Homework 2

Due Friday, March 14.

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You may work with others if you like, but please list their names if you do.

1) Suppose you put a piece of salt into a sealed, saturated, horizontal soil column. Describe the resulting process(es) and the ultimate end product.

2) Do the same as #1, but for an unsaturated sealed horizontal soil column (say, q = 0.5). Is there a semi-permeable membrane in the soil? If so, where? If not, is osmotic potential important?

3) You have 2 blocks of an impermeable metal, each one measuring 1 cm³ with 2 holes drilled through it. In block A, one hole has radius 1 mm, and the other has radius 0.1 mm. In block B, one hole has radius 1 mm halfway through, then radius 0.1 mm the rest of the way; the other hole is the opposite (first small, then large). What are the hydraulic conductivities of the two blocks (hint: note the similarity to a question on Exam 1)? How does this relate to soil structure? How does it not relate to soil structure (that is, what difference(s) between soil and solid metal are relevant to this question)?

4) A given soil has K_sat = 3 cm/hr, and q_s = porosity = 0.5. Plot K(q) from q = 0.0 to 0.5 for the case of A: K(q) = K_sat * (q / q_s), and B: K(q) = K_sat * (q / q_s)⁴. Assuming that the driving force is simply gravity (i.e., the gravitational potential due to the height of the sample), why is the total potential gradient NOT linear?

5) A tensiometer is buried at a depth of 50 cm in a soil with a water table at 3 m. A thin tube comes up out of the tensiometer, and goes into a container of mercury (density 13.6 g/cm) whose upper surface is 1 m above the soil surface (see diagram). The system is at equilibrium when the mercury in the tube is 47 mm above the mercury surface. What is the matric potential of the soil around of tensiometer? Is water moving upward or downward in the soil between the tensiometer and the water table?

6) Water with a non-reactive neutral tracer flows into a soil saturated with tracer-free water. You collect water at a depth of 2 m and see a breakthrough curve like this:

What conceptual model does this correspond to? What can you conjecture about the Retardation? Should you expect the standard deviation of the tracer spread to increase with depth, or with the square root of depth?

7) You have the following setup:

A to B is ponded water.

B to G is saturated soil.

G to H is a water-filled tube.

Distance from C to D: 40 cm.

Distance from E to F: 60 cm.

Use point B as your gravitational reference level.

Assuming the system is at equilibrium, make a table of y_T, y_g, and y_m for points A through H. If air leaked into the system at the rubber stopper at G, what additional information would you need (and how would you obtain it) to determine K(q) between E and F?