Filtration in Centrifugal Field

Using Darcy s law one can write an equation for pressure drop (AP ) across the filter cake of small thickness dl (please see Equations 12.1 and 12.4) as a function of velocity across the cake. 

In general the centrifngal force is large compared with the gravitational force, therefore, the filtrate will flow in an approximately radial direction, and will be evenly distributed over the axial length of the bowl. Therefore, Equation 13.18 can be written as 

If we want to include the resistance of the medium also in the equation, then the pressure drop across the medium can be written as 

If V is the bulk volume of incompressible cake deposited by the passage of unit volume of filtrate, then we can write the relation between P and V as follows. 

Substituting in Equation 13.24 and integrating from r = r to r = R as t goes from 0 to t results in 

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