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- You have the setup shown below at your research site, with the elevations shown (note: figure is not to scale!). The mercury has risen 188 mm for tensiometer A, and 193 mm for tensiometer B.
a) What are the values of the matric potential and total potential, at the point of measurement for the 2 tensiometers? Give your answers in units of meters.
A: On the mercury side, the downward pull is 0.188 m * (13.5/1.0) = 2.538 m. On the water side, the downward pull due to water is (0.188+0.63+0.1 m) = 0.918 m. The difference must be matric potential: ψm = -1.62 m.
Taking the soil surface as the reference elevation, the tensiometer is 0.1 m lower, so the total potential is -1.72 m.
Similar calculations for B give ψm = -1.5825 m, and total potential = -1.7825 m
b) In which direction is water flowing between A and B?
Water flows from a higher to a lower total potential. The total potential at B is less than (more negative than) that at A, so water is flowing from A to B.
A
B
1.74 m
-0.2 m
-0.1 m
0.0 m
0.63 m
A
B
A
B
1.74 m
-0.2 m
-0.1 m
0.0 m
0.63 m
- You have performed some water retention measurements, and have the following data:
a) Using the Solver capabilities of your spreadsheet, calculate the values of the van Genuchten parameters α, n, and θs. You may assume that θr = θ at 1500 m tension, and that m = 1-(1/n). I recommend using a sum of squared θ differences as the error term. Assume θr = 0.1. A reasonable seed value for θs is 0.5. You quickly find that you need n ≥ 1.0. m = 1 – (1/n) That reasoning, plus the solver, give these final values (see the posted spreadsheet for details). The equation to use is the van Genuchten water retention function:
m
r s r n α h
θ θ θ θ
b) Before starting the water retention trial, you found that your soil has a saturated hydraulic conductivity K s = 9.3 cm/day. Using the van Genuchten parameters obtained in (a), and the Mualem-van Genuchten formulation shown in class, estimate K ( θ) values for each θ value given above. Plot your results as K ( θ). The Mualem–van Genuchten (MvG) function takes S, not θ, as its argument, so first get values of S for each point. Then use MvG’s K( S) equation:
( ) [ ( ) ]
1 2
m m
K S = Ks S − − S. Here’s what I got:
1.E-
1.E-
1.E-
1.E-
1.E-
1.E-
1.E+ 0 0.1 0.2 0.3 0.4 0.5 0.
theta
K(theta)
ψm, m θ 0.1 0. 0.2 0. 0.5 0. 1 0. 3.33 0. 10 0. 20 0. 50 0. 300 0. 1500 0. parameter Value α (^) 3. n 1. θs 0. θr 0. m 0.
S K(s), cm/day 1.000 9. 0.951 1. 0.876 0. 0.700 0. 0.549 2.04E- 0.327 5.98E- 0.193 1.72E- 0.137 1.81E- 0.089 1.02E- 0.024 1.70E- 0.000 0.
