Geology 441 Midterm Test 1
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Groundwater Hydrology
Geology 441
First Midterm
October 3, 2007
Due in class on Friday, October 12
Answer the questions completely, but concisely. You may refer to class notes or
any written sources. However, you may not discuss this test with anyone else. If
you have questions concerning the test, direct them to me.
1. Darcy’s Law: Darcy’s Law relates the hydraulic gradient (∆h/x) to the
specific discharge (q). Under Darcy flow conditions the specific discharge
is the product of the hydraulic gradient and the hydraulic conductivity (k)
(Equation 1). (24 pts total)
q  k
h
x
(Equation 1)
a. How does hydraulic conductivity relate to permeability? Are they
the same or different? (4 pts)
b. Results from Darcy’s experiment (Figure 1) show the linear
relationship between specific discharge and the hydraulic gradient.
Which of the experiments (1-5) shows the greatest hydraulic
conductivity? Which of the experiments (1-5) shows the lowest
hydraulic conductivity? Explain how you arrived at your answer.
(6 pts)
c. Figure 2 shows a horizontal version of Darcy experiment. On the
figure draw an arrow showing the direction of water flow. Show
on the figure how the hydraulic gradient would change if the sand
were replaced with a material with a greater hydraulic
conductivity. (4 pts)
d. A modified version of Darcy’s experiment is shown in figure 3. The
column has material with two different hydraulic conductivities.
The sand has a higher hydraulic conductivity than the clay. Choose
a direction of flow (left or right) and indicate the direction of flow
with an arrow. Show the hydraulic heads in each of the
piezometers. Also, show the hydraulic gradient. To complete this
exercise it is necessary to assume that q is constant through the
column. Is this reasonable? How would the gradient change if q
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were not constant, for instance there was a leak in the tube that
allowed water to escape? (10 pts)
2. Bernoulli’s Equation. Bernoulli’s equation (Equation 2) relates the
hydraulic head to the sum of the elevation head, pressure head and
velocity head. (Total 16 pts)
H z
P u2

g 2 g
(Equation 2)
a. Using the piezometer in figure 2 labeled (1), show the hydraulic
head, the elevation head and the pressure head. You may use your
own datum, but be certain to identify the datum. (6 pts)
b. Again, referring the figure 2, which piezometer, has the greatest
elevation head? Which piezometer has the greatest pressure head?
In groundwater we don’t normally consider velocity head,
however, it does exist, it is just too small to measure. Which of the
piezometers in figure 2 would have the greatest velocity head, if
one could measure velocity head in groundwater? (6 pts)
c. Describe any circumstances, if any exist, that water would flow
from a lower hydraulic head to a higher hydraulic head. (2 pts)
d. Hydraulic head is a measure of energy in the water; however the
units of hydraulic head are length. Energy has units of force ∙
distance. Why are the units of hydraulic head different than the
units of energy? (2 pts)
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0.006
1
0.005
q (m/s)
0.004
2
0.003
0.002
3,4
5
0.001
0.000
0
2
4
6
8
10
H/e
12
14
16
18
20
Figure 1: Results from Darcy’s experiment. The specific discharge (q) is on the
y-axis. The hydraulic gradient (H/e) is on the x-axis. Each experiment is
represented as a separate set of symbols. The lines are best-fit lines through the
data.
1
2
Piezometers
Hydraulic
heads
3
4
Sand
Figure 2: This is a horizontal version of Darcy’s experiment. The piezometers
show the hydraulic heads. The line shows the hydraulic gradient.
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Clay
Sand
Figure 3: This is a modified version of Darcy’s experiment. The column has
material with two different hydraulic conductivities. The sand has a higher
hydraulic conductivity than the clay. Choose a direction of flow (left or right)
and indicate the direction of flow with an arrow. Draw what the hydraulic heads
in the piezometers would be. Also, show the hydraulic gradient.
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