CE 473/573 Groundwater
Fall 2007
Homework 5
Due Wednesday October 17
*26. There are no 2’s in equation (4.64) of Fetter’s book, but there are seven 2’s in equation
(4.65). Explain where the seven 2’s came from.
27. Do problem 13 on p. 149 of Fetter’s book. Let me know if you get the same answer
as Fetter for part D.
*28. 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.
c. Comment on the values of the parameters and results in this problem. Are any
unreasonable? If so, suggest better values.
Recharge
Ground surface
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Roots
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Drains
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Aquifer bottom
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L
*29 In the case of unconfined flow between two reservoirs with recharge (Fetter pp. 143144), a groundwater divide may occur.
a. Derive an expression for the recharge rate below which no divide will occur.
b. Argue that your answer in part a makes sense.
c. Suppose the crew installing one of the drains in problem 28 goofed and installed
it 0.3 m deeper than they should have. Compute the limiting recharge rate.
*30. 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.
c. Plot the effective conductivity as a function of x.
d. Suppose the downstream water level is below the top of the Fort Thompson
formation. Outline how you would find the water table in this case (but do not
actually do it.) In particular, explain why this problem is more difficult than that
for parts (a)-(c).
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
*31. The confined, layered aquifer below has leakage of 0.2 mm/d into the aquifer. The
head at x = 0 m is 40 m, and the flow (per unit width) at x = 0 m in the upper layer
is 2.8 × 10−4 m2 /d. Your colleagues found that soil 1 is sand and soil 2 is silt. They
measured hydraulic conductivities of 10 m/d and 0.1 m/d, but they do not remember
which value of K corresponds to which soil layer.
a. Plot the head as a function of x.
b. Plot the flow (per unit width) as a function of x.
c. Locate the groundwater divide, if there is one.
Leakage
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7m
Soil 1
3m
Soil 2
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x=0m
x = 1400 m