In examining the right side of this expression, we note that the quotient is equal to the inverse value of the rate at the moment of obtaining the filtrate volume, which is equal to the mean arithmetic value of volumes V, and V2:

Filtration constants C and K can be determined on the basis of several measurements of filtrate volumes for different time intervals.

dr dv

Figure 6. Plot of Equation 20.

Figure 6. Plot of Equation 20.

As follows from Equations 14 and 15, values of C and K depend on r0 (specific volumetric cake resistance), which in turn depends on the pressure drop across the cake. This Ap, especially during the initial stages of filtration, undergoes changes in the cake. When the cake is very thin, the main portion of the total pressure drop is exerted on the filter medium. As the cake becomes thicker, the pressure drop through the cake increases rapidly but then levels off to a constant value. Isobaric filtration shows insignificant deviation from Equation 16. For approximate calculations, it is possible to neglect the resistance of the filter plate, provided the cake is not too thin. Then the filter plate resistance Rf = 0 in Equation 15, C= 0 (Equation 15) and t0 = 0 (Equation 17). Therefore, the simplified equation of filtration takes the following form:

For thick cakes, Equation 23 gives results close to that of Equation 16.

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