A rotary drum filter is to be installed in your plant. You run a test in the lab on the slurry to be filtered using a $0.1 \mathrm{ft}^{2}$ sample of the filter medium at a constant pressure drop of $10 \mathrm{psi}$. After $1 \mathrm{~min}$, you find that $500 \mathrm{cc}$ of the filtrate has passed through the filter, and after $2 \mathrm{~min}$, the filtrate volume is $715 \mathrm{cc}$. If the rotary drum filter operates under a vacuum of $25 \mathrm{in}$. of $\mathrm{Hg}$ with $25 %$ of its surface submerged, determine the following:

(a) The capacity of the rotary drum filter, in gallons of filtrate per square foot of surface area, if it operates at (1) $2 \mathrm{rpm}$ and (2) $5 \mathrm{rpm}$.

(b) If the drum has a diameter of $4 \mathrm{ft}$ and a length of $6 \mathrm{ft}$, what is the total filter capacity in gallons/day for each of the operating speeds of 2 and $5 \mathrm{rpm}$ ?