You want to select a rotary drum filter to filter a coal slurry at a rate of $100,000 \mathrm{gal}$ of the filtrate per day. The filter operates at a differential pressure of $12 \mathrm{psi}$, and $30 %$ of the surface is submerged in the slurry at all times. A sample of the slurry is filtered in the lab through a 6 in. diameter sample of the filter medium at a constant rate of $1 \mathrm{gpm}$. After $1 \mathrm{~min}$, the pressure drop across this filter is $3 \mathrm{psi}$, and after $5 \mathrm{~min}$ it is $10 \mathrm{psi}$. If the drum rotates at a rate of $3 \mathrm{rpm}$, what total filter area is required?