Question
Download Solution PDFWhen a liquid rotates at constant angular velocity about a vertical axis of a rigid body:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
- 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.
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