Geoscience Reference
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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
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