CE 473/573 Groundwater
Fall 2010
Homework 3
Due before Wednesday October 6
*16. The Biscayne aquifer consists mainly of two layers: the Miami Limestone formation and the Fort Thomson formation. The hydraulic conductivity of the former is
1500 m/d, and the hydraulic conductivity of the latter is 12, 000 m/d.
a. Plot the water table.
b. Compute the flowrate per unit width. (Ans. 10.7 m2 /d)
c. Plot the effective conductivity as a function of x.
d. Repeat parts a-c if the downstream water elevation is -6 m.
1 km
Elev. 2.44 m
Elev. 1.07 m
Miami limestone formation
Elev. 1.00 m
Elev. -3.00 m
Fort Thompson formation
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Elev. -15.24 m
*17. Your supervisor asks you to design an agricultural drain system for a corn field.
Suppose the hydraulic conductivity of the soil is 5 × 10−7 m/s, the recharge rate
is 6 mm/day, the drain spacing is 10 m, the depth of the aquifer is 20 m and the root
depth is 0.8 m.
a. If the drains are to be placed at the same elevation, compute the depth from the
ground surface below which the water table will be below the roots.
b. Compute the flow per unit width into both drains and convince me that your
answer is correct.
c. Suppose the crew installing one of the drains mistakenly installed it 0.3 m deeper
than they should have. Compute the recharge rate below which no groundwater
divide will occur.
Recharge
Roots
Ground surface
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Drains
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Aquifer bottom
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L
*18. (From a previous exam) The figure below shows a top view of a confined aquifer with
hydraulic conductivity 4×10−6 m/s and thickness 35 m. The dots indicate monitoring
wells, and the piezometric head near each well is given in meters.
a. Plot the 20 m head contour on the figure.
b. Indicate the flow direction with an arrow on the figure.
c. Estimate the flow across the line A-A .
4000 m
A
4000 m
35
11
30
10
29
5
A'
19. (From a previous exam) A manual of groundwater engineering gives the following
formula for the effective conductivity in the aquifer shown below:
Kef f =
K1 K2 K3
K1 K2 + K1 K3 + K2 K3
Explain why you do or do not trust this formula. You do not have to derive it.
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Flow
K1
K2
K3
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L
L
L
20. (From a previous exam) A confined aquifer of width 200 m and thickness 10 m has a
hydraulic conductivity of 0.01 m/d for 0 < x < 500 m and 0.09 m/d for 500 < x <
1000 m.
a. What is the flow through the aquifer?
b. What is the head at x = 500 m?
c. Sketch the contours of the potentiometric surface in a top view of this aquifer.
h (m)
K1 = 0.01 m/d K 2 = 0.09 m/d
10
?
8
0
500
1000
x (m)
21. (From an old exam) An aquifer of width 1000 m has a constant thickness of 25 m
and constant hydraulic conductivity of 2 × 10−4 m/s. Observation wells and other
instruments are placed at x = 0. From x = 0 to x = xa = 500 m, the confining layer
is an aquifuge. From x = xa to x = L = 1000 m, the confining layer is leaky; flow
enters the confined aquifer at a uniform specific discharge qv = 2.3 × 10−9 m/s.
a. Is the hydraulic conductivity homogeneous or inhomogeneous?
b. If the measurements at x = 0 show the head to be 10 m and the flow to be a
steady value of 0.004 m3 /s in the x-direction, what is the head at x = 500 m?
c. What is the total flow at x = L?
d. Sketch (do not compute) the profile of head as a function of x from x = 0 to
x = L. Briefly explain your sketch.
e. Sketch contours of the potentiometric surface. Assume that the difference in head
between contours is constant.
qv
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Flow
25 m
x=0
x = xa
x=L