Work required to pump

Question

A water tank has the shape of an upright cylinder with radius 𝑟 = 1 meter and height 10

meters. If the depth of the water is 5 meters, how much work is required to pump all the

water out the top of the tank?

Answer 1

The weight density of water δ = 1000 kg/m³

Work = Force • distance moved (with the direction of the force)

W = F•d

V_slice = π (1)² dy

F_slice = π•δ dy

W_slice = F_slice• d

Since y=d then:

W_slice = F_slice• y

Subsitute F_slice:

W_slice = π•δ•y dy

Then the integral will be:

W = ∫₅¹⁰ π•δ•y dy = ∫₅¹⁰ 1000 π•y dy

W = 37,500π N-m