CE 473/573 Groundwater
Fall 2012
Homework 2
Due Friday September 7
*5. The automobile service center Iffy Lube has been illegally burying used motor oil
behind its building for years. You have been hired to develop a groundwater model
for the remediation, and you need to estimate the hydraulic conductivity. Pump tests
in the same geologic formation have shown that the hydraulic conductivity for water
is 4 × 10−7 m/s. Estimate the conductivity for motor oil and explain your reasoning.
*6. (From 2011 exam 1) Developers would like to build the Rose Prairie subdivision about
300 m north of Ada Hayden Lake in Ames, but city officials and residents are concerned
about contaminants (such as fertilizer) from the subdivision entering the groundwater
and polluting the lake, which is a secondary water supply for the City. The developers
claim that Rose Prairie will be a model of low impact development, but they agree
to hire Weakhit Consultants to monitor water quality in the lake each month for two
years immediately after Rose Prairie is completed. A report on groundwater in the
area says that the hydraulic gradient is 0.01, and the soil has a hydraulic conductivity
of 10 m/d and porosity of 0.3.
If the city asked you to comment on the developers’ plans, what would you say?
Support your arguments with calculations, if possible.
Proposed subdivision
Groundwater flow
300 m
North basin of
Ada Hayden Lake
7. A constant-head permeameter has a soil sample of length 10 cm and cross sectional
area 9 cm2 and a head difference of 5 cm. The flow out of the apparatus is 3 ×
10−6 cm3 /s, and the average grain diameter is 0.1 mm.
a. What is the hydraulic conductivity?
b. What type of soil is it?
c. Does Darcy’s law apply?
*8. Fetter recommends Δh/L < 1/2 for constant-head permeameters so that Darcy’s law
remains valid. Evaluate this recommendation for various types of soils.
a. A soil of a certain type can have a range of mean grain diameters (Figure 3.3
in Fetter’s book) and a range of hydraulic conductivities (Table 3.7 in Fetter’s
book). If you wanted a conservative estimate in evaluating whether Darcy’s law
is valid, which value (i.e., low, medium, or high) of the mean grain size would you
choose? Which value of the hydraulic conductivity would you choose? Why?
b. Estimate whether Fetter’s recommendation would work for clay, silt, sand, and
fine gravel.
9. To save some time in testing soil samples, you build a constant-head permeameter
that can hold two samples. The cross-sectional area of both sample tubes is 75 cm2 ,
and the free surfaces in the sample tubes are at the same elevation.
a. You run a test in which the flow Q1 is 1700 cm3 /d, and the flow Q2 is 5000 cm3 /d.
Determine the hydraulic conductivities of soils 1 and 2.
b. Your colleagues, who were educated elsewhere, wanted to save money on flow
meters by measuring the flow only at section A-A . Explain why their plan, while
less expensive, will not allow you to determine the conductivities of both soils.
25 cm
Q1
10 cm
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Soil 1
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Q2
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Soil 2
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10 cm
A
A'
*10. Explain physically why the head in a falling-head permeameter experiment decrease
less quickly when the area of the tube is increased.
11. A falling-head permeameter has a tube area of 0.5 cm2 , and the soil sample has a
length of 6 cm and a cross sectional area of 90 cm2 . The initial head is 50 cm, and
the head after 3 days is 5 cm.
a. What is the hydraulic conductivity?
b. Plot the head and flow out as a function of time.