A slurry containing $40 %$ solids by volume is delivered to a rotary drum filter, which is $4 \mathrm{ft}$ in diameter and $6 \mathrm{ft}$ long and operates at a vacuum of $25 \mathrm{in}$. $\mathrm{Hg}$. A lab test is run with a $50 \mathrm{~cm}^{2}$ sample of the filter medium and the slurry, at a constant flow rate of $200 \mathrm{~cm}^{3} / \mathrm{min}$. After $1 \mathrm{~min}$, the pressure across the lab filter is $6 \mathrm{psi}$ and after $3 \mathrm{~min}$ it is $16 \mathrm{psi}$. If $40 %$ of the rotary drum is submerged under the slurry, how fast should it be rotated (rpm) in order to filter the slurry at an average rate of $250 \mathrm{gpm}$ ?