Scale$-$up of Batch Filtration of Protein Precipitate A small test filtration of a protein precipitate in an aqueous suspension uses a conventional filter with an area of $89c{m}^2$ at a pressure drop of $0\mathrm{.}4$atm to give data for the filtrate volume as a function of time $($see Table P$4\mathrm{.}12).$ We would like to filter a much larger batch of the precipitate at the same temperature containing $1000$ liters of solvent by using a filter of $1\mathrm{.}3m^2$ area having the same filter medium as for the small$-$scale filtration. However, this larger batch has a concentration of $0\mathrm{.}28\frac{g}{100}c{m}^3$ of solvent, less than in our test filtration, which is $0\mathrm{.}34\frac{g}{100}c{m}^3$ of solvent. How long will it take to filter this new batch at the same pressure drop? What is the error in the calculated time if the resistance of the filter medium is neglected?

TABLE P$4.12$

$\backslash$table$[[$Time $($s$),$Filtrate volume $($liters$)],[10,0\mathrm{.}489],[20,0\mathrm{.}703],[30,0\mathrm{.}864],[40,0\mathrm{.}995],[50,1\mathrm{.}120]]$