Example Problem

A company is filtering a powder from a water$/$solvent mixture $cP,=1009k\frac{g}{m^3})$ containing $0\mathrm{.}1\%$ solid particles by volume that have an average diameter of $10m.$ The cake formed has a porosity of $=0\mathrm{.}2.$ A plate and frame filter is used that is $1\mathrm{.}5m$ by $2m$ and a pump that delivers a constant pressure of $30$kPa. The frame used is only $1\mathrm{.}5cm$ wide, so that it can only be operated until the cake is $0\mathrm{.}5cm$ thick. What would be the volume filtered then, and the time $($in min $)$ it takes to filter it$?$