Page 127 - 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 89

3.12 Multiple-Well Systems 89

(a) Drawdown at face of pumping well:
s 1 0.765 21.89 16.73 m
Drawdown in central well:
s 2 0.765 8.08 6.18 m
Drawdown in other outside well:
s 3 0.765 6.69 5.12 m
(b) Drawdown in outside wells:
s 1 s 2 s 3 16.73 6.18 5.12 28.03 m
Drawdown in central well:
s 1 s 2 s 3 16.73 6.18 6.18 29.09 m

A problem of more practical interest is to determine the discharges of the wells when
their drawdowns are given. This involves simultaneous solution of linear equations, which
can be undertaken by numerical methods or by trial and error.

EXAMPLE 3.7 DISCHARGE FROM THREE WELLS AT A GIVEN DRAWDOWN

Suppose we want to restrict the drawdown in each of the wells from Example 3.6 to 60 ft (18.3 m).
What will be the corresponding discharges for the individual wells?
Solution 1 (U.S. Customary System):
Eq. 3.15 is s = (114.6 Q>T) W(u)
Well 1: [114.6>T][Q 1 W(u 1 ) Q 2 W(u 1,000 ) Q 3 W(u 2,000 )] 60 ft
Well 2: [114.6>T][Q 1 W(u 1,000 ) Q 2 W(u 1 ) Q 3 W(u 1,000 )] 60 ft
Well 3: [114.6>T][Q 1 W(u 2,000 ) Q 2 W(u 1,000 ) Q 3 W(u 1 )] 60 ft
4
114.6>(3.2 l0 )[21.89 Q 1 8.08 Q 2 6.69 Q 3 ] 60 ft
4
114.6>(3.2 l0 )[8.08 Q 1 21.89 Q 2 8.08 Q 3 ] 60 ft
4
114.6>(3.2 l0 )[6.69 Q 1 8.08 Q 2 21.93 Q 3 ] 60 ft
21.89 Q 1 8.08 Q 2 6.69 Q 3 16,800
8.08 Q 1 21.89 Q 2 8.08 Q 3 16,800
6.69 Q 1 8.08 Q 2 21.93 Q 3 16,800
Solving the three equations for the three unknown discharges Q 1 , Q 2 , and Q 3 :
3
Q 1 Q 3 468 gpm (2,550 m /d)
3
Q 2 420 gpm (2,289 m /d)
Solution 2 (SI System):
Eq. 3.12 is s = (Q>4pT) W(u)
Well 1: [1>4pT][Q 1 W(u 0.3048 m ) Q 2 W(u 304.8 m ) Q 3 W(u 609.6 m )] 18.3 m
Well 2: [1>4pT][Q 1 W(u 304.8 m ) Q 2 W(u 0.3048 m ) Q 3 W(u 304.8 m )] 18.3 m
Well 3: [1>4pT][Q 1 W(u 609.6 m ) Q 2 W(u 304.8 m ) Q 3 W(u 0.3048 m )] 18.3 m