Page 169 - Water and wastewater engineering

4-24 WATER AND WASTEWATER ENGINEERING

Piezometric surface
before pumping begins
Well A Well B Well C

9.00
S C on A S 10.86 S on C 9.00
A
10.86
S B on A 10.86
S on C
B
Piezometric surface
S 26.14 S 26.14 of individual S 26.14
well pumping
by itself
S A 46.00 S C 46.00
Piezometric surface S 47.86
B
with all wells
pumping
Depth of well
100.0 m Depth of well 25 m
87.5 m
25 m
FIGURE 4-10
Interference drawdown of three wells.
( Source: Davis and Cornwall, 2008.)

Comment. Note that if the wells are pumped at different rates, the symmetry would be destroyed
and the value Q /(4 T ) would have to be calculated separately for each case. Likewise, if the
distances were not symmetric, then separate u values would be required.

Unsteady Flow in an Unconfined Aquifer. There is no exact solution to the transient-flow
problem for unconfined aquifers because T changes with time and r as the water table is lowered.
Furthermore, vertical-flow components near the well invalidate the assumption of radial flow that
is required to obtain an analytical solution. If the unconfined aquifer is very deep in comparison
to the drawdown, the transient-flow solution for a confined aquifer may be used for an approxi-
mate solution. For larger drawdowns, Boulton (1954) presented a solution that is valid if the
water depth in the well is greater than the half of the height of the nonpumping water level above
the bottom confining layer, that is 0.5H in Figure 4-11 .
The height of the water level in a pumping well (taking into account the surface of seepage
but neglecting well losses) can be estimated from
⎧
2
2
b ⎬
h iw H Q ln ⎨ 1 5 a Kt ⎫ 0 5 . (4-8)
.
K ⎩ Sr w ⎭
p
where h iw height of water inside pumped well, m
H static height of piezometric surface (the water table), m
K hydraulic conductivity, m/s
t time from beginning of pumping, s
S specific yield
r w radius of well, m