Work problem/calc A gas station stores its gasoline in a tank under the ground.

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 2 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=9.8m/s^2 .)

Work=_______

(include units)

Answer 1

r = 2 m

l = 2 m

x² + y² = r

y = √(4-x²)

Δx = (4-x)

V = lwh

V = 2m * 2√(4-x²) * Δx m³

mass = density × V = 673 kg/m³ × 2m * 2√(4-x²) * Δx m³

force = gravity × mass

force = 9.81 m/s² × 673 kg/m³ × 2m * 2√(4-x²) * Δx m³

W = ∫ Force dx

W = ²_-2 ∫ 9.81 × 673 × 2 × 2√(4-x²) × (4-x) π dx

W = 663718.49939 π Joules = 2085133.16174 Joules