A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides, if the radius of vessel is ` 0.05 m` and the speed of rotation is `2 rev//s`, find difference in the height of the liquid at the centre of the vessel and its sides.

Explanation

When the liquid is rotated along its axis, the velocity is greater at its sides than in the middle, fig. Ac cording to Bernoulli's theorem pressure is lower near the sides than in the middel when the level is horizontal. Therefore, the liquid rises at the sides to height h to compensate for this drop in pressure. let `upsilon` be the velocity of layer of water near the sides of tube and r be the radius of the tube. then

`1.2 rho upsilon^(2) = rho g h`
or `h=(upsilon^2)/(2g) = ((r omega)^(2))/(2g) = ((r2 pi upsilon)^(2))/(2g) = (2 pi^(2)r^(2)upsilon^(2))/(g)`
`=(2 xx (22/7)^(2) xx(0.05)^(2) xx (2)^(2))/(9.8) = 0.02m`.