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A liquid is kept in a cylindrical vessel which is rotated alon

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.

h = \frac{2 π ^{2} n ^{2} r ^{2}}{g}

h = \frac{4 π ^{2} n ^{2} r ^{2}}{g}

h = \frac{π ^{2} r ^{2} n ^{2}}{g}

None of these

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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.

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Text solutionVerified

From Berpoulli's theorem

P_{A} + \frac{1}{2} ρ V_{A}^{2} + ρ g h_{A}

= P_{B} + \frac{1}{2} P V_{B}^{2} + ρ g h_{B}

Here

h_{A} = h_{B}

P_{A} - P_{B} = \frac{1}{2} ρ (V_{B}^{2} - V_{A}^{2})

V_{A} = 0, V_{B} = r ω

P_{A} - P_{B} = h ρ g

\Rightarrow h = \frac{r ^{2} ω ^{2}}{2 g}

ω = 21 m

n \to

rotation / second

1 sec \to n

rotation

1 sec \to 21 m

angle

h = \frac{4 π ^{2} n ^{2} r ^{2}}{2 g}

h = \frac{2 π ^{2} n ^{2} r ^{2}}{g}

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Question Text	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.
Answer Type	Text solution:1
Upvotes	150