# NUMERICAL EXPERIMENTS

**STEADY-STATE FLOW EXPERIMENTS**

**Exercise 1. Water Movement in Homogeneous Saturated Soils**

- A soil column 20 cm in length and 5 cm in diameter was packed uniformly and saturated with water. The column was oriented horizontally. The saturated hydraulic conductivity of the soil is 12 cm/day. Water was supplied to the inlet of the column (x = 0) at a constant matric potential of 35 cm. Water was collected at the outflow end of the system (x = 20 cm) which was maintained at a matric potential of 25 cm. These flow conditions were imposed for a long time so the system was at steady-state.
- What is the water content of the soil? Does the water content change with position from the inlet?
- What is the flux density of water in the soil column? What volume of water would be collected at the outflow in a 15 minute period?
- Does the flux density of water equal the saturated conductivity?
- If it does not, adjust the matric potential at x = 0 (keeping the matric potential zero or greater) so that the flux density is equal to the saturated hydraulic conductivity. Record the matric potentials and length values. As the potential at x = 0 increases, what happens to the flux density?
- Reset the potentials to their original values. Now adjust the matric potential at x = 20 cm (keeping the matric potential zero or greater) so that the hydraulic conductivity and flux density are equal. Record the matric potentials and length values. As the potential at x = 20 increases, what happens to the flux density?
- Reset the potentials to their original values. Adjust the length and observe the changes in flux density. As the length increases, what happens to the flux density? Is it possible to adjust the length of the soil column so that the hydraulic conductivity and flux density are equal. If so, record the matric potentials and length values.
- Set the length to 20 cm and the matric potential at x = 0 to 20 cm and that at x = 20 cm to 10 cm. What is the flux density? How does it compare to the flux density observed in part B above?
- Set the length to 10 cm and the matric potential at x = 0 to 20 cm and that at x = 10 cm to 10 cm. What is the flux density? How does it compare to the flux density observed in part B above?
- Set the length to 20 cm and the matric potential at x = 0 to 30 cm and that at x = 20 cm to 10 cm. What is the flux density? How does it compare to the flux density observed in part B above?
- Set the length to 10 cm and the matric potential at x = 0 to 30 cm and that at x = 20 cm to 10 cm. What is the flux density? How does it compare to the flux density observed in part B above?
- Reset the input parameters to the original values.
- Examine the graphs of total, matric, and gravitational potentials. Note that all of them are straight lines. Also note that the gravimetric potential is a constant for this horizontal column.
- Verify that the total potential is the sum of the matric potential and the gravitational potential at any specified point.
- Modify the matric potentials so that the flow through the soil column is zero.
- What is the difference between the matric potentials at the ends of the column in this case?
- What is the difference between total potentials?
- What is the equivalent conductivity of the soil now?
- Write an expression involving the total potentials at at the ends of the column and the length of the soil column that can be multiplied by the saturated conductivity to give the flux of water through the column. Design some additional experimental conditions to test your expression. Does it continue to work?
- Repeat exercise 1 with the column oriented vertically with x = 0 at the top (90 degree angle). Remember the matric potential must be zero or positive in this exercise.
- Repeat exercise 1 with the column oriented vertically with x = 0 at the bottom (270 degree angle). Remember the matric potential must be zero or positive in this exercise.
- Compare results of exercises 1, 2, and 3. Compare the expressions written in step F. Are they different? Can you find an expression that works for all three orientations? Does it still work for angles of 30, 45, and 60 degrees? Write the complete form of Darcy's equation for saturated flow.

Written by D.L. Nofziger, July, 2000. Send comments and suggestions to dln@mail.pss.okstate.edu.