Answer:
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
[tex]\int dW = \int_0^7 (819.2\pi (7-y)) dy[/tex]
[tex]W = [819.2\pi(7-y)^2]_7^0[/tex]
on solving
W = 126106 ft-lbs
Hence, Work done to pump the kerosene is equal to W = 126106 ft-lbs
