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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