Theory for elutriators

For streamline flow the velocity profile is parabolic, the velocity at a point at a distance r from the axis of the tube being given by Poisieulle s equation  

The volume flow rate through the tube is given by  

If it is assumed that there is no radial flow of particles, the possibility of a particle being elutriated depends on its position in the tube. 

Since is the velocity usually taken as the elutriation velocity, from equation (5.23)  

a particle of terminal velocity v can ascend if it is in a coaxial circle of radius r. Assuming a homogeneous distribution of particles, the fraction of this size contained in a cylinder of radius r is  

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