We model pumping from spherical containers the way we do from other containers,

Question

We model pumping from spherical containers the way we do from other containers, with the axis of integration along the vertical axis of the sphere. Use the figure shown to the right to find how much work it takes to empty a full hemispherical water reservoir of radius 4 m by pumping the water to a height of 12 m above the top of the reservoir. Water weighs 9800 N/m^3. The amount of work required to pump the water to a height of 12 m above the top of the reservoir is approximately. (Do not round until the final answer. Then round to the nearest hundredth as needed.)

Explanation / Answer

Consider a very thin strip of ht dy at a height y from the base

dW = mgh = g dA (R-y+12) = g dA (16-y)

W = [0 , 4] g ( (16-y²)(16-y) dy

= g * (1856/3) =27.10 MJ

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