CE 473/573 Groundwater Fall 2008 Comments on homework 6

```CE 473/573 Groundwater
Fall 2008
37. I asked for the four curves on a single graph because the curves are easier to compare
that way. Part b can be discussed with conservation of mass and Darcy’s law. For
larger values of K ′ , more of the flow to the well can be supplied by leakage, and the
drawdown in the confined aquifer is less.
38. Several groups varied both K and K ′ , but a more efficient approach is to divide the
two expressions for drawdown to get
s1
K0 (r1 /λ)
=
s2
K0 (r2 /λ)
and solve for λ using Goal Seek or another iterative method.
39. One common problem was to add the drawdown from each well. I should have emphasized to you that while that approach works for confined aquifers, it does not work for
unconfined aquifers. The flow equation for unconfined aquifers is linear in terms of h2 .
Therefore, for N wells pumping at the same flow rate Q0 , the water table elevation is
given by
!
N
X
Q
R
0
ln
,
h2 = H 2 −
1/2
πK j=1
[(x − xj )2 + (y − yj )2 ]
where the jth well is at (xj , yj ). I placed my wells along both of the long sides of
the site with equal spacing. Then the minimum drawdown occurs on the end of the
centerline. With 12 total wells, the maximum water table elevation was 22.2 m, which
is lower than the required 23 m.
41. The easiest approach is to use the spreadsheet I gave you. The Jacob method, which is
an approximate method that applies for large time (or small u), gives T = 0.0125 m2 /s
and S = 4.4 &times; 10−4 . Using the spreadsheet with Solver to improve the estimates gives
T = 0.01 m2 /s and S = 9.9 &times; 10−4 .
```