# ps_2 - DOWNSTREAM PROCESSING Problem Set#2 Problem 1 A key...

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D OWNSTREAM P ROCESSING Problem Set #2 Problem 1 A key to understanding centrifugation is understanding the equations that describe it. One can begin to understand these equations by deriving the relationship between volumetric throughput, terms that describe the process medium, and terms that describe the separator design. Consider the following schematic of a sedimenting centrifuge: where r 1 = distance between fluid outer layer and the axis of rotation r 2 = radius of bowl ω = angular rotation rate (radians/sec) b = height of bowl a) Please derive a general expression that relates volumetric throughput (Q) to the centrifuge physical dimensions, fluid properties, and characteristics of the particle being separated. In your b Liquid Discharge Liquid Surface ω Feed r 1 r 2 1

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derivation, please consider the terminal velocity of a particle in a centrifugal field (i.e. Stoke’s law in a centrifugal field ). b) For design purposes, the equations that describe centrifugation incorporate a parameter called Σ
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ps_2 - DOWNSTREAM PROCESSING Problem Set#2 Problem 1 A key...

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