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The equations for sizing rotary-drum filters are summarized in Table 6.18.
Equation 6.18.1 is the liquid mass balance. In this procedure, y is a mass fraction.
Because the cake is wet, the liquid entering the filter will be less then the liquid
leaving. Equation 6.18.2 is the solids mass balance, assuming that all the solids in
the slurry are removed. Solve Equation 6.18.2 for the cake formation rate, me.
Then, solve Equation 6.18.1 for the filtrate volumetric flow rate, V 2. Next, calcu-
late the filtration area from Equation 6.18.5 and the drum area from Equation
7.18.6. Finally, select a standard rotary filter from Table 6.20. The calculation
procedure for sizing a rotary filter is outlined in Table 6.19. Example 6.5 illus-
trates the sizing procedure.
Operating data for filtering slurries could also be used to estimate rotary-
filter areas. Some filtration rates are given by Walas [6]. Thus, by dividing the
feed rate of solids onto the filter by the filtration rate, expressed as kg of solids/h
2
m , the filter area can be estimated.
Table 6.18 Summary of Equations for Sizing Rotary-Drum Filters____

First Subscript: Entering Stream =1 — Leaving Stream = 2
Second Subscript: Liquid =1 — Solids = 2 — c = wet cake
Mass Balance
v
Yu Pi i'= Ye/me + p z 'V 2 (6.18.1)
Yi/Pi V^yc^mc (6.18.2)

yu+yi, 2 ' = l (6.18.3)
y c/ + yc,2=i (6.18.4)

Rate Equation
2
(l-n')an'c u V F
2 2
A F = ——————————— (6.18.5)
2 V ' - P v')
(P 0
f (6.18.6)
A F = 'A T
System Properties
Pi=yuPu' + yu'Pu' (6.18.7)

c 1 ,2=yi, 2 'pi (6.18.8)
a = ao'0V - Pv')° (6.18.9)
Variables
yi.i - yc,2 - m s - pi - V 2 - c,, 2 - a - A F - A T

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