Physics Exam

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(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.

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 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.

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.

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 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