# Homework Help: Pumping gasoline

1. Dec 7, 2009

### greenpick

1. The problem statement, all variables and given/known data

Gasoline is stored in a cylindrical tank buried on its side, with the highest part of the tank 5 ft below the surface. The tank is 6 ft in diameter and 10 ft long. Density of gasoline is 45 lb/cubic ft. Assume that the filler cap of each automobile gas tank is 2 ft above the ground.
(a) How much work is done in emptying all the gasoline from the tank, which is initially full?

(b) Recall that 1 hp is equivalent to 33,000 ft-lbs/min. For electrical conversions 1 kW (1000W) is the same as 1.341 hp. The charge for use of electricity generated by a power company is about 7.2 cents per kWh. Assume that the electrical motor in the gas pump is 30% efficient. How much does it cost to pump all the gasoine from this tank?

2. Relevant equations

see above

3. The attempt at a solution
(a)volume of a generic "slice" = 10 * 2x$$\Delta$$y = 20$$\sqrt{9-y^2}$$$$\Delta$$y
Force acting on that slice = 45 * 20$$\sqrt{9-y^2}$$$$\Delta$$y
W to pump that slice up =
900$$\sqrt{9-y^2}$$$$\Delta$$y(10-y)
Total work = $$\int900\sqrt{9-y^2}(10-y)$$ from -3 to 3 $$\approx$$ 127,234.5 ft-lbs

(b)I know this isn't right... And it's probably very confusing as well.
127,234.5 ft-lbs * (1 hp/ 33,000 fl-lbs/min) = 3.8559 hp * min * (1 kW/ 1.341 hp) = 2.875 * 1000 J/s * min = 2.875 * 1000 J/s * 60 s = 175,209.66 J * (1 kWh/ 3,600,000 J) = .0479 kWh * 7.2 cents = .345 cents
for efficiency, I divided the final answer by .3 which gives me 1.15 cents, which is obviously not right.

The first part may be right, but I really don't know what to do on the second part. Any help would be greatly appreciated.

2. Dec 7, 2009

### Dick

Ok, so 1 cent worth of power will buy you 1.341*33000*60*(0.3)/7.2 ft-lbs of energy counting the efficiency factor. If I divide 127234 by that I get 1.15 cents. I don't think that's obviously not right. Though I've got to confess the units conversions are making me dizzy.

Last edited: Dec 8, 2009
3. Dec 8, 2009