Exam Question

### Fundamental Principle of Centrifugal Separation
The separation of two immiscible liquids, such as lubricating oil and water, in a centrifuge is governed by the principles of Stokes' Law, adapted for a centrifugal field. The efficiency of separation depends on creating a stable interface (e-line) between the oil and water layers within the purifier bowl. Oil, being less dense, moves inwards towards the center, while water and heavier solids move outwards. Oil carryover with the water discharge occurs when this stable separation process is disrupted.
The settling velocity (separation rate) of a particle (e.g., a water globule in oil) is given by:
$$ v_g = \frac{d^2 (\rho_w - \rho_o)}{18\mu} \times \frac{\omega^2 r}{g} $$