## Question

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

### Solution

2.0 cm

According to Bernoulli’s theorem, we have

.

At the sides the velocity is higher so the pressure is lower. Since the pressure on a given horizontal level must be same, the liquid rises at the sides to compensate for the drop in pressure.

But,

= 0.628 m/s.

= 0.02 m.

= 2.0 cm.

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