Chapter 2, Problem 2.6P

Interpretation Introduction

Interpretation: The value of gauge pressure which is exerted on the wall of centrifuge bowl is to be calculated.

Concept introduction: When a liquid is rotated in a centrifugal bowl at higher speed, a thick layer of the liquid is thrown outward and held against the wall of the bowl by a centrifugal force. The pressure variation is found from radius $r_1$ and $r_2$ .

Here, $r_1$ is the radius from the axis of rotation to the free liquid surface.

  $r_2$ is the radius of the centrifuge bowl.

The gauge pressure is the pressure difference between absolute pressure and atmospheric pressure.

The formula for calculating the gauge pressure is,

  $p_2-p_1=\frac{{\omega }^2\rho \left(r_2^2-r_1^2\right)}{2}$