The concentration of slurry to be filtered is $30k\frac{g}{m^3}.$ The liquid of the slurry has a viscosity of $8\mathrm{.}93{10}^{-4}$Pas. The bench top unit has a filter area of $0\mathrm{.}05m^2.$ The unit is operated at a constant flow rate of $500m\frac{l}{m}in.$ At the beginning of the filtration process $)=(0,$ the pressure drop was measured to be $5$kPa. After $5$ minutes of filtration, the pressure drop was measured to be $150$kPa.

Calculate the cake and filter resistivity for this filtration unit.

The unit is scaled up to a pilot plant unit. It will be operated as a constant pressure process of $150$kPa and filter area of $5m^2.$ Determine the time necessary to filter $1200$ liter of slurry.

If you cannot solve part $(1)$ use the following cake and filter resistivity data for a maximum of $80\%$ credit for part $(2)$: $=1\mathrm{.}0{10}^{11}\frac{m}{k}g,Rm=1\mathrm{.}0{10}^{11}\frac{1}{m}.$

$Pa=\frac{N}{m^2}$

$N=kg\frac{m}{s^2}$