##### From Chemical Engineering License Review, Second Edition

Given the filtration conditions and the specifications of a filter, the common problems to be solved are (1) the amount of the filtrate obtainable in a given time, (2) the amount of the solvent that can be passed through the cake in a given time, and (3) concentration of the recovered material in the wash solvent.

Filtration can be carried out in two ways: (1) constant-pressure filtration, i.e., the filtration rate varies, and (2) constant-rate filtration in which the ? P varies. Two methods are available to treat filtration problems. They are (1) Ruth's equation [1] and (2) the Kozeny-Carman [2] relation.

## Ruth's Equation

To establish Ruth's equation, the following variables are first defined:

• V = filtrate, ft 3

• ? = filtrate density, lb/ft 3

• W = filterable solids, lb

• x = mass fraction of the solids in a slurry

Using these definitions, the following relations are developed:

from which

The Hagen-Poiseuille equation for the laminar flow of fluids in tubes of circular cross section is given by

Assuming Eq. (11-2) applies to the filtrate flow, it can be shown that the rate of filtration is given by

 where A = total filtering area, ft 2 ? = time of filtration, h ? = viscosity of filtrate, lb/ft h L = thickness of cake, ft ? P C = pressure drop across cake, lbf/ft 2 R C = resistance of cake = 32 L/ g cD 2 e, h 2 lbf/ft

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Filtration Equipment
Filtration equipment is used to filter, thicken or clarify a mixture of different elements.
Dewatering Equipment
Dewatering equipment uses force, including vacuum and centrifugal motion, to separate water from solids.
Filter Cleaners and Cleaning Equipment
Filter cleaners and filter cleaning equipment is used to clean or deblind filtration media in air and fluid filter units.
Cyclone Separators
Cyclone separators and centrifugal separators utilize centrifugal, gravitational, and inertial forces to remove fine particles suspended in air or gas.
Filter Housings
Filter housings are vessels that hold replaceable cartridges, elements, bags or media. They hold one or many filters at varying pressures.

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