sub: chemical engineering $($filtration$)$

caption: please answer both subquestions, will upvote

A slurry containing $0\mathrm{.}2kg$ solids $\frac{?}{kg}$ water is filtered through a rotary drum filter

operating at a pressure difference of $65k\frac{N}{m^2}.$ The drum is $0\mathrm{.}6m$ in diameter

and $0\mathrm{.}6m$ long, rotates once every $350s,$ and has $20\%$ of its surface submerged

in the slurry.

$($a$)$ If the overall average filtrate flow rate is $0\mathrm{.}125k\frac{g}{s},$ the cake is incompres$-$

sible with a porosity of $50\%,$ and the solids $SG=3\mathrm{.}0,$ determine the max$-$

imum thickness of the cake on the drum $($you may neglect the filter medium

resistance$).$

$($b$)$ The filter breaks down, and you want to replace it with a plate$-$and$-$frame

filter of the same overall capacity, which operates at a pressure difference of

$275k\frac{N}{m^2}.$ The frames are $10cm$ thick, and the maximum cake thickness at

which the filter will operate properly is $4cm.$ It will take $100s$ to disas$-$

semble the filter, $100s$ to clean it out, and $100s$ to reassemble it$.$ If the

frames are $0\mathrm{.}3m$ square, how many frames should the filter contain?