Pb$4$: The following filtration data where obtained on a $5\%$ by weight calcium carbonate slurry using $4\mathrm{.}14{10}^4\frac{N}{m^2}$ gauge pressure differential. Filtrate collected $kg$ and time is given

$\backslash$table$[[$Weight in kg$,$Time min$],[0,0],[2\mathrm{.}275,0\mathrm{.}7],[4\mathrm{.}55,1\mathrm{.}22],[6\mathrm{.}825,1\mathrm{.}87],[9\mathrm{.}08,2\mathrm{.}62],[11\mathrm{.}37,3\mathrm{.}62],[13\mathrm{.}65,4\mathrm{.}7]]$

A plate and frame filter press was used with area $0\mathrm{.}816m^2.$ Obtain the specific cake resistance $$

Assume density of filtrate $=$ density of water. The ratio of weight of wet cake to dry cake is $1\mathrm{.}5.$