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76 Chapter 3 Water Sources: Groundwater

Table 3.3 Variation of Drawdown with Time for Example 3.2
Time, days u W(u) Drawdown, s, ft (m)
(a) 1>1440 2.86 10 6 12.19 30.6 (9.33)
(b) 1>24 4.8 10 8 16.27 40.8 (12.44)
(c) 1>3 6.0 10 9 18.35 46.0 (14.02)
(d) 1 2.0 10 9 19.45 48.8 (14.87)
(e) 30 6.6 10 11 22.86 57.3 (17.46)
(f) 180 1.1 10 11 24.66 61.8 (18.84)

2
From Eq. 3.16: u = 1.87 r S>Tt
4
2
-5
= 1.87 * 1 * 3.4 * 10 >(3.2 * 10 )t
-9
= (2.0 * 10 )>t
For various values of t, compute u, then from Table 3.2 obtain the well function, W(u), for the cal-
culation of drawdown. The values of drawdown for various values of time are given in Table 3.3.
Solution 2 (SI Units):
From Eq. 3.12: s = [Q>(4pT)][W(u)]
= [3,815>(4 * 3.14 * 398.72)][W(u)]
= 0.72 m[W(u)]
2
From Eq. 3.13: u = r S>(4Tt)
2
-5
= (0.3048) * 3.43 * 10 >(4 * 398.72t)
-9
= (2.0 * 10 )>t
For various values of t, compute u, then from Table 3.2 obtain the well function, W(u), for the cal-
culation of drawdown. The values of drawdown for various values of time are given in Table 3.3.

3.10.2 Semilogarithmic Approximation

It was recognized that when u is small, the sum of the terms beyond ln u in the series expansion
of W(u) (Eq. 3.14) is relatively insignificant. The Theis equation (Eq. 3.12) then reduces to:
2
s [Q>(4 T)]{ln[(4Tt)>(r S)] 0.5772}
2
s Q>(4 T) ln[(2.25Tt)>(r S)] (SI Units) (3.17)
3
3
where Q is in m /d, T in m /d/m, t in days, and r in m
When Q is in gpm, T in gpd/ft, t in days, and r in ft, the equation becomes:
2
s 264(Q>T) log[(0.3Tt)>(r S)] (U.S. Customary Units) (3.18)
A graphical solution was proposed for this equation. If the drawdown is measured in a
particular observation well (fixed r) at several values of t, the equation becomes:
s 264(Q>T) log(Ct)
where
2
C 0.3T>(r S)