A cylinder tank of water is laying on it's side. Radius is 2 and height is 10. How much work is required to pump all of the water out of the tank?
The simple answer is that the tank volume is 40π ft³ and the cg moves 2 feet:
40π ft³ (2 ft) (62.4 lbs/ft³) = 4992π ft-lbs
By integration:
W = ∫ F dx
= 62.4 (10) ∫ (2 + y) √(4 - y²) dy .... y = -2 to 2
= 62.4 (80π)
= 4992π ft-lbs
Answer: 4992π ft-lbs ≈ 15674.88 ft-lbs
Comments
The simple answer is that the tank volume is 40π ft³ and the cg moves 2 feet:
40π ft³ (2 ft) (62.4 lbs/ft³) = 4992π ft-lbs
By integration:
W = ∫ F dx
= 62.4 (10) ∫ (2 + y) √(4 - y²) dy .... y = -2 to 2
= 62.4 (80π)
= 4992π ft-lbs
Answer: 4992π ft-lbs ≈ 15674.88 ft-lbs