CE 473/573 Groundwater
Fall 2012
Homework 3
Due Friday September 14 (depending on lab times)
12. (Optional for students who can attend the lab session on campus, required for others)
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
*13. (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. 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?
*14. In problem 4 you designed a constant-head permeameter to measure the hydraulic
conductivity of sandy loam, and you considered two ways to measure the flow. Now
evaluate the measurement uncertainty for both approaches and explain what, if anything, you would improve in your design to measure the hydraulic conductivity better.
15. (From 2011 exam 1) Two colleagues measure the hydraulic conductivity of a soil
sample in a falling-head permeameter. The soil sample is in a cylinder of area 38.5 ±
0.011 cm2 and length 8 ± 0.001 cm. The tube has an area of 2 ± 0.004 cm2 . Your
colleagues measured only two points: the initial head of 75 ± 0.1 cm and the final head
of 35 ± 0.1 cm at a time of 180 ± 0.1 seconds.
a. Compute the hydraulic conductivity.
b. Identify the likely soil type.
c. If your colleagues had measured more points, they would (or should) have fit a
function of the form y = a exp(−bx) in Excel (or other program). Estimate a and
b for this experiment.
d. Compute the maximum flow rate Qmax through the soil during the experiment.
e. Your colleagues started an uncertainty analysis in the table below. Although
the maximum flow can be computed in at least two ways, the table contains
information for only one of the two ways. Complete the table by listing the
values of Y1 and Y2 .
f. Compute the uncertainty ΔQmax .Warning: Your colleagues included one
parameter in the table that they should not have included.
g. Briefly discuss the results of the uncertainty analysis: (i) Is the uncertainty large?,
(ii) Which parameter would you measure more accurately to reduce the uncertainty in the maximum flow rate?
Parameter z
Sample length (cm)
Sample area (cm2 )
Tube area (cm2 )
Hyd. conductivity (cm/s)
Head difference (cm)
∂Qmax /∂z
[(∂Qmax /∂z)Δz]2 ((cm3 /s)2 )
−6.11 × 10−2
1.27 × 10−2
8.20 × 10−3
3.61 × 102
Y1
3.73 × 10−9
1.95 × 10−8
1.08 × 10−9
5.97 × 10−6
Y2
75 cm
Initial level
35 cm
Final level
Outlet
Soil sample