Problem $1(50$ points$).$ In a filtration of suspended cells under full vacuum using a $20cm$ in diameter Buchner funnel. You collected data for the volume of filtrate as a function of time $($see table below$).$ The concentration of cells was $100\frac{g}{?}$ liter $($mass of dry cake solids per volume of filtrate$),$ and the viscosity of the filtrate was $1\mathrm{.}0cp.$

a$)$ What is the resistance of the filter medium?

b$)$ What is the specific resistance of the cake layer?

c$)$ Being disappointed in the amount of time required, you decide to give the vacuum filter a boost by pressurizing the funnel to $1$atm gage pressure. The result is the same. Concerned that you may have done the wrong thing, you then remove the funnel pressure and reduce the vacuum in the flask to $0\mathrm{.}5$atm. The result is the same. Comment and quantify what is happening in the experiment.

$\backslash$table$[[$Time $(min),$Volume filtered $($liters$)],[0,0],[20,4],[30,5],[40,6\mathrm{.}5],[50,7],[60,7\mathrm{.}5],[70,7\mathrm{.}8]]$