Page 313 - Hydrogeology Principles and Practice

HYDC08 12/5/05 5:31 PM Page 296

296 Chapter Eight

3 the borehole or well fully penetrates the aquifer;
4 the pumping rate is steady;
5 the residual effects of previous pumping are
negligible.
The model further assumes that the aquifer is
confined or that, for an unconfined aquifer, the
water-table drawdown is negligible compared to the
saturated aquifer thickness (in other words, the trans-
missivity remains constant). The temperature of the
stream is assumed to be constant and equal to the
temperature of the groundwater. A cross-section
through the idealized conceptual model is shown in
Fig. 8.11.
The mathematical solution to the problem shown
in Fig. 8.11 gives the rate of stream depletion as a
proportion of the groundwater abstraction rate as
follows:

q ⎛ 1 ⎞
=
erfc ⎜ ⎟ eq. 8.3
Q ⎝ 2τ ⎠

where τ is a dimensionless length scale for the system
given by:

=
τ tT eq. 8.4
2
LS
where T is the aquifer transmissivity, S is the aquifer
storage coefficient (specific yield for unconfined
aquifer approximations), L is the perpendicular dis-
tance of the borehole or well to the line of the
river, Q is the abstraction rate of the borehole or
well, q is the rate of stream flow depletion, t is time
and erfc is the complementary error function (see
Fig. 8.10 The history of Chalk groundwater abstractions in the Appendix 8).
River Ver catchment, north London, and the impacts on river
Similarly, the volume of stream depletion, v, as a
flow including: (a) a graph of annual groundwater abstractions;
proportion of the groundwater abstraction rate is
(b) a sketch of the reduction in length of the perennial section of
the River Ver; (c) a location map of the River Ver tributary in the given by:
Colne catchment. After Owen (1991).
⎛ ⎞
v 1
=
2
4 i erfc ⎜ ⎟ eq. 8.5
Qt ⎝ 2τ ⎠
1 the aquifer is isotropic, homogeneous, semi-
infinite in areal extent and bounded by an infinite,
straight, fully penetrating stream; where v is the volume of stream depletion during
2
2 water is released instantaneously from aquifer time, t, and i erfc is the second repeated integral of
storage; the error function.