Page 123 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

JWCL344_ch03_061-117.qxd 8/17/10 7:48 PM Page 85

3.11 Prediction of Drawdown 85
3.11.2 Variable Discharge

The rate at which water is pumped from a well field in a water supply system will vary
with time in response to changes in demand. The continuous rate of pumping curve can be
approximated by a series of steps as shown in Fig. 3.9. Then each step can be analyzed,
using one of the conventional equations. From the principle of superposition, the draw-
down at any point at any specific time can be obtained as the sum of increments in draw-
downs caused by the step increases up to that time.
s s 1 s 2 . . . s t (3.33)

Using a semilogarithmic approximation,
2
s (264 Q i >T) log[(0.3 Tt i )>(r S)] (3.34)
where

t i t t i 1
Q 3

Q 2
Discharge Q 1 Variable discharge

t 0 t 1 t 2 t
Time
(a)
Q 3
Q 2 ΔQ 3
Discharge Q 1 ΔQ 2

ΔQ 1

t 0 t 1 t 2 t
Time
(b)

s 1
Drawdown s 2

s 3
Figure 3.9 Step Function Approximation of
(c) Variable Discharge