Traditional formulas used for design of filters and interpretation of experimental data depend upon a number of simplifications including negligible solid velocity u s and a superficial liquid flow rate q L which is assumed to be a function of time and independent of distance x through a filter cake. The extent of variation of u s and q L for highly compactible biosolids is discussed in this article. An approximate method based on well-known equations which rest on the assumption the q L is constant throughout a compressible cake at a given time is presented. Using previously available formulas, the assumption of constancy of q L is abandoned; and approximate equations yielding q L as a function of x are developed. Comparisons are made of the variation with distance of q L , u s , and relative velocities for cakes of different degrees of compactibility and slurries of varying concentrations. Problems related to verification of a given model are discussed.