CE 473/573 Groundwater
Fall 2010
Homework 5
Due Friday November 12
*29. Three wells with radius of influence 450 m are pumping steadily (but at different
rates). The transmissivity of the aquifer is 430 m2 /d.
a. Compute the drawdown at point A.
b. Which well has the greatest influence on the drawdown at point A?
3
Q = 1000 m /d
(x,y) = (150, 200) m
Point A: (x,y) = (0, 0) m
Q = 2000 m3/d
(x,y) = (-300,100) m
Q = 1500 m3/d
(x,y) = (200,-150) m
30. To capture some contaminant, a well is pumped at a rate of 2500 m3 /d in a confined
aquifer with a hydraulic conductivity of 1425 m/d, an initial hydraulic gradient of
0.00076, and a thickness of 31 m.
a. What is the maximum width of the capture zone?
b. What is the maximum distance downgradient of the well that the well will capture
contaminant?
*31. A contaminant plume of width 65 m is advancing from a leaky underground storage
tank in a confined aquifer of conductivity 40 m/d and thickness 14 m. The hydraulic
gradient is 0.002. You can install a well at point A.
a. If the plume advances in the x-direction, at what rate must you pump to capture
the plume?
b. Compute the area of the aquifer captured by the well downgradient of the well.
x
Well
Leaking tank
Advancing plume
*32. You are asked to design a system of wells to lower the water table at a construction
site for a rectangular excavation area that has dimensions of 100 m and 500 m. The
hydraulic conductivity is 5 m/d, and the initial saturated thickness is 30 m. The
water table must be lowered 7 m everywhere in the excavation. Design the system by
determining the number, placement, and pumping rate of the wells. The wells must
be at least 50 m outside the excavation area. Each well can pump up to 450 m3 /d.
Assume steady state and a radius of influence of 800 m. (Hints: Remember that this
aquifer is unconfined. Also, think about where the drawdown will be smallest inside
the excavation.)
*33. 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 m3 /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. Determine the hydraulic conductivities of the
aquifer and the confining layer.
34. 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.
*35. 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, 104 , 105 , and 2×105
seconds are 4.02, 123.6, 366.4, 627.6, and 705 cm, respectively.
a. Determine the aquifer’s storativity, transmissivity, and hydraulic conductivity.
b. Use the Jacob approximation to determine the storativity, transmissivity, and
hydraulic conductivity of the aquifer. Compare to the answers in part a.
*36. An unconfined aquifer is pumped at 0.08 m3 /s The aquifer has an initial saturated
thickness of 30 m, a horizontal hydraulic conductivity of 1.3 × 10−3 m/s, a vertical
hydraulic conductivity of 3 × 10−5 m/s, a storativity of 2 × 10−3 , and a specific yield
of 0.03. An observation well is 88 m away.
a. What is the drawdown 0.1 hours after the pumping starts?
b. When will the drawdown be 0.25 m?
*37. Consider the effect of Γ = r 2 Kv /b2 Kh on the drawdown caused by unsteady flow to
a well in an unconfined aquifer.
a. As Γ increases, does the drawdown become larger or smaller? Explain your
answer.
b. For which value of Γ does the behavior approach that for a confined aquifer?
Explain your answer.
38. (From exam 2, 2009) A well in a regional flow is pumped to capture contaminant.
The farthest point downstream of the well that the well draws water is 50 m. What
is the width of the capture zone?
Limit of capture zone
50 m
max. width
Well
39. (From exam 2, 2009) You set up a numerical solution of a confined, heterogeneous
aquifer of thickness 20 m. The heads are defined at the centers of the cells, shown by
the black dots. The boundary conditions are that the head in the first cell is 10 m
and that the flow per unit width into the first cell is 1 m2 /d. Compute the head in
the third cell.
K = 20 m/d
K = 5 m/d
K = 0.1 m/d
19 m
19 m
19 m
40. (Adapted from exam 2, 2009) Consider an agricultural field with tile drains. The
drains are 10 m apart and both located 8 m above the bottom of the unconfined
aquifer. The hydraulic conductivity is 0.1 m/d, and the recharge rate is 0.01 m/d.
Suppose you solve this problem in Excel on a grid with spacing of 1 m. If all values
of the water table elevation are set initially to 8 m, what is the water table elevation
at the grid point next to the left drain after the first iteration?
Recharge
Ground surface
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Drains
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Aquifer bottom
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10 m
8m
41. Two wells are used to lower the water table in a rectangular area, shown by the solid
rectangle, in an unconfined aquifer with hydraulic conductivity 4 m/d. The wells have
the same characteristics, and they are located 50 m outside the inner area, on the
dashed rectangle. The initial elevation of the water table is 100 m.
a. If both wells are pumped at 5000 m3 /d for a long time and the drawdown at point
A is 6 m, estimate the radius of influence.
b. If both wells are pumped at equal rates, at what rate must they be pumped to
draw down the water table a minimum of 4 m over the entire area?
300 m
200 m
Well 1
125 m
Well 2
150 m
250 m
150 m
A