Page 41 - Hydrogeology Principles and Practice

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Application of Darcy’s law to simple hydrogeological situations
2.1

The following two worked examples illustrate the application contact with the water table and is directly contaminating the
of Darcy’s law to simple hydrogeological situations. In the first aquifer. The problem is to estimate the time taken for dissolved
example, the alluvial aquifer shown in Fig. 1 is recharged by solutes to reach a spring discharge area located down-gradient of
meltwater runoff from the adjacent impermeable mountains that the waste tip. Assuming that the contaminant is unreactive and
run parallel to the axis of the valley. If the groundwater that collects moves at the same rate as the steady, uniform groundwater flow,
in the aquifer discharges to the river, then it is possible to estimate then from a consideration of equation 2.10 and the information
the river flow at the exit from the valley. To solve this problem, and given in Fig. 2, the average linear velocity is calculated as follows:
assuming that the river is entirely supported by groundwater dis-
charge under steady, uniform flow conditions, the groundwater q Kh dd
/ l
discharge (Q) can be calculated using equation 2.5 and the infor- 2 = = eq. 2
n n
mation given in Fig. 1, as follows: e e
×
510 −4 × 10 −3
⋅ 5
dh 2 = eq. 3
Q =−KA . 025
dl
Q = 1 × 10 −3 ⋅ 20 ⋅ 5000 ⋅ 4 × 10 −3 2 = 1 × 10 ms −1 eq. 4
−5
3 −1
Q = 0.4 m s eq. 1
Therefore, the time taken, t, to move a distance of 200 m in the
Accounting for both halves of the valley floodplain, the total dis- direction of groundwater flow from the waste tip to the spring is:
3 −1
charge from the alluvial aquifer as river flow is 0.8 m s .
In the second example (Fig. 2), a municipal waste disposal facil- t 200 10 s 230 days eq. 5
×
=
≈
7
= 2
×
ity is situated in a former sand and gravel quarry. The waste is in 110 −5

Fig. 1 Alluvial aquifer bounded by
impermeable bedrock.

Fig. 2 Municipal waste disposal site contaminating a sand and gravel aquifer.