ERS 482/682 Small Watershed Hydrology
Fall Semester 2002
Homework #4
Due October 11, 2002
Instructor: Dr. Scott Tyler (LMR 265; x6250; tylers@.unr.edu)
In this lab, you will measure hydraulic conductivity and porosity in soils to gain a better
understanding of groundwater principles. You will be divided into two groups, and each group
will perform both measurements. Each group will turn in one lab report.
PART I: MEASUREMENT OF HYDRAULIC CONDUCTIVITY
Hydraulic conductivity is the rate (volume per unit time per unit area) at which water moves
through a porous medium under a unit potential-energy gradient. In groundwater flow, we are
always dealing with saturated flow, so Kh implies saturated hydraulic conductivity. This lab will
illustrate how Darcy’s Law is used to determine hydraulic conductivity.
Darcy’s Law for saturated flow is as follows (Equation 8-1 in Dingman (2002)):
dh
Q   K hx Ax
dx
where Q
= volume rate of flow [L3 T-1]
Khx
= saturated hydraulic conductivity in the x-direction [L T-1]
Ax
= unit area of porous medium at right angles to the x-direction [L2]
h
= total potential energy (hydraulic head) of the fluid [L]
The equation can be rearranged to solve for hydraulic conductivity between points 1 and 2:
Qx2  x1 
K hx 
Ax h2  h1 
In this lab, you will use the permeameter illustrated in the figure below to apply this equation and
find the hydraulic conductivity of two soil samples. Because both reservoirs are open to the
atmosphere, the pressure head is zero, so the total potential energy is due only to gravitational
head, and the change in gravitational (elevational) head is therefore the same as the change in
total potential energy.
ERS 482/682 (Fall 2002)
Homework #4
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For this lab, you will need the following equipment:
 permeameter apparatus with two soil sample tubes, as set up in the lab
 yardstick
 clock or timing device that is accurate to seconds
Procedure:
Note: Before proceeding, it is important to get all of the air out of the tubes in the system. Any
bubbles in the system will affect the ability to measure head directly from the elevation difference
in the reservoirs. If there are any bubbles in the tube between the upper reservoir and the
permeameter sample tubes, drain the larger reservoir until the water surface level is below the
upper reservoir. Clamp off the tubes leading into both permeameter sample tubes. Open both
the valves on the Y and let the head differential between the smaller upper reservoir and larger
upper reservoir force the air bubble into the larger upper reservoir. This will be shown in class.
1.
Test the blue sample tube filled purely with sand (i.e., make sure both ends of the red
sample tube are clamped off)
2.
a.
Turn the faucet on and slowly fill the upper reservoir until the water level reaches
the overflow tube. When the water level stabilizes at the overflow tube, its height
will be h2, which can be measured in cm above the countertop (i.e., the countertop
is the datum).
b.
Measure the height of the outflow tube from the lower reservoir, which is h1.
c.
Place the overflow tube from the lower reservoir into a graduated cylinder (make
sure the top of the graduated cylinder is below the outflow of the lower reservoir)
until 100 mL is collected. Record the time it takes to collect 100 mL. The flow,
Q, is equal to the volume of water collected divided by the time it took to collect
that volume.
d.
As the system stabilizes, the manometers will fill to steady levels. If water is
coming out of the system, the upstream manometer tube should be higher than the
downstream one because the higher head is driving the water downstream (i.e.,
there is positive head). Record the elevations of the head on the upstream
manometer (hu) and the downstream manometer (hd).
Unclamp the tubes in the red sample tube and clamp off the tubes leading into and out of
the blue sample tube and repeat steps a) through d) above.
PART II: MEASUREMENT OF POROSITY OF AQUIFERS
Porosity is a measure of the volume of the voids of any aquifer or porous material. In granular
material, the porosity is primarily determined by the shape of the particles and their packing, not
by the particle size. This will be shown in this experiment.
In other aquifer materials, such as limestones and fractured rocks, the fracture spacing an dsize
of fractures control the porosity. The porosity is often much lower in these aquifers than in sand
ERS 482/682 (Fall 2002)
Homework #4
3
aquifers, but they can still be very productive aquifers due to the ease with which water can be
transmitted (i.e., high conductivity).
Procedure:
The two Plexiglas cylinders have each been filled with 850 grams of sand or gravel.
1.
Take a look at the grain size of each of the materials and compare it with the average size
of the pores between the grains.
2.
Calculate the bulk density of each of the aquifer materials by measuring the internal
volume of each of the cylinders. The bulk density is given by:
bulk density,  b 
3.
mass of dry aquifer material, M m
total volume of soil sample, Vs
Slowly fill each of the Plexiglas cylinders with water from the side tubes, making careful
note of the volume or mass of water you are adding. Fill the aquifer material with water
just to the top of the aquifer material. The porosity of the material is calculated as:
porosity,  
volume of voids, Vv
total volume of soil sample, Vs
The volume of voids is equivalent to the volume of water added.
4.
Lower the water filling tubes carefully to approximately the base of the Plexiglas
cylinders and record the volume of water that drains from the sand and the gravel.
WHAT TO TURN IN:
Note: Each group should turn in ONE report; be sure to write the names of all of your group
members on your report!
1.
Data sheet with the results of the blue sample tube
2.
Data sheet with the results of the red sample tube
3.
Compare the conductivities calculated with both methods (i.e., based on the head
differential in the entire tube and the head differential between the manometers). If there
is a difference, why do you think that is?
4.
Compare the conductivities calculated for the blue tube and the red tube. Comment on
why the conductivities are different.
5.
Data sheet with results of the porosity measurements
6.
Comment on the grain size of each of the materials and compare the grain size with the
average size of the pores between grains
7.
Is there a significant difference in bulk density between the two materials? Why or why
not?
8.
Is there a significant difference between the porosities you calculate for the two aquifer
materials? Why or why not?
ERS 482/682 (Fall 2002)
9.
10.
Homework #4
Which material yields a greater volume of water? Why do you think that is?
Which material would make a better aquifer and why?
4
ERS 482/682 (Fall 2002)
Homework #4
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ERS 482/682 Small Watershed Hydrology
Fall Semester 2002
Homework #4
Data Sheet
Experiment on BLUE TUBE
(sample made entirely of sand)
Head measurements:
Larger upper reservoir head, h2
Smaller upper reservoir head, h1
Upstream manometer head, hu
Downstream manometer head, hd
=
=
=
=
cm
cm
cm
cm
Water collection:
Volume of water collected, V
Time it took to collect volume V, t
=
=
mL
s
Tube dimensions:
Tube diameter, d
Length of entire tube, LT
Length between manometers, Lm
=
= 35.4 cm
= 19.8 cm
cm
Calculations:
 
Cross-sectional area, A   d 2 in cm2
4
V
Flow rate, Q 
in mL s-1
A
Hydraulic conductivity for entire tube, KT
Hydraulic conductivity for tube between manometers, Km
Comments:
ERS 482/682 (Fall 2002)
Homework #4
6
ERS 482/682 Small Watershed Hydrology
Fall Semester 2002
Homework #4
Data Sheet
Experiment on RED TUBE
(sample with sand and a band of alternate material in the middle)
Head measurements:
Larger upper reservoir head, h2
Smaller upper reservoir head, h1
Upstream manometer head, hu
Downstream manometer head, hd
=
=
=
=
cm
cm
cm
cm
Water collection:
Volume of water collected, V
Time it took to collect volume V, t
=
=
mL
s
Tube dimensions:
Tube diameter, d
Length of entire tube, LT
Length between manometers, Lm
=
= 35.4 cm
= 19.8 cm
cm
Calculations:
 
Cross-sectional area, A   d 2 in cm2
4
V
Flow rate, Q 
in mL s-1
A
Hydraulic conductivity for entire tube, KT
Hydraulic conductivity for tube between manometers, Km
Comments:
ERS 482/682 (Fall 2002)
Homework #4
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ERS 482/682 Small Watershed Hydrology
Fall Semester 2002
Homework #4
Data Sheet
Porosity experiment on cylinder filled with 850 grams of SAND
Internal volume of cylinder, Vs
=
cm3
Bulk density, b
=
g cm-3
Volume of voids, Vv
=
mL
Porosity, 
=
Volume of water drained, V
=
Comments:
Porosity experiment on cylinder filled with 850 grams of GRAVEL
Internal volume of cylinder, Vs
=
cm3
Bulk density, b
=
g cm-3
Volume of voids, Vv
=
mL
Porosity, 
=
Volume of water drained, V
=
Comments: