How much work in Joules

Question

A circular swimming pool has a diameter of 20 m. The circular side of the pool is 4 m high, and the depth of the water is 2.5 m. (The acceleration due to gravity is 9.8 m/s^2 and the density of water is 1000 kg/m^3.)

How much work (in Joules) is required to:

(a) pump all of the water over the side? 



(b) pump all of the water out of an outlet 1 m over the side? 

Answer 1

density, ρ = 1000 kg/m³

gravity, g = 9.8 m/s²

Center a cylinder on the x/y-axis

ΔV = area Δy = πr²Δy = 100πΔy

ΔW = distance ×(ρg)ΔV

a) distance = 4-y

W = 100πρg∫^2.5₀ (4-y)dy = 100πρg(4y-y²/2)|₀^2.5 joules

b) distance = 5-y

W = 100πρg∫^2.5₀ (5-y)dy = 100πρg(5y-y²/2)|₀^2.5 joules

Can you complete the arithmetic?