Integration of this equation over the limits from 0 to t for 0 to q we obtain:


and on simplification:

Equation 67 may be used to evaluate constants K (mi1) and Win.

Finally, for the case of intermediate filtration, the intensity of increase in total resistance with increasing filtrate volume is less than that occurring in the case of gradual pore blocking, but greater than that occurring with cake filtration. It may be assumed that the intensity of increase in total resistance is directly proportional to this resistance:

Integration of this expression between the limits of 0 to q, from Rf to R gives:

Replacing V by q, and denoting the actual filtration rate (dq/dx) as W, the governing filtration equation may be rewritten for a unit area of filtration as follows:

At the initial moment when q = 0, the filtration rate is

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