HW #1 - Darcy's Law, Head Calculations

1. 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 0.01 m² and is filled with a sand with hydraulic conductivity of 0.01 m/s.  The average length of the pipe is 10.0 m.  Point B is exactly halfway along the length of the pipe.  Point B is 1.0 m above the datum and the top of the soil column (the bottom of the pressurized reservoir) is at elevation = 6.0m.   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?

2. A flow path computed from a particle tracking analysis is shown below.  The particle travels from the river to point A.  The length of the flow path is approximately 985 m.  The aquifer has a relatively uniform thickness.  The water table elevation of point A is about 705 m.  Estimate the travel time (in days) from the river to point A.

3. The hydraulic conductivity of water in a rock mass has been found to be 0.002 cm/sec. Determine the intrinsic permeability of the rock (cm²) and the "gasoline conductivity" (cm/sec) which you would use to calculate the rate of flow of gasoline should it be spilled in the rock. The specific gravity, G_s, of gasoline is 0.68 and the dynamic viscosity of gasoline is 6.2 x 10^-6 lb-sec/ft².

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 foot 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?

5. A lake lies above an aquifer as shown below.  Water is draining from the lake to the aquifer through the silt and clay layers.  When an observation well is inserted in the aquifer, water rises to 1258.5 ft.  Compute how many cubic feet of water are lost in one year from the lake to the aquifer per square foot of the lake bottom.

Submittal Instructions

Enter your solutions into either a Word document or an Excel Spreadsheet.  Show as much of your work as you can.