A swimming pool is built in the shape of a rectangular parallelepiped 12 ft deep, 10 ft wide, and 15 ft long. How much work is required to fill
the swimming pool to 1 ft below the top if the water is pumped in through an opening located at the bottom of the pool?
Use 62.4 lb/ft as the weight density of water. Enter the exact answer.
Answers
Answer:
100litre
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To find,
Work is required to fill the swimming pool.
Given,
A swimming pool is built in the shape of a rectangular parallelepiped 12 ft deep, 10 ft wide, and 15 ft long.
Solution,
To calculate the work required to fill the swimming pool, we need to find the volume of water that needs to be pumped in and then multiply it by the weight density of water.
The swimming pool is in the shape of a rectangular parallelepiped with dimensions 12 ft (height) x 10 ft (width) x 15 ft (length). The volume of the swimming pool is therefore:
Volume = height x width x length
Volume = 12 ft x 10 ft x 15 ft
Volume = 1800 cubic feet
To fill the pool to 1 ft below the top, we need to fill it to a height of 11 ft. Therefore, the volume of water that needs to be pumped in is:
Volume of water = (11 ft - 0 ft) x 10 ft x 15 ft
The volume of water = 1650 cubic feet
Now we can calculate the work required to pump this volume of water into the pool:
Work = Force x Distance
The force required to pump the water is the weight of the water, which can be calculated using the weight density of water given in the problem as 62.4 lb/ft³. The weight of the water is:
Weight = Volume of water x Weight density of water
Weight = 1650 ft³ x 62.4 lb/ft³
Weight = 102960 lb
The distance the water is being lifted is the height of the pool, which is 12 ft. However, we are only filling the pool to a height of 11 ft, so the distance the water is being lifted is:
Distance = 11 ft - 0.5 ft = 10.5 ft
(Note that we subtracted 0.5 ft from the height to account for the fact that the water is being pumped in 1 ft below the top of the pool.)
Now we can calculate the work required:
Work = Force x Distance
Work = 102960 lb x 10.5 ft
Work = 1081080 ft-lb
Therefore, the work required to fill the swimming pool to 1 ft below the top is 1,081,080 ft-lb.
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