CE 473/573 Groundwater
Fall 2010
Homework 1
Due Friday September 10
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. Indicate your interest in the course topics by filling out the survey. See the instructions
on the survey and submit one for your group. I will use this information to determine
the emphasis placed on the various topics.
*2. 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.
3. 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.)
*4. 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.
*5. Design a constant-head permeameter for sand so that Darcy’s law will be valid. In
other words, recommend a maximum value for the hydraulic head (as a multiple of
the sample length) such that laminar flow occurs. Compare your recommendation to
Fetter’s.
6. The analysis of the falling-head permeameter in my version of Fetter’s book contains
this intermediate step:
At L dh
K=−
Ac dt
Explain in convincing terms why this cannot possibly be correct.
7. (Optional for on-campus students, required for off-campus students) To determine the
hydraulic conductivity of a clay, you conduct a test with a falling head permeameter.
The soil sample is 10 ± 0.05 cm long, and its cross sectional area is 100 ± 0.5 cm2 .
The cross sectional area of the tube in which the water falls is 4 ± 0.02 cm2 . The
uncertainty in the head is 0.1 cm, and the uncertainty in the time is 5 seconds. Do
parts a-e of problem 8 for this problem.
Time (days)
0
1
2
5
10
15
20
25
Head (cm)
5.0
4.6
4.4
3.4
3.1
1.8
1.4
0.9
*8. (Required for on-campus students, not required for off-campus students) Measure the
hydraulic conductivity of a soil sample using a falling-head test. Your group will
schedule a time to meet in the lab with me and Delise Lockett of ABE. Before you
go to the lab, discuss the measurements that you will need and prepare a data sheet.
You will also need to estimate the measurement uncertainty for each parameter that
you measure.
a. Measure and plot the head as a function of time since the start of the test.
b. Compute the hydraulic conductivity.
c. Compute the measurement uncertainty in the hydraulic conductivity.
d. Verify that Darcy’s law is valid for this experiment.
e. Write a paragraph discussing your results. Discuss the magnitude of the hydraulic
conductivity by comparing it with the ranges in Fetter’s book. Are any of the
points in your plot suspect? Is the uncertainty in K large? What could be done
to improve this experiment? If you wanted to decrease the uncertainty, where
would you put your effort?