CE 473/573 Groundwater
Fall 2011
Homework 1
Due Friday September 9
These exercises are meant to help you practice the concepts from lecture. Only the
exercises with starred numbers (e.g., #1) are mandatory. On-campus students will submit
the mandatory exercises in their groups. The other exercises are optional; I will give you
some extra credit if you submit them. As always, feel free to ask me if you have any
questions.
*1. The first lecture used examples of groundwater issues or problems to motivate the
material from class. This problem will add to that list.
a. Find an article or webpage on a contemporary groundwater issue in a U.S. state
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;
and indicate what you might like to learn in this class to address problems of this
nature.
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).
*2. The Des Moines Register reported that more than half of the water used by ethanol
plants evaporates during production or is treated and released back into streams.
Responding to complaints about the ethanol industry’s use of water, the executive
director of the Iowa Renewable Fuels Association said that the evaporation and release
into streams essentially continues the natural cycle of water. Do you agree with his
argument? Why or why not?
*3. 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.
4. Provide a physical explanation for why the hydraulic conductivity increases when the
fluid density increases. (By “physical explanation”, I mean one that does not appeal
solely to a mathematical formula. In other words, explain in a way that a non-technical
person might understand.)
*5. In class we considered slow flow through a tube of diameter d and obtained a result
similar to Darcy’s law. Because we were interested mainly in how K depends on
the properties of the soil and the fluid, we did not worry about numerical factors.
Now assume that the tube is cylindrical, for which slow flow has the wall shear stress
τ = 8μU/d, where U is the mean velocity and μ is the dynamic viscosity.
a. Compute the hydraulic conductivity for water in a soil with grain size (and pore
diameter) 40 μm.
b. Use the classification scheme (e.g., Fetter, Fig. 3.3) to compare your estimate in
part a to the range of conductivities in Table 3.7.
*6. 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.
7. 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'