Subtopic: Centrifugal separation of solids, liquids and gases
Question Statement:
A high speed tubular ultracentrifuge with bowl radius of 100 mm and height 500 mm rotates at 20000 rpm and settles starch particles (average diameter of 20µm) on the wall. The ratio of centrifugal force to the gravitational force acting on the particle is ______
Official Answer Key:
44700 to 44800
Step-by-Step Solution & Explanation
The ratio of centrifugal to gravitational acceleration (and hence force, for the same particle mass) is ω²r/g, where ω is the angular speed and r is the bowl (particle) radius at which settling occurs (taken as the bowl radius, 0.1 m). ω = 2πN/60 = 2π×20,000/60 = 2094.4 rad/s. Ratio = ω²r/g = (2094.4)²×0.1/9.81 = 4,386,528×0.1/9.81 = 44,714, within the accepted band 44,700–44,800. (The particle diameter and bowl height do not enter this ratio.)
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