A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is r and angular velocity of rotation is ω ,

Question

A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is r and angular velocity of rotation is ω , then the difference in the heights of the liquid at the centre of the vessel and the edge is

TestHub · Accepted Answer

From Bernoulli's theorem, P A ​ + 2 1 ​ d v A 2 ​ + d g h A ​ = P B ​ + 2 1 ​ d v B 2 ​ + d g h B ​ Here, h A ​ = h B ​ ​ ∴ P A ​ + 2 1 ​ d v A 2 ​ = P B ​ + 2 1 ​ d v B 2 ​ P A ​ − P B ​ = 2 1 ​ d [ v B 2 ​ − v A 2 ​ ] Now, v A ​ = 0 , v B ​ = r ω and P A ​ − P B ​ = h d g ​ ∴ h d g = 2 1 ​ d r 2 ω 2 or h = 2 g r 2 ω 2 ​

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