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Soil physics is the study of soil physical properties and processes. It is applied to management and prediction under natural and managed ecosystems. (Wikipedia). Keywords in this solved assignment are: Matric Potential, Total Potential, Tensiometers, Genuchten Parameters, Water Retension Apparatus, Hydraulic Gradient, Initial Instantaneous Discharge Rate
Typology: Exercises
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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) 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
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.