Problem Set #2
SCOR470 Fall
201
5
Topics: Soil water potential
, unit
conversions
, soil water content
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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
.
2
0 x 10
5
J/Kg in a journal
a
rticle. 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
10
6
er
g/cm
3
.
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/cm
3
, calculate the crush
–
depth of the
submarine in m and ft.
2.
a.
Calculate the
energy/volume (in J/m
3
) of water a plant root must overcome to withdraw
water
laterally from
a soil with a matric potential of
–
1
500
0 cm with an EC of 8 dS/m.
b
. Assuming
15
o
C, 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 followingf
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) = θ
S
for |h|
≤
|h
e
|
θ(h) = (θ
S
–
θ
r
)[(h
e
/h)
λ
] + θ
r
for |h| > |h
e
|
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
θ
S
θ
r
|
h
e
|
(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
P
air
(absolute)=
0.90 atm
15 cm
40 cm
60 cm
5cm
0.05
M
KCl
P
air
=1.0 atm
T=25
o
C
No evaporation
M
is moles/liter
Liquid saturated
porous
plate
5.
Refer to Problem# 4.
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 de
fense 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 d
reams 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
)
=
(
θ
S
−
θ
r
)
[
1
+
(
α
|
h
|
)
n
]
m
+
θ
r
where m =
(
1
–
1/n
)
where
h
(cm)
is the soil water pressure head (matric potential in 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
θ
s
θ
r
α(cm
–
1
)
n
s
andy
loam
0.
39
0.0
3
0.
0
7
0
1.
6
0
s
ilt
loam
0.4
4
0.
07
0.0
2
5
1.
35
clay
0.5
5
0.1
2
0.0
10
1.
20
a.
For 0.1<|h|<
5
00
00 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 ra
nge of
–
0
.0
1
00
to
–
1
.
5
00
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
6
0% 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
6
0 cm depth and assume no rainfall.
d
. Suppose the
sandy
loam is at θ=0.
1
00
, the
silt loam
is at θ=0.
150
, and the clay is at
θ=0.
3
5
0
. Samples of each soil ar
e then placed in horizontal
contact;
Upon contact, what is the direction of flow between the layers? Explain.
Sandy
loam
Silt
loam
Clay
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