Problem Set #2 SCOR470 Fall 2015 Topics: Soil water potential, unit conversions, soil water content Honor code opportunity- It is required that the work you are turning in is your effort. In addition, you may wish to sign the honor code statement. Declining to sign this statement will not count against you. "I have not given, received, or used any unauthorized assistance." Signature 1. Unit conversions a. You are curious about the matric potential of an air-dried soil. This depends on the relative humidity of the air of course but you find a value of -2.20 x 105 J/Kg in a journal article. Express this in MPa and m. (Note that the permanent wilting point for plants is typically assumed to be -1.5 MPa.) b. You need a value for the osmotic pressure of maple tree sap and find a table in a reliable older reference stating 2.23 x 106 erg/cm3. Convert this to m, ft., and Pa. c. Your grandfather’s WWII submarine could withstand about 1.5 MPa of water pressure. Assuming a saltwater density of 1.03 g/cm3, calculate the crush-depth of the submarine in m and ft. 2. a. Calculate the energy/volume (in J/m3) of water a plant root must overcome to withdraw water laterally from a soil with a matric potential of -15000 cm with an EC of 8 dS/m. b. Assuming 15 oC, calculate the relative humidity in the soil air for the soil in part (a). Note that this soil is near the wilting point for many plants. Helpful information: The EC, electrical conductivity, is a measure of the total dissolved salts in a system. For a wide range of soils, the following empirical relationship relates the EC of the soil solution to the osmotic pressure (Π) of the solution; Π(bars)= 0.36 x EC (dS/m). The EC unit is decisiemen per meter. 3. Consider a soil profile above a shallow water table: clay loam water table loamy sand loam silt loam 0.40 m 0.30 m 0.15 m 0.20 m Soil surface Suppose the θ(h) in this profile is described by the Brooks-Corey formulation: θ(h) = θS for |h| ≤ |he| θ(h) = (θS -θr)[(he/h) λ] + θr for |h| > |he| Using the parameters in the following table, calculate and plot the equilibrium water content profile, θ(z), from the soil surface to the water table. 4. The following system is at equilibrium. Determine each component of the total soil water potential in energy/volume and energy/weight at the points indicated (A, B, …). If a component is zero, state why. Soil θS θr |he| (cm) λ Silt Loam 0.49 0.10 12 0.21 Loamy sand 0.40 0.02 3 0.47 Loam 0.44 0.05 7 0.23 Clay loam 0.51 0.14 19 0.18 Loamy sand Clay loam A∙ B∙ Semi-permeable membrane Soils slightly saline EC=0.75 dS/m Pair(abso.

1. Problem Set #2
SCOR470 Fall 2015
Topics: Soil water potential, unit conversions, soil water
content
Honor code opportunity- It is required that the work you are
turning in is your effort. In addition,
you may wish to sign the honor code statement. Declining to
sign this statement will not count
against you.
"I have not given, received, or used any unauthorized
assistance."
Signature
1. Unit conversions
a. You are curious about the matric potential of an air-dried
soil. This depends on the
relative humidity of the air of course but you find a value of -
2.20 x 105 J/Kg in a journal
article. Express this in MPa and m. (Note that the permanent
wilting point for plants is
typically assumed to be -1.5 MPa.)

2. b. You need a value for the osmotic pressure of maple tree sap
and find a table in a
reliable older reference stating 2.23 x 106 erg/cm3. Convert this
to m, ft., and Pa.
c. Your grandfather’s WWII submarine could withstand about
1.5 MPa of water
pressure. Assuming a saltwater density of 1.03 g/cm3, calculate
the crush-depth of the
submarine in m and ft.
2. a. Calculate the energy/volume (in J/m3) of water a plant
root must overcome to withdraw
water laterally from a soil with a matric potential of -15000 cm
with an EC of 8 dS/m.
b. Assuming 15 oC, calculate the relative humidity in the soil
air for the soil in part (a).
Note that this soil is near the wilting point for many plants.
Helpful information: The EC, electrical conductivity, is a
measure of the total dissolved salts in a
system. For a wide range of soils, the following empirical
relationship relates the EC of the soil
solution to the osmotic pressure (Π) of the solution; Π(bars)=
0.36 x EC (dS/m). The EC unit is
decisiemen per meter.
3. Consider a soil profile above a shallow water table:

3. clay loam
water table
loamy sand
loam
silt loam
0.40 m
0.30 m
0.15 m
0.20 m
Soil surface

4. Suppose the θ(h) in this profile is described by the Brooks-
Corey formulation:
θ(h) = θS for |h| ≤ |he|
θ(h) = (θS -θr)[(he/h)
λ] + θr for |h| > |he|
Using the parameters in the following table, calculate and plot
the equilibrium water content
profile, θ(z), from the soil surface to the water table.
4. The following system is at equilibrium. Determine each
component of the total soil water
potential in energy/volume and energy/weight at the points

5. indicated (A, B, …). If a component
is zero, state why.
Soil
θS
θr

6. |he|
(cm)
λ
Silt Loam
0.49
0.10
12
0.21
Loamy sand
0.40
0.02
3

7. 0.47
Loam
0.44
0.05
7
0.23
Clay loam
0.51
0.14
19
0.18
Loamy
sand Clay loam
A∙ B∙

8. Semi-permeable
membrane
Soils slightly saline
EC=0.75 dS/m
Pair(absolute)=
0.90 atm
15 cm
40 cm
60 cm
5cm
0.05 M KCl
Pair=1.0 atm
T=25 oC
No evaporation
M is moles/liter
Liquid saturated porous
plate
5. Refer to Problem# 4.

9. a. Consider a microorganism at point A in the loamy sand.
Assuming the cell wall of the
microorganism is semipermeable, what osmotic (solute)
potential is necessary within the cell
to avoid loss of cellular fluid to the soil water? You may
assume that osmotic adjustment of
the cellular fluid is the only defense against lower water
potentials outside of the cell.
b. Using the θ(h) parameters for the soils listed in Problem 3,
calculate the water content at
Point A and Point B in the figure.
c. Suppose the microorganism at point A has had enough of
fighting the water robbing forces
in her loamy sand home and dreams of moving to a wetter
environment. Her life coach
recommends she follow her dreams so she packs up and moves
to the wetter soil(?) at
position B (the clay loam). What cellular solute potential is
necessary to prevent
dehydration in the new home?
6. A common representation of the moisture retention function
first used by van Genuchten
(1980) is as follows:
θ(h) = (θS−θr)[1+(α|h|)n]m + θr where m = (1-
1/n)
where h(cm) is the soil water pressure head (matric potential in

10. head units), θs is the saturated
water content, θr is the so-called residual water content, and α
(cm-1) & n are shape parameters.
The purpose of this problem is to give you practice working
with and interpreting this function.
Consider the following soils with their typical parameter values
(based on texture);
Soil Texture θs θr α(cm
-1) n
sandy loam 0.39 0.03 0.070 1.60
silt loam 0.44 0.07 0.025 1.35
clay 0.55 0.12 0.010 1.20
a. For 0.1<|h|<50000 cm, plot θ(h) for each soil in the table. I
recommend that you use a log
scale for h.
b. If water is available for plant uptake over the matric potential
range of -0.0100 to -1.500
MPa, calculate the cm of plant available water (PAW) in a 60
cm deep root-zone of each
texture.
c. If you allow a crop to deplete 60% of PAW prior to
irrigating, estimate the time between
irrigations in each of the soils if the evapotranspiration loss is
0.7 cm/day. You may ignore soil
water drainage below 60 cm depth and assume no rainfall.

11. d. Suppose the sandy loam is at θ=0.100, the silt loam is at
θ=0.150, and the clay is at
θ=0.350. Samples of each soil are then placed in horizontal
contact;
Upon contact, what is the direction of flow between the layers?
Explain.
Sandy
loam
Silt
loam
Clay
7. Tensiometers are used to measure matric potential (soil water
pressure) and thus can be helpful
in determining the direction of water flow and estimating soil
water content if θ(h) is known for the
soil. The three tensiometers shown here are in the silt loam and
clay soils of problem # 6.

12. Readings (the gauge pressure of the air in the headspace) are
reported for three dates during the
early summer:
Tensiometer 1 Tensiometer 2 Tensiometer 3
June 1 -80 cm -110 cm -150 cm
June 15 -240 cm -200 cm -300 cm
June 30 -450 cm -400 cm -350 cm
a. For the three dates, calculate the water content at each depth
and sketch the water content profile
between 20 and 60 cm depth.
b. For each date, determine the total soil water potential at each
depth and then indicate the
direction of water flow between 20 and 40 cm depth and
between 40 and 60 cm depth. Note that

13. you can assume that the tensiometer is at equilibrium with the
soil water.
Water saturated
porous cup
Water filled
tube
Sealed
headspace #1 #2 #3
Silt Loam
Clay
20 cm
40 cm
60 cm
10 cm