*39. A pump test was conducted in a 25-m thick, confined aquifer in which the initial piezometric surface was at elevation 15 m. The well was pumped at 30 L / s, and after one day the piezometric levels at distances of 35, 75, 110, and 150 m from the well were 14.1, 14.4, 14.7, and 14.9 m, respectively.
a. Estimate the transmissivity and the hydraulic conductivity of the aquifer.
b. Aquifers with transmissivity less than 10 m 2 / d can supply only enough water for domestic wells and other low-yield uses (Lehr et al. 1988; Chin 2000, p. 501).
How does this aquifer’s transmissivity compare to that value?
c. Estimate the radius of influence of the well.
*40. A pump test was conducted in an unconfined aquifer of saturated thickness 15 m (in the absence of pumping). The well was pumped at 8000 m 3 / d, and after one day the drawdowns at 50 m and 100 m from the well were 0.42 m and 0.27 m, respectively.
a. Show that in steady state the hydraulic conductivity can be computed from
K =
1
π ( H −
Q
0 ln( r
2
/r
1
) s
2
) 2 − ( H − s
1
) 2
, where Q
0 is the pumping rate, H is the saturated thickness in the absence of pumping, and s i is the drawdown at radial distance r i
.
b. Compute the hydraulic conductivity for this aquifer.
41. Plot I
0
( x ), 10 K
0
( x ), and K
1
( x ) for the range 0 ≤ x ≤ 5.
*42. A pump test is conducted in a leaky confined aquifer. The confining layer has a thickness of 1.5 m, while the aquifer has a thickness of 10 m. The well is pumped at
1000 m 3 / d, and it has a radius of 0.6 m. The drawdowns at 30 and 75 m from the well are 0.4 m and 0.25 m, respectively.
a. Determine the hydraulic conductivities of the aquifer and the confining layer.
b. Redo part a assuming that r w
/λ ≪ 1. How close are the answers?
43. Consider a well of radius r w pumping for a long time at flow rate Q
0 in an unconfined aquifer with constant recharge w . If you derived an expression for the water table elevation and used it to compute the hydraulic conductivity from two observations of drawdown ( s
1 and s
2 measured at distances r
1 and r
2
), you would find
K = w ( r
1
2
− r 2
2
) / 2 ± ( Q
0
/π + wr 2 w
) ln( r
2
/r
1
)
( H − s
2
) 2 − ( H − s
1
) 2

Should the ± sign be a plus or a minus? Give two reasons. (Hint: If you can find two convincing explanations, you do not have to go to the trouble of deriving the expression.)
44. A well is placed in a confined aquifer with thickness 8 m, storativity 3 × 10
−
5 , and hydraulic conductivity 4 × 10
−
4 m / s. The well starts pumping at 500 gpm.
a. Plot the drawdown as a function of time (for one day) at an observation well 250 m away.
b. Plot the drawdown as a function of distance from the well 6 hours after the well starts pumping.
*45. A confined aquifer of thickness 30 m is pumped at a rate of 150 L / s from a well of radius 0.3 m. The drawdowns measured 100 m away at 100, 1000, 10 4 , 10 5 , and 2 × 10 5 seconds are 4.02, 123.6, 366.4, 627.6, and 705 cm, respectively.
a. Use the graphical method to determine the storativity, transmissivity, and hydraulic conductivity of the aquifer.
b. Use the Jacob approximation to determine the storativity, transmissivity, and hydraulic conductivity of the aquifer. Compare to the answers in part a.
c. The Jacob approximation allowed us to estimate the radius of influence as R =
1 .
5( T t/S ) 1 / 2 , while Sichard developed the empirical estimate R = 3000 s w
K 1 / 2 , where K is measured in m / s and the drawdown at the well, s w
, is measured in m. Compare the two estimates by plotting them as a function of time for the duration of the pump test.
46. The Jacob approximation allows the radius of influence to be estimated as R =
1 .
5( T t/S ) 1 / 2 . Compute the value of u corresponding to r = R and discuss whether the Jacob approximation actually holds.