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Question

A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid is rises at the sides. If the radius of the vessel is r and the speed of revolution is n rotations/second, find the difference in height of the liquid at the centre of vessel and its sides.

A
h=2π2n2r2g
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B
h=4π2n2r2g
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C
h=π2r2n2g
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D
None of these
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Solution

The correct option is A h=2π2n2r2g
From Berpoulli's theorem
PA+12ρV2A+ρghA
=PB+12PV2B+ρghB
Here hA=hB
PAPB=12ρ(V2BV2A)
VA=0,VB=rω
PAPB=hρg
h=r2ω22g
ω=21m
n rotation / second
1secn rotation
1sec21m angle
h=4π2n2r22g
h=2π2n2r2g

1345014_985574_ans_cb4a908078e64d1295833d3762cdf07c.png

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