We want to filter $15,000li\frac{t}{h}r$ of feed containing solute using rotary drum vacuum filter. The filter has a cycle time of $50sec$ and an area of $37\mathrm{.}2m^2.$ It operates under a vacuum of $20$ inches Hg$.$ Assume that incompressible cake is formed on the filter medium with the resistance is $\frac{{}_0}{2P}=29\frac{sec}{c{m}^2}.$ We want to wash the cake until only $1\%$ of the retained soluble is left, and we expect that the washing efficiency will be $70\%$ and that $1\%$ of the filtrate is retained.$($a$)$ Calculate the filtration time $($b$)$ calculate the washing time. $($Answer: $t_f=9\mathrm{.}06($:$sec$;$t_t=0\mathrm{.}693sec\}$