A vertical right-circular cylindrical tank measures 7 ft high and 8 ft in diameter. It is full of kerosene weighing 51.2 pounds per cubic feet. How much work does it take to pump the kerosene to the level of the top of the tank?

W = 126106 ft-lbs

Explanation:

given,

Height of the cylinder = 7 ft

Diameter of cylinder = 8 ft

radius of the cylinder = 4 ft

Weight of the kerosene = 51.2 lb/ft³

Calculating the volume of cylinder for dy height

dV = π r² dy

dV = π 4² dy

dV = 16πdy

Force acting on the cylinder

dF = W x dV

dF = 51.2 x 16πdy..........(1)

We know

work done = Force x displacement

displacement = 7 - y

dW = 51.2 x 16πdy x (7 - y)

integrating both side

on solving

W = 126106 ft-lbs

Hence, Work done to pump the kerosene is equal to W = 126106 ft-lbs

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