CE 473/573 Groundwater
Fall 2009
Homework 4
Due Wednesday October 14
20. The Des Moines Water Works (DMWW) takes some of its water from the Raccoon
River. About a century ago, the DMWW installed an infiltration gallery, a system
of slotted pipes that collects groundwater. This system is modeled as an unconfined
aquifer below. For this problem, assume the infiltration gallery collects water over a
length of 2 km into the page.
a. The hydraulic conductivity is unknown, but the flow from the gallery is measured
to be 700 m3 /d. However, without further modeling, the fraction of the flow intercepted by the infiltration gallery is unknown. Therefore, assume that between
10% and 100% of the flow is incepted and compute the conductivity. Plot the
hydraulic conductivity as a function of the fraction of flow intercepted.
b. One problem with taking water from the Raccoon River is the high nitrate concentration. To assess how much denitrification occurs in the soil, one must know
the travel time for water to reach the gallery. Plot the travel time as a function
of the fraction of flow intercepted.
75 m
River
Water table
Infiltration
gallery
30 m
10 m
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21. 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.
*22. 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. Suppose the crew installing one of the drains goofed and 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
*23. Use a numerical method and Excel to compute the water table and the flow per unit
width for the situation in problem 22c (with the recharge rate specified for parts a
and b.)
*24. 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
*25. A leaky confined aquifer has hydraulic conductivity 0.5 m/d and thickness 30 m. The
overlying aquitard has thickness 3 m, and the head outside the confined aquifer is 15
m. Heads measured at various points in the aquifer are given below.
a. What is the conductivity K ′ of the confining layer?
b. What is the total flow (per unit width) past the observation point at 1000 m?
c. At what value of the head outside the aquifer will there be a groundwater divide?
Distance (m)
0
200
450
650
850
1000
Head (m)
12.00
11.75
11.11
10.29
9.14
8.00
26. Show that the fraction of flow due to leakage in a leaky confined aquifer is λ/b where
b is the aquifer thickness, λ = (K ′ /Kbb′ )1/2 , K ′ is the conductivity of the confining
layer, and b′ is the thickness of the confining layer.
*27. A confined aquifer with thickness 10 m, conductivity 1 m/d, and width 400 m has an
upstream head of 15 m. The flow at that point is 6 m3 /d. Use a numerical method in
Excel to compute the head profile for a length of 800 m.