Question

A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides as shown in figure below. If the radius of the vessel is 0.05 m and the speed of rotation is 2 rad $s^{-1}$, find the difference in the height of the liquid at the centre of the vessel and its sides

• A. 20 cm
• B. 4 cm
• C. 2 cm
• D. 0.2 cm

Answer 1

The correct option is C 2 cm

According to Bernoulli's theorem
$\rho =\frac{1}{2}\rho v^2$=constant
Near the ends, the velocity of liquid is higher so that pressure is lower as a result the liquid rise at the sides to compensate for this drop of pressure
i.e.,$\rho gh=\frac{1}{2}\rho v^2=\frac{1}{2}\rho r^2{w}^2$

Hence,$h=\frac{r^2{w}^2}{2g}$
$=\frac{r^2(2\pi v{)}^2}{2g}$
$=\frac{2{\pi }^2{r}^2{v}^2}{g}$
$=\frac{2\times {\pi }^2\times (0.05{)}^2\times 2^2}{9.8}$
= 0.02 m = 2 cm