Engineering Board Exam Reviewer · Applications: Centroid, Work, and Moment of Inertia · hard

A hemispherical tank of radius 3 m, with its flat face on top, is full of water. How much work, in kilojoules, is needed to pump all the water to the top of the tank? Use =1000 kg/m3 and g=9.81 m/s2.

1. 1040.14
2. 624.09
3. 1664.23
4. 520.07

Answer

A. 1040.14

Solution

At depth y below the top, the cross-section has radius2 =9-(3-y)2=6y-y2 and the layer must be lifted y. W= gπ 03y≤ft(6y-y2 )dy= gπ≤ft[2y3-y4/4 ]03= gπ≤ft(135/4 ) 1040.1 kJ.

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