Download 53-102 Assignment #1

53:102 GROUNDWATER
Homework #2 -- Due: Friday, Sept. 9 (in-class)
Readings: Schwartz & Zhang – 3.7 through 3.8 + Class notes
1.
Define in words and as a formula “hydraulic head”. We neglected kinetic energy in our derivation
of hydraulic head by arguing that groundwater velocities were slow. If a unit mass of groundwater
accelerates from rest to an average linear velocity of 1 m per year and climbs a vertical distance of
1 m, compare the kinetic energy to the potential energy of the unit of groundwater. Is it reasonable
for us to ignore the kinetic energy associated with groundwater movement?
2.
Water in an aquifer is 6.5 m above a reference datum, the water pressure is 1800 N/m2, and the
flow velocity is 3.4 x 10-5 m/s. The density of the water is 1.01 x 103 kg/m3.
a) What is the total energy per unit mass?
b) What is the total energy per unit weight?
c) What is the pressure head?
d) What is the elevation head?
e) What is the velocity head?
f) What is the total head?
3.
A confined aquifer is 8 ft. thick. The potentiometric surface drops 1.33 ft between wells that are
685 ft apart. The hydraulic conductivity is 241 ft/day and the effective porosity is 27%.
a) How many cubic feet per day move through a strip of aquifer that is 10 ft wide?
b) What is the specific discharge?
c) What is the average linear velocity?
d) How long will it take the water to travel between the two wells?
4.
Darcy’s equation in 2-D. There are three piezometers in an unconfined sand aquifer as shown
below. The head measurements at A = 104.56 ft, B = 104.53 ft, C = 103.42 ft. The rate of recharge
here is estimated to be 1.25 ft/yr. The average horizontal hydraulic conductivity (K x) is 8 ft/dy.
Assume that in the vicinity of these three piezometers, the vertical specific discharge (qz) equals
the recharge rate.
a. Estimate the vertical hydraulic conductivity using the heads at wells A and B.
b. Estimate the horizontal specific discharge (qx), using the heads at wells B and C.
c. Make a scaled vector sketch showing the x and z components of the specific discharge and the
resulting total specific discharge. Assume there is no flow in the y-direction.
5. Based on the figure below answer the following:
a.
b.
c.
d.
e.
f.
What is the elevation head at point A (ft)?
What is the pressure head at point A (ft)?
What is the total head at point A (ft)?
What is the direction of flow at point B?
The aquifer at point B is what type?
The geologic unit at point C is clay.
What type of hydrostratigraphic unit is it?
g. What is the vertical hydraulic gradient at C?
h. What is the pressure head at point E?
i. What is the elevation head at point E
j. What is the total head at point E (ft)?
k. What is the direction of flow at point F?
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