A slurry is processed in a rotary drum filter that incorporates $8$ sectors$,$ each with an area of $0\mathrm{.}5$m$^(2)$ and a thickness of $30$mm $.$ In the initial $120$s $,$ the pressure difference for filtration is gradually increased to a stable value of $500$k$($N$)/($m$^(2)),$ during which the filtration rate is held constant. After this ramp$-$up phase, filtration proceeds under constant pressure, and the filter cakes are fully developed after another $800$s $.$ Determine the total volume of filtrate collected per cycle and the final rate of filtration. In a related test, a sample of this slurry was evaluated using a disk filter with a filtering surface of $0\mathrm{.}1$m$^(2)$ under a vacuum creating a pressure difference of $80$k$($N$)/($m$^(2)).$ The volume of filtrate gathered in the initial $400$s was $300$cm$^(3),$ and an additional $200$cm$^(3)$ was collected over the next $400$s $.$ It is presumed that the filter cake is non$-$compressible, and that the cloth resistance is equivalent in both the disk and the rotary drum filter.