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This study was completed by an extensive mathematical analysis. New equation to sludge filtration processes has been proposed for use in routine laboratory. The equation has been suggested to replace Ademiluyi’s cake filtration equation in view of the limitations of the latter. The new equation can be used for sludges whose compressibility factor is more than one but Ademiluyi’s cake filtration equation can only be used for sludges whose compressibility coefficient is less than one. The new sludge filtration equation was derived using tannθ reduction method. The generalized equation thus obtained resembles Ademiluyi’s equation in the mode of parameter combination except the presence of summation notation in the new equation.

Cake Filtration Equation Using tan&lt;sup&gt;n&lt;/sup&gt;&lt;i&gt;θ&lt;/i&gt; Reduction Method

Cake Filtration Equation Using tan<sup>n</sup><i>θ</i> Reduction Method