Applied Hydrogeology - Fetter - 4t Edition - Chapter 2 - Solutions

2.1 The standard U.S. Class A evaporation land pan has an inside diameter of 47.5 in. and a depth of 10.0 in.
(A) Calculate the surface area of water in the pan in square meters.
(B) Calculate the volume of the pan in cubic meters.
(C) If the initial volume of water in the pan is 11.5 U.S. gallons, what is the depth of the water in millimeters?
(D) If after a 24-h period with no precipitation the volume of water in the pan is measured and found to be 10.2 U.S. gallons, what is the evaporation rate in millimeters/day?
(E) What would be the depth of water in millimeters?
(F) During the succeeding day there was a 3-h period of precipitation at a constant rate of 5 mm/h. Assuming that the 24-h evaporation rate calculated in step D also occurs during this 24-h period, what would be the depth of water in the pan?
(G) If there is no further rain, and no water is added to the pan, how long would it take for the water in the pan to totally evaporate, assuming the constant 24-h evaporation rate of step D?

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2.2 During the period of time that the water in step G above is evaporation, how many calories of heat are being absorbed? Assume that the density of water is 1000 kg/m3.
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2.3 Figure 2.26 is a map of a drainage basin and the rainfall amounts during a storm at a number of precipitation stations both within and outside the drainage basin. Make a Thiessen network drawing for the drainage basin. The exact station location is the decimal point in the rainfall amount. The relative size of the area associated with each Thiessen polygon can be measured with a planimeter or estimated by tracing the Thiessen network on cross-section paper and counting the number of squares in each polygon. Estimate the effective uniform depth of precipitation over the drainage basin.
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2.4 Make a copy of the drainage basin in Figure 2.26. Contour the precipitation data to create isohyetal lines and determine the effective uniform depth of precipitation.
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2.5 A pond has a surface area of 35 ac. If the mean daily air temperature is 66°F, the mean daily dew-point temperature is 55°F, the solar radiation is 480 langleys, and the daily wind movement is 115 mi, what is the daily lake evaporation in acre-feet?
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2.6 Make a cross-sectional plot of saturation humidity as a function of temperature using the data in Table 2.1. Label the areas of the graph that are undersaturated and supersaturated.
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2.7 Consider an air mass that has an absolute humidity of 10 g/m3 at a temperature of 22°C. Using the graph that you created for Problem 2.6, find (a) the dew point, and (b) the relative humidity.
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2.8 Analysis of baseflow recession curves from a drainage basin has yielded a recession constant of 1.55 × 10−2 d−1 when discharge is in cubic feet per second and time is in days.
(A) If a recession begins with a discharge of 328 ft3/s and t is in days, what will be the flow after 35 d and 70 d?
(B) If the recession begins with a discharge of 2356 ft3/s, what would be the flow in 5 d?

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2.9 The flow of a river at the start of a baseflow recession was 712 m3/s; after 60 d the flow declined to 523 m3/s.
(A) What is the recession constant?
(B) What would be the flow after 112 d?

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2.10 Assume that the hydrograph in Figure 2.15 has a drainage basin area of 722 mi2. How long will overland flow continue after the flood peak passes?
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2.11 A V-notch weir is placed in a road culvert to measure the flow of a stream passing through the culvert. The value of H is 2.72 ft. Compute the discharge of the stream.
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2.12 A rectangular weir is placed in a small stream to measure flow. The value of L is 1.5 ft and H is 0.22 ft. Compute the discharge of the stream.
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2.13 An industrial park with flat-roofed buildings, large parking lots, and little open area has a drainage basin area of 398 ac. The 25-year rainfall event (the amount that would on an average occur once in 25 years) has a precipitation intensity of 2.382 in./h. If the C factor is 0.75, what is the maximum rate that overland flow will drain from the industrial park?
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2.14 Figure 2.27 shows the hydrograph of a stream, which is partially fed by baseflow, with several precipitation events. Compute the ground-water recharge that occurs between the first and second precipitation events.
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2.15 Figure 2.28 is the hydrograph of a river with a long summer baseflow recession. Compute the volume of annual recharge that occurs between runoff year 1 and runoff year 2.
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2.16 The annual flow of the Colorado River at Lees Ferry for the period from 1896 to 1956 is given in Table 2.4.
(A) Construct a table of probability values.
(B) Plot a duration curve showing-the percent of the time an indicated discharge was equaled or exceeded using standard probability paper (Figure 2.29).

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2.17 An aqueduct has smooth earthen sides and bottom. The slope of the water surface is 1.7 ft/mi. The channel is trapezoidal in shape with a 45° angle to the sides of the trapezoid and a bottom segment that is 8.5 ft wide. The water in the aqueduct is 3.6 ft deep in the center.
(A) What is the average velocity of water in the aqueduct?
(B) What is the volume of flow in the aqueduct?

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2.18 A winding natural stream with weeds has an average depth of 0.86 m and is 7.25 m across. The stream channel drops 0.34 m/km. What is the stream’s average velocity of flow?
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