A gas station stores its gasoline in a tank under the ground. The tank is a cyli

Question

A gas station stores its gasoline in a tank under the ground. The tank is a cylinder lying horizontally on its side. (In other words, the tank is not standing vertically on one of its flat ends.) If the radius of the cylinder is 2 meters, its length is 7 meters, and its top is 5 meters under the ground, find the total amount of work needed to pump the gasoline out of the tank. (The density of gasoline is 673 kilograms per cubic meter; use g=9.8 m/s2)

What I know: I will need to integrate the top half and the bottom half of the gas tank separately, I will need to put my width in terms of height, I will need to use density to find mass since F=mg and I don't have a mass and I know the tank is lying on its side...What I can not do is the integration correctly, I keep running into an "unreal" number.

Explanation / Answer

We have given the radius of the cylinder is 2 meters, its length is 7 meters, and its top is 5 meters under the ground

we assume the tank is initially full and you need the work to empty it and get the fuel to ground level.

The centre of gravity of the fuel in the full tank is the tank centre line.

Its distance below ground is 5+2=7meters
Mass of fuel = (pi)*r2*h*density=(pi)*(2)^2*7*673=(pi)*4*7*673=59200 kg

Work required =weight*height=mass*g*height=59200*(9.8)*(7)=4061120 k.joules

Work required=4061120 k.joules

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