It is desired to sift $200$ Ton$/$hr of a copper material, separating the material into different fractions. Using sieves whose openings are shown below, as well as the fraction that is retained in each drum. $($image$)$

Determine the length of the sieve, as well as its operating speed if the diameter must be $4$ ft and what slope it must have for the rejection residence time to be $3$ minutes. thank u :)