Page 112 - 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 75

3.10 Nonsteady Radial Flow 75

EXAMPLE 3.1 CALCULATION OF THE FORMATION CONSTANTS T AND S USING THE THEIS METHOD
The observed data from a pumping test are shown plotted in Fig. 3.4 along with a Theis-type curve,
as if the transparency of the observed data had been moved into place over the type curve. The ob-
servation well represented by the data is 225 ft (68.58 m) from a pumping well where the rate of
3
discharge is 350 gpm (1,324.75 L/min; 1908 m /d). Calculate the formation constants T and S.
Solution 1 (U.S. Customary System):

The match-point coordinates are:
W(u) = 4.0
s = 5.0 ft (1.524 m)
u = 10 -2
2
6
5
r >t = 5 * 10 (4.645 * 10 for SI Units)
Compute the formation constants:
T = 114.6QW(u)>s
T = 114.6 * 350 * 4.0>5.0
4
T 3.2 : 10 gpd/ft
2
S = uT>(1.87 r >t)
-2
4
6
S = 10 (3.2 * 10 )>[1.87(5 * 10 )]
S 3.4 : 10 -5
Solution 2 (SI System):
T = [Q>(4ps)]W(u)
T = [1808>4 * 3.14 * 1.524)] * 4
3
T 398.72 m /d/m
2
S = 4Tu>(r >t)
-2
5
S = 4 * 398.72 * 10 >(4.645 * 10 )
S 3.43 : 10 5

EXAMPLE 3.2 CALCULATIONS OF DRAWDOWN WITH TIME IN A WELL
In the aquifer represented by the pumping test in Example 3.1, a gravel-packed well with an effective
3
diameter of 24 in. (610 mm) is to be constructed. The design flow of the well is 700 gpm (3,815 m /d).
Calculate the drawdown at the well with total withdrawals from storage (that is, with no recharge or
leakages) after (a) 1 minute, (b) 1 hour, (c) 8 hours, (d) 24 hours, (e) 30 days, and (f) 6 months of con-
tinuous pumping, at design capacity.
Solution 1 (U.S. Customary System):
From Eq. 3.15: s = [114.6 Q>T][W(u)]
4
= [114.6 * 700>(3.2 * 10 )][W(u)]
= 2.51 ft [W(u)]