Applied Hydrogeology - Fetter - 4t Edition - Chapter 1 - Solutions

1.1 A vertical water tank is 15 ft in diameter and 60 ft high. What is the volume of the tank in cubic feet?
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1.2 What is the volume of the above tank in cubic meters?
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1.3 If the above tank were measured and found to have an inside diameter of exactly 15.00 ft and a height of 60.00 ft, what would be the volume in cubic feet?
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1.4 What would be the above tank’s volume in cubic meters?
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1.5 If a well pumps at a rate of 8.4 gal per minute, how long would it take to fill the tank described above?
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1.6 The only swimming pool at the El Cheapo Motel is outdoors. It is 5.0 m wide and 12.0 m long. If the weekly evaporation is 2.35 in., how many gallons of water must be added to the pool if it does not rain?
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1.7 If during the next week the pool still loses 2.35 in. of water to evaporation, even with 29 mm of rainfall, how many liters of water must be added?
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1.8 A ground-water basin has a surface area of 125 km². The following long-term annual averages have been measured:

Precipitation 60.6 cmEvapotranspiration 46.3 cmOverland flow 3.4 cmBaseflow 10.6 cm

There is no streamflow into the basin and no groundwater flow either into or out of the basin.

(A) Prepare an annual water budget for the basin as a whole, listing inputs in one column and outputs in another. Make sure that the two columns balance as these are long-term values and we assume no change in the volume of water stored in the basin.
(B) Prepare an annual water budget for the streams.
(C) Prepare an annual water budget for the groundwater basin.
(D) What is the annual runoff from the basin expressed in centimeters?
(E) What is the annual runoff from the basin expressed as an average rate in cubic meters per second?

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1.9 The parking lot of the Spendmore Megamall has an area of 128 ac. It is partially landscaped to provide some areas of grass. Assume that an average 63% of the water that falls on the parking lot will flow into a nearby drainage ditch, and the rest either evaporates or soaks into unpaved areas. If a summer thunderstorm drops 3.23 cm of rain, how many cubic feet of water will flow into the drainage ditch?
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1.10 What mass of water at 15°C can be cooled 1°C by heat necessary to melt 185 g of ice at 0°C?
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1.11 What mass of water at 15°C can be cooled 1°C by the amount of heat needed to sublime (go from a solid to a vapor state) 18 g of ice at 0°C?
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1.12 A 500-milliliter (mL) bottle of spring water, which is at room temperature of 25°C, is poured over 120 g of ice that is at −8°C. What will be the final temperature of the water when all of the ice has melted, assuming that it is in an insulated container that does not change temperature?
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1.13 At a water elevation of 6391 ft, Mono Lake has a volume of 2,939,000 ac-ft, and a surface area of 48,100 ac. Annual inputs to the lake include 8 in. of direct precipitation, runoff from gauged streams of 150,000 ac-ft per year, and ungauged runoff and groundwater inflow of 37,000 ac-ft per year. Evaporation is 45 in. per year.

(A) Make a water budget showing inputs, in ac-ft per year and outputs in ac-ft per year. Does the input balance the output?
(B) Will the average lake level rise or fall from the 6391-ft elevation over the long term?
(C) What would be the lake surface area when the inputs balance the outputs? (Assume that the volume of gauged and ungauged runoff and ground-water inflows remain constant with a change in lake surface area.)
(D) What is the residence time* for water in Mono Lake when the water surface is at 6391 ft?

*The residence time of a body of water is the average time that it would take for the volume of water to be exchanged once.
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1.14 Assume that Mono Lake stood at an elevation of 6391 ft, as described in problem 13, and a total annual diversion of 85,000 ac-ft of water were allowed from the Mono Lake basin.

(A) Would the average lake level rise or fall?
(B) What would the final lake surface area be after a new equilibrium is established? (Assume that the volume of gauged and ungauged runoff and ground-water inflows remain constant with a change in lake surface area.)

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