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. $h=\frac{2{\pi }^2{n}^2{r}^2}{g}$
• B. $h=\frac{4{\pi }^2{n}^2{r}^2}{g}$
• C. $h=\frac{{\pi }^2{r}^2{n}^2}{g}$
• D. None of these

Answer 1

The correct option is A $h=\frac{2{\pi }^2{n}^2{r}^2}{g}$

From Berpoulli's theorem

$P_A+\frac{1}{2}\rho V_A^2+\rho g{h}_A$

$=P_B+\frac{1}{2}P{V}_B^2+\rho g{h}_B$

Here $h_A=h_B$

$P_A-P_B=\frac{1}{2}\rho (V_B^2-V_A^2)$

$V_A=0,V_B=r\omega$

$P_A-P_B=h\rho g$

$\Rightarrow h=\frac{r^2{\omega }^2}{2g}$

$\omega =21m$

$n\to$ rotation / second

$1\sec \to n$ rotation

$1\sec \to 21m$ angle

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

$h=\frac{2{\pi }^2{n}^2{r}^2}{g}$