Class 11

Physics

Mechanics

Mechanical Properties of Fluids

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.

- $h=g2π_{2}n_{2}r_{2} $
- $h=g4π_{2}n_{2}r_{2} $
- $h=gπ_{2}r_{2}n_{2} $
- None of these

$P_{A}+21 ρV_{A}+ρgh_{A}$

$=P_{B}+21 PV_{B}+ρgh_{B}$

Here $h_{A}=h_{B}$

$P_{A}−P_{B}=21 ρ(V_{B}−V_{A})$

$V_{A} =0,V_{B}=rω$

$P_{A}−P_{B}=hρg$

$⇒h=2gr_{2}ω_{2} $

$ω=21m$

$n→$ rotation / second

$1sec→n$ rotation

$1sec→21m$ angle

$h=2g4π_{2}n_{2}r_{2} $

$h=g2π_{2}n_{2}r_{2} $