You must filter $1000 \mathrm{lb}_{\mathrm{m}} / \mathrm{min}$ of an aqueous slurry containing $40 %$ solids by weight using a rotary drum filter with a diameter of $4 \mathrm{~m}$ and a length of $4 \mathrm{~m}$, which operates at a vacuum of $25 \mathrm{in}$. Hg with $30 %$ of its surface submerged beneath the slurry. A lab test is run on a sample of the slurry using $200 \mathrm{~cm}^{2}$ of the same filter medium, under a vacuum of $25 \mathrm{in} . \mathrm{Hg}$. During the first minute of operation, $300 \mathrm{~cm}^{3}$ of the filtrate is collected, and during the second minute, an additional $140 \mathrm{~cm}^{3}$ is collected.

(a) How fast should the drum be rotated?

(b) If the drum is rotated at $2 \mathrm{rpm}$, what would the filter capacity be in $\mathrm{lb}_{\mathrm{m}}$ of the slurry filtered per minute?