Scale-up of Cyclones

For such a curve, the particle size for which the grade efficiency is 50%, X50, is often used as a single number measurement of the efficiency of the cyclone. X50 is also know as the equiprobable size since it is that size of particle which has a 50% probability of appearing in the coarse product. This also means that, in a large population of particles, 50% of the particles of this size will appear in the coarse product. X50 is sometimes simply referred to as the cut size of the cyclone (or other separation device). 

The concept of X50 cut size is useful where the efficiency of a cyclone is to be expressed as a single number independent of the feed solid size distribution, such as in scale-up calculation. 

The scale-up of cyclones is based on a dimensionless group, the Stokes number, which characterizes the separation performance of a family of geometrically similar cyclones. The Stokes number Stk o is defined as  

The use of the two dimensionless groups Eu and Sffcso in cyclone scale-up and design is demonstrated in the worked examples at the end of this chapter. 

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Define the two dimensionless numbers which are used in the scale up of cyclone separators. 

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