HW#1 - Head Calculations, Darcy's Law

1. A piezometer is placed in the ground at a site. The screen on the piezometer is at a depth of 172.7 ft. The elevation of the ground surface where the piezometer is located is 2193.0 ft above mean sea level. The pore pressure measured by the piezometer is 38.4 psi. Assume that sea level is the datum. At the location of the piezometer screen:

a) What is the elevation head? [ft]
b) What is the pressure head? [ft]
c) What is the total head? [ft]

2. The figure below shows a pressurized reservoir with the water level at point A.  The discharge is into the atmosphere at point C.  The connecting pipe is of constant diameter with a cross-section of 0.02 m^2 and is filled with a sand with hydraulic conductivity of 0.015 m/s.  The average length of the pipe is 9.0 m.  Point B is exactly halfway along the length of the pipe.  The discharge at C is 0.0001 m3/s.  Compute the following:

(a) The head loss from A to C.
(b) The total head at A.
(c) The pressure head at A.
(d) The total head at B.
(e) The pressure head at B
(f) Is there flow from a region of low pressure to a region of high pressure? Where and why?
(g) What would happen to the heads and discharge if the hydraulic conductivity of the medium decreased to 0.001m/s assuming that the water levels and pressures remain constant?

3. The water level in an observation well A is measured at 3785.4 ft. At a point 1238 ft downgradient from that point, the water level in a second well (B) is measured at 3629.3 ft.

a. What is the hydraulic gradient between the well A and well B?
b. Assuming that the hydraulic conductivity is 3.0 ft/day and the effective porosity is 0.3, what is the seepage velocity between the two points? [ft/day]
c. How long would it take for a particle to travel from point A to point B? [days]

4. At a site owned by Company X, it is decided to remediate a plume using a double trench system as shown below. A plume lies between the two trenches in a sand layer that is capped by a relatively impermeable clay layer. Nutrient and oxygen laden water will be injected in the trench on the right. The water will flush from right to left and be pumped out of the left trench. To ensure maximum biodegradation, it is best if the sand layer stays saturated. Thus, the trench on the left will be pumped just enough to keep the sand layer saturated. The trench on the right will be kept as full as possible. For the sand layer, assume than n = 0.35 and k = 10^-2 cm/s.

a)  For a one meter thick slice of the sand layer, how much water would need to be pumped to flush through one pore volume*?
b)  How long would it take (in days) to pump five pore volumes of water through the sand?

*A "pore volume" is a common term used in analysis of site remediation projects involving flushing. A pore volume is defined as the total volume of the voids in the region being flushed. So when you flush "five pore volumes" it means that you have flushed enough water to displace all the water in the voids five times. To find the pore volume, calculate the total volume of the region being flushed and multiply by the porosity.

Submittal Instructions

Do your calculations in Excel.  Show as much of your work as you can. Upload your Excel file via Learning Suite.