A circular swimming pool has a diameter of 14 m, the sides are 4 m high, and the depth of the water is 3 m. How much work (in Jo

Question

2 years ago

8

ules) is required to pump all of the water over the side

1 answer:

vredina [299] · Answer 1 · 2023-08-12T20:35:32+03:00

The work required is Wa = 2954112 J

Given:

swimming pool diameter = 14 m

length of sides = 4 m

height of water = 3 m

To Find:

work required to pump water

Solution: The radius of the swimming pool is

r = 14/2 = 7 m

The work is mathematically given as

W = Force x distance

Now force is mathematically given as

F = density x area x height of pool = p*(πr²)dx

Now the work done to pump all of the water over the side

W = ∫p*(πr²)(H-x)dx = ∫1000*9.81*(π*7^2)(4-x)dx

W = 64000*9.8π∫(4-x) dx = 64000*9.8π{4(3) - 3/2}

W = 2954112 J

So, work required is Wa = 2954112 J

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