Question

When a liquid rotates at constant angular velocity about a vertical axis of a rigid body:

1. the pressure varies as the square of the radial distance
2. the velocity vector remains constant at a point
3. the velocity vector varies inversely as the altitude along any vertical line
4. the pressure vector varies inversely as the altitude along any vertical line

Answer 1

Correct Answer - Option 1 : the pressure varies as the square of the radial distance

Explanation:

• A fluid is rotating at constant angular velocity ω about the central vertical axis of a cylindrical container.
• The variation of pressure in the radial direction is given by:

            \(\frac{{dp}}{{dr}}\; = \;r{\omega ^2}\rho \)

• It is given that the pressure at the axis of rotation is Pc.
• Therefore, the required pressure at any point r is :

            \(p\; = \;{p_c} + \frac{1}{2}\rho {r^2}{\omega ^2}\)

Hence we can say that pressure varies as the square of the radial distance.