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 2.5 meters, its length is 7 meters, and its top is 2 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/s^2.)

Question

Mathematics

Ice Queen

26 January, 10:51

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 2.5 meters, its length is 7 meters, and its top is 2 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/s^2.)

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Tramp · Answer 1

initially full and you need the work to empty it and get the fuel to ground level

The centre of gravity (useful concept that!) of the fuel in the full tank is the tank centre line. Its distance below ground

2.5 m + 2 m=4.5 m

Mass of fuel = π x (2.5) ² x 7 x 673 = 29443.75 kg

Work required = weight x height = mass x g x height = 29443x 9.81 x 4.5 =

1299794 k. Joules