Soil Physics 375:16:555
Homework 4
due 10/13
1. A clod with a mass of 8.99 g, perfectly sealed with paraffin wax, is attached through a
string to a torsion balance and lowered in water until is completely submerged (see
diagram 1). At equilibrium, the balance reads 2.79 g. Assume that the masses of the
wax and the string are negligible. 1) calculate the weight of the clod, 2) calculate the
contact force, the gravity force and the net vertical static force, 3) what is the bulk
density of the clod?
2. Calculate the height of rise of water in clean glass capillaries (contact angle γ = 0)
with radius r = 5 µm and r = 1000 µm, respectively. Repeat the calculations but using
contact angles of 66± and 110± (see Lecture notes 2, page 4). Discuss the results
3. A soil physicist decides to apply water to a research area to investigate the movement
of a conservative tracer to a depth of 0.40 m. The bulk density of the soil is ρ = 1.37
Mg m-3 and the gravimetric water content is w = 0.19 kg kg-1. (a) What volume of
water must be applied per m2 of soil surface to saturate a soil to a depth of 0.4 m? (b)
If the scientist uses 23% less water than needed, to what depth would the tracer
move? Assume that the tracer will move to the maximum depth of the wetting front.
4. The picture below shows a capillary fringe formed above a groundwater. Unsaturated
soil is between the capillary fringe and the soil surface. Draw diagrams showing the
spatial variation of the hydraulic potential, H, the gravitational potential, g, and the
pressure potential, h, by assuming two situations: 1) the reference level is at soil
surface (shown in picture), and 2) the reference level is taken as the interface between
the unsaturated zone and the capillary fringe. For each case, calculate the value of H
in the saturated region of the soil and explain why you could not predict the value of
H in the unsaturated portion of the soil.
Z=0m
Z=-1m
Z = - 1.5 m
Z=-2m
5. Suppose you have two piezometers. The bottom of piezometers 1 and 2 are at a depth
of z = -1.2 m and z = -0.7 m, respectively (see diagram in the lecture notes). The
liquid level in piezometer 1 is at z = -0.65 m, and in piezometer 2 is at z = -0.55 m.
Draw a potential diagram assuming that H is a linear function of depth. At what depth
is the groundwater table? Is this an equilibrium situation? In which direction would
the water flow?
6. Suppose you have two tensiometers. The cups of tensiometers 1 and 2 are at a depth
of 0.6 and 0.8 m, respectively. Gauges are at 0.2 m above the soil surface. The gauge
of tensiometer 1 indicates hgauge = -0.9 m. Draw the potential diagram assuming that
the water in the soil is at static equilibrium. Calculate the gauge reading at
tensiometer 2.
7. In an irrigated, completely wetted soil, the non-cylindrical pores have an air-entry
value of -20 kPa. Calculate the height of capillary rise in this soil and the equivalent
capillary diameter of the pores.
8. Assuming complete wetting, what is the air-entry value for a capillary with a diameter
of 18 µm?
9. A soil sample is placed inside a pressure plate apparatus (see Fig. 6.15 in your
textbook) and subjected to a gage pressure (the pressure difference between the
pressure inside the pressure plate chamber and the atmospheric pressure) of 1 MPa.
The sample is left until equilibrium is established. Find the pressure potential (Jm-3)
of the sample at equilibrium.
Electronic
balance
Water
Soil aggregate
Laboratory Jack
Diagram 1 showing the experimental setup described in question 1.