The rectangular tank shown here, with its top at ground level, is used to catch runoff water. Assume that the water weighs 62.3 lb/ft³. a. How much work does it take to empty the tank by pumping the water back to ground level once the tank is full? b. If the water is pumped to ground level with an (8/11)-horsepower (hp) motor (work output 400 ft-lb/sec), how long will it take to empty the tank (to the nearest minute)? c. Show that the pump in part (b) will lower the water level 15 ft (halfway) during the first 20 minutes of pumping. d. What are the answers to parts (a) and (b) in a location where water weighs 62.16 lb/ft³? 62.42 lb/ft³? a. Set up an integral to find the work done. W= 5 ft level of Ground 14 ft

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The
rectangular tank shown here, with its top at ground level, is used to catch runoff water. Assume that the water weighs 62.3 lb/ft³.
a. How much work does it take to empty the tank by pumping the water back to ground level once the tank is full?
b. If the water is pumped to ground level with an (8/11)-horsepower (hp) motor (work output 400 ft-lb/sec), how long will it take to empty the
tank (to the nearest minute)?
c. Show that the pump in part (b) will lower the water level 15 ft (halfway) during the first 20 minutes of pumping.
d. What are the answers to parts (a) and (b) in a location where water weighs 62.16 lb/ft³? 62.42 lb/ft³?
a. Set up an integral to find the work done.
W =
Ground
5 ft
level
0
30
14 ft
Transcribed Image Text:The rectangular tank shown here, with its top at ground level, is used to catch runoff water. Assume that the water weighs 62.3 lb/ft³. a. How much work does it take to empty the tank by pumping the water back to ground level once the tank is full? b. If the water is pumped to ground level with an (8/11)-horsepower (hp) motor (work output 400 ft-lb/sec), how long will it take to empty the tank (to the nearest minute)? c. Show that the pump in part (b) will lower the water level 15 ft (halfway) during the first 20 minutes of pumping. d. What are the answers to parts (a) and (b) in a location where water weighs 62.16 lb/ft³? 62.42 lb/ft³? a. Set up an integral to find the work done. W = Ground 5 ft level 0 30 14 ft
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