Chapter 5 - Groundwater
1. Suppose there is a saturated sand aquifer. What is the volume of water contained in a volume of sand that is 3.0 m3? What volume would be released from a volume of sand that is 3.0 m3?

2. A confined aquifer, 20.0 m thick has two wells spaced 500 m apart along the direction of flow. One well has a piezometric level at 50 m above a datum; the second
well has a level of 48 m above datum. What is the flow rate per meter of width into the aquifer? The hydraulic conductivity is 50 m/day .

3. Suppose the groundwater head in a confined aquifer changes by 32 m within a horizontal distance of 300 m. The hydraulic gradient is

?h / ? x = 32 m / 300m = 0.107

The hydraulic conductivity in the aquifer is 75 m/day and the effective porosity is 0.20. What is the Darcy velocity of the groundwater?

4. If the limestone aquifer under the farmhouse is 200 m thick and has an effective porosity of 0.15, how much water (km3) can be stored in an area of 0.1 km by 0.1 km of the aquifer?

3. The hydraulic gradient of a confined aquifer is 0.00295. The hydraulic conductivity of the aquifer is 150 m/day and the effective porosity is 0.32.
a. What is the average velocity of the groundwater?
b. If the nitrogen travels with the same velocity as the groundwater, how many years will it take to travel 1 km?
c. The concentration of Contaminant X at the point where it enters the aquifer is 0.524 mg/L. If the decay rate of Contaminant X is 0.020/yr, what is the concentration of it 1 km away in the direction of groundwater flow?

d. The EPA has found the potency factor of Contaminant X to be 0.75 kg-day/mg. If a town of 35,000 people takes its drinking water out of the aquifer 1 km downflow from where it enters the aquifer, what is the lifetime cancer risk to an individual living in the town?

e. What is the upper bound on the number of people expected to die from cancer from Contaminant X each year in the town after Contaminant X arrives?15. Dry soil particles exactly fill a 50 cm3 container and weigh 100 g. When the particles are poured into another beaker of water, they displace 35 cm3 of water.
a. What is the porosity of the soil?

b. What is the average density of the actual solids contained in the soil?

16. A soil sample with an effective porosity of 27% is placed in a cylinder (permeameter) to determine the hydraulic conductivity in the laboratory. The cylinder is 0.2 m high and it has a cross-sectional area of 0.06 m2. The head on the upstream end is 3.0 m and on the downstream side is 0.55 m. A flow rate of 3.0 m3/day is observed.
a. What is the hydraulic conductivity?
b. What is the Darcy velocity?

c. What is the true velocity?

17. A 3000 m long section of river runs parallel to a ditch 800 m away. A confined aquifer connecting the two has a hydraulic conductivity of 0.525 m/d and an average height of 25 m. The water surface elevation of the river is 5.0 m higher than the water surface elevation of the ditch. What is the discharge of the groundwater from the river section to the ditch?

18. Field determination of hydraulic conductivity in an unconfined aquifer: Drawdown at a 0.15 diameter well, which has been pumping with a discharge of 1200 m3/d for a long enough time that steady state condition have been reached, is determined to be 0.55 m. The aquifer is originally 25.0 m thick. An observation well 12 m a way has been drawn down by
0.18 m. What is the hydraulic conductivity of the aquifer? (assume the first observation well is the well itself at a distance of the well radius)

19. Field determination of hydraulic conductivity: A confined aquifer, 24.0 m thick, has been pumped from a well at a steady rate of 3500 m3/d for a very long time. Drawdown at an observation well, 5.00 m away from the pumped well, is 3.00 m and drawdown at a second observation well 25.0 m away is 0.220 m. What is the hydraulic conductivity of the aquifer?

20. An oil storage area, abandoned 19 years ago, had oil spilled on the ground, which saturated the soil at a concentration of about 275 mg/kg of soil. A fast food chain wants to build a restaurant there and samples the soil for contaminants. They discover the soil contains oil at a concentration of 13.8 mg/kg. A local geologist concludes that the oil much have been destroyed by soil microorganisms at a rate of 13.8 mg/kg each year, and in one more year the site will be free of all contaminants. Do you agree with this conclusion? How long would you estimate the soil will take to reach an acceptable contamination concentration of 0.500 mg/kg?