CE 473/573 Groundwater
Fall 2011
Homework 3
Due Wednesday October 12
*16. Continue adding to our list of contemporary issues involving groundwater, but expand
to include international issues:
a. Find an article or webpage on a contemporary groundwater issue in a country
(not the U.S.) that starts with the same first letter as one of last names of your
group members. Provide the web address.
b. In a paragraph of 200 words or fewer, summarize the problem; explain the effect of
the problem or an engineering solution on the economy, environment, or society;
relate the problem or solution to the material in class; and discuss whether the
problem or solution would be different in the U.S.
c. Find an image that illustrates this problem—e.g., a photograph, map, drawing,
schematic, etc. Provide image and the link.
d. Submit your text, links, and images via email to me (so that I can compile them
easily).
*17. Suppose a confined aquifer has a width that can be approximated as w = w0 exp(−αx).
The hydraulic conductivity is K, the thickness of the aquifer is b, and the heads are
h0 and hL at x = 0 and x = L, respectively.
a. Derive an expression for the flow Q in terms of these parameters.
b. Derive an expression for the head as a function of x and show that it satisfies the
case of α → 0.
c. Compute the flow and plot the head as a function of x for K = 5 m/d, b = 30 m,
w0 = 500 m, α = 8 × 10−4 m−1 , L = 1000 m, h0 = 35 m, and hL = 33 m.
d. Explain the variation of head with x physically.
18. An unconfined aquifer of length 2700 m, width 1500 m, and hydraulic conductivity
0.5 m/d lies between two reservoirs. The bottom of the aquifer is at elevation 120 m
(above some datum). The reservoir levels are at elevations of 150 m and 146 m.
a. Compute the flow between the two reservoirs.
b. Your colleague computed a flow of 329 m3 /d. What is your colleague’s mistake?
*19. Fig. 3.32 of Fetter’s book shows ground water elevations in wells screened in an unconfined aquifer in Milwaukee, WI (See analysis problem B, p. 109). Further information
is in
http://www.public.iastate.edu/∼ rehmann/CE573/milwaukeeusgsreport.pdf
http://www.public.iastate.edu/∼ rehmann/CE573/milwaukeeusgstables.pdf
http://www.public.iastate.edu/∼ rehmann/CE573/milwaukeeusgsfigures.pdf
a. Are the soils in the study area homogeneous? Are they isotropic? Cite evidence.
b. Estimate the flow across (i.e., normal to) the line between R21E and R22E in the
row T8N. Assume the line is in the till. Recall that the aquifer is unconfined, so
that the flow thickness is not constant.
c. Does water flow into or out of the lake in T8N, R22E? What about in the other
areas of R22E?
*20. The Biscayne aquifer consists mainly of two layers: the Miami Limestone formation and the Fort Thomson formation. The hydraulic conductivity of the former is
1500 m/d, and the hydraulic conductivity of the latter is 12, 000 m/d.
a. Plot the water table.
b. Compute the flowrate per unit width. (Ans. 10.7 m2 /d)
c. Plot the effective conductivity as a function of x.
d. Repeat parts a-c if the downstream water elevation is -6 m.
1 km
Elev. 2.44 m
Elev. 1.07 m
Miami limestone formation
Elev. 1.00 m
Elev. -3.00 m
Fort Thompson formation
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Elev. -15.24 m
*21. Your supervisor asks you to design an agricultural drain system for a corn field.
Suppose the hydraulic conductivity of the soil is 5 × 10−7 m/s, the recharge rate
is 6 mm/day, the drain spacing is 10 m, the depth of the aquifer is 20 m and the root
depth is 0.8 m.
a. If the drains are to be placed at the same elevation, compute the depth from the
ground surface below which the water table will be below the roots.
b. Compute the flow per unit width into both drains and convince me that your
answer is correct.
c. Suppose the crew installing one of the drains mistakenly installed it 0.3 m deeper
than they should have. Compute the recharge rate below which no groundwater
divide will occur.
Recharge
Roots
Ground surface
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Drains
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Aquifer bottom
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L
22. Investigate the accuracy of finite difference approximations for the first derivative.
Consider f (x) = sin(x) from 0 ≤ x ≤ π.
a. Use a grid with 11 points (i.e., Δx = π/10), and make a single plot comparing
the exact first derivative, the forward difference approximation, the backward
difference approximation, and the centered difference approximation. Which is
most accurate?
b. Repeat part a with 31 points. What is the effect of increasing the number of
points?
23. Construct a numerical model of flow in a confined aquifer with thickness 10 m, length
1500 m, and hydraulic conductivity varying linearly from 1 to 5 m/d. The upgradient
head is 35 m, and the downgradient head is 34 m.
a. Plot the variation in piezometric head.
b. Compute the flow per unit width.
c. Convince me that your result in part a is correct.
d. Compute the effective conductivity.