,
n
=
3 and
b
=
3;
curve 3 represents the case in which the partly
saturated zone above the water table is neglected
(see Section 10.2). (After Verma and Brutsaert,
1971b.)
Fig. 10.10 Scaled outflow rate
q
+
from an aquifer with
rectangular cross section and with
D
c
+
=
5, plotted against scaled time
t
+
. The rate of flow is scaled with (
Dk
0
) and the
time variable with [(
θ
0
− θ
r
)
D
]
/
k
0
. Curve 1
describes the outflow hydrograph for soil
properties (
aD
)
−
1
0
,
B
+
=
=
0
.
36,
n
=
3 and
b
=
1
.
5;
curve 2 for (
aD
)
−
1
=
0
.
1,
n
=
3 and
b
=
3;
curve 3 represents the case in which the partly
saturated zone above the water table is neglected
(see Section 10.2). (After Verma and Brutsaert,
1971b.)
The boundary conditions (see Figure 10.3) are a combination of Equations (10.2) and (10.3),
namely
h
=
D
c
x
=
0
0
≤
z
≤
D
c
h
=
z
x
=
0
D
c
≤
z
≤
D
∂
h
∂
x
=
0
x
=
B
0
≤
z
≤
D
(10.6)
∂
h
∂
z
=
00
≤
x
≤
Bz
=
0
h
=
D
0
≤
x
≤
Bz
=
D
The solution can be obtained in several different ways. Kirkham (1950) derived it by
generalizing an earlier solution in cylindrical coordinates for the problem of flow into an