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Suppose that a cylindrical tank 6 meters high with a radius of 2 meters is filled to the rim with water. The tank is buried so that the top of the tank is 1 meter below ground level. The space above the tank is not filled with water. Calculate how much work needs to be done by a pump to pump the water out of the tank up to ground level. (The water weighs 9,800 newtons per cubic meter.)

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Answer:

940800π Nm

Explanation:

Given the following :

Radius of cylindrical tank(r) = 2m

Weight of water = 9800N/m^3

Volume of a cylindrical tank is given as:

πr^2h

Height of tank = Δy

Volume = π2^2Δy = 4πΔy

Weight of water layer = weight of arer × volume of cylindrical tank = 9800 × 4πΔy = 39200πΔy

Distance from any point from tank top

Height - y = 6 - y

1 metre below ground level

Distance = 6 - y + 1 = 7 - y

Δy = 7- y

Taking the integral:

See attached picture for final calculations

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