(a)
Consider an elementary disc of water. Volume of this elementary disc = where dy = thickness of the elementary disc.
Mass = Density x Volume = 62.4 x
Potential Energy of the elementary disc of water =
where y =height of the elementary disc of wter from the ground
Potential Energy of the of all the water = = 18029.1 lbf ft
We integrate till y=0.5 as the trough is hallf full,i.e, full till y=0.5.
Potential energy of all water = Work done to pump out all the water to the top = 18029.1 lbf ft
(b)
Force of the water on the semicircular face =
= 24038.8 lbf
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