Hydraulics

Q1: When a liquid rotates at constant angular velocity about a vertical axis of a rigid body, the pressure

A increases linearly to its radial distance

B varies inversely as the altitude along any vertical line

C varies as the square of the radial distance

D decreases as the square of the radial distance

E none of these.

ANS:C - varies as the square of the radial distance

I apologize for the confusion in the previous response. Let me correct it. When a liquid rotates at a constant angular velocity about a vertical axis of a rigid body, the pressure varies as the square of the radial distance from the axis of rotation. This variation in pressure is due to the centrifugal force experienced by the liquid particles as they move away from the axis of rotation. The centrifugal force is proportional to the square of the angular velocity and the radial distance from the axis of rotation. As the radial distance increases, the centrifugal force experienced by the liquid particles also increases. According to the principles of hydrodynamics, the pressure in the liquid decreases with increasing centrifugal force. Therefore, the pressure varies inversely with the square of the radial distance from the axis of rotation.



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