CE 473/573 Groundwater
Fall 2009
Homework 2
Due Friday September 11
Again, this homework assignment is to be completed in your homework group. If your
group has not already submitted a sheet on its expectations, please submit it with this
assignment.
*7. Suppose one soil sample is saturated with water, and another sample of the same
soil is saturated with oil. In which sample will the hydraulic conductivity be larger?
Explain your reasoning.
*8. Design a constant-head permeameter for sand so that Darcy’s law will be valid. In
other words, recommend a maximum value for the hydraulic head (as a multiple of
the sample length) such that laminar flow occurs. Compare your recommendation to
Fetter’s.
*9. To determine the hydraulic conductivity of a clay, you conduct a test with a falling
head permeameter. The soil sample is 10 cm long, and its cross sectional area is
100 cm2 . The cross sectional area of the tube in which the water falls is 4 cm2 . Determine the hydraulic conductivity from the measurements listed below.
Time (days)
0
1
2
5
10
15
20
25
Head (cm)
5.0
4.6
4.4
3.4
3.1
1.8
1.4
0.9
10. A confined aquifer has length L = 7.5 km, thickness b = 30 m, hydraulic conductivity
K = 3 × 10−5 m/s, and effective porosity n = 30%. The head on the west side of the
aquifer is h0 = 2.5 m, and the head on the east side is hL = 1 m.
a. What is the flow per unit width?
b. Is Darcy’s law valid in this aquifer?
c. How long does it take water to travel from one side of the aquifer to the other?
*11. Test PMWIN and Modflow by solving for flow in the aquifer in problem 10.
a. Run the model and plot the head contours as well as the head as a function of
distance. Explain whether the model produces results that match the analytical
result.
b. Verify that the flow is correct.
c. Double the hydraulic conductivity but keep the same boundary heads. Check the
heads and flows and convince me that the model is working properly.
12. A profile view of a heterogeneous, confined aquifer is shown below. The head h0 on
the left side is 10 m, and the head hm at x = xm = 600 m is 9 m. The thickness of
the aquifer is 15 m, and the flow per unit width in the left soil is 7.5 × 10−8 m2 /s.
a. What type of soil is soil 1?
b. If K2 is 10−4 m2 /s and L2 = 300 m, what is the head hL at x = L?
c. Explain the differences in the gradients in soils 1 and 2.
h = h0
L1
h = hm L
2
K1
K2
h = hL
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Flow
xxxxx
b
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x=0
x = L1
x=L
*13. Construct a Venn diagram for the terms aquifer, aquifuge, aquitard, confining layer,
unconfined aquifer, confined aquifer, artesian aquifer, phreatic aquifer, and perched
aquifer.