how much work in joules

Question

A circular swimming pool has a diameter of 20 m, the sides are 4 m high, and the depth of the water is 3 m. How much work (in Joules) is required to pump all of the water over the side? (The acceleration due to gravity is 9.8  and the density of water is 1000 .)

Answer 1

Consider a slice of the water distance x from the top, height dx.

Volume of water = πr² dx, where r = 10 . Mass = 1000 πr²dx, it has to be raised through x m to pump it out, so work done is mgh = 1000πr² g x. = 100000 ^π gx

Integrate this from x=1 to x=4 (because the top of the water is 1m below the top of the tank) giving

100000πg (x²/ 2) which evaluated between x= 1 and 4 gives 50000πg (16-1) = 750000πg J = 7350000π J