Calculus: Work Done Pumping Water Out Of A Cylindrical Tank?
A cylindrical gasoline tank 3 feet in diameter and 4 feet long is carried on the back of a truck is used to fuel tractors. The axis of the tank is horizontal. Find the work done in pumping the entire contents of the fuel tank into a tractor if the opening on the tractor tank is 5 feet above the top of the in the truck.
the Gasoline weighs 42 lbs per cubic foot.
Tags: Calculus, Cylindrical, Done, Pumping, Tank, Water, Work
November 22nd, 2009 at 6:48 pm
The potential energy of the gasoline is (taken as zero its top point).
Ep1 = -M g R
where M is the mass of gasoline, g gravity acceleration and R the radius of the tank.
If raised by a height h above the truck, its new potential energy will be
Ep2 = M g h.
Then the work will be
W = Ep2 – Ep1 = M g (h+R).
M = rho pi R^2 L = 4750 pounds = 2155 kg
h+R = 8 ft = 2.4384 m
W = 51550 J