Integrating from 0 to Vf and from 0 to Tf gives the following equations:

ajW /Tf


vf _


A "

where Vf and Tf are the filtrate volume and time, respectively, for one batch of a batch filter.

For one cycle of a small area A on a continuous filter, if n = cycles per minute and Tc = minutes per cycle, then n = 1/Tc. Also, Tf = BTc when 0 < B < 1.00. B is the fraction of total area that is filtering at any given time. The cycles per hour = 60n.

On a continuously rotating drum, the following equation gives the continuous filtrate volume per unit area per hour:

7200(AP)Bn a/xW

The exponent As on this equation holds for many solids as shown in Figures 7.47.5 and 7.47.6. For activated sludge, the exponent on the group can be different than As; occasionally, the individual variables in the group have different exponents. Nevertheless, the equation is a valuable guide in data correlation.

In principle, a value of a from a leaf test allows the calculation of total full-scale filter area A required to achieve a total filtrate rate V' in gph, i.e., A = V'/Zc. In practice, leaf tests give only approximate values of a, and the accuracy is usually not enough for precise design. This inaccuracy is partially because the filter cake does not pack and compress the same way on a test leaf as on a continuous filter. The wall effects in the filter funnel are also important.

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