A slurry is being filtered at a net rate of $10,000 mathrm{gal} /$ day by a plate-and-frame


A slurry is being filtered at a net rate of $10,000 \mathrm{gal} /$ day by a plate-and-frame filter with 15 frames with an active filtering area of $1.5 \mathrm{ft}^{2}$ per frame, fed by a positive displacement pump. The pressure drop varies from 2 psi at start-up to 25 psi after $10 \mathrm{~min}$, at which time it is shut down for cleanup. It takes $10 \mathrm{~min}$ to disassemble, clean out, and reassemble the filter. Your boss decides that it would be more economical to replace this filter by a rotary drum filter, using the same filter medium. The rotary filter operates at a vacuum of $200 \mathrm{~mm} \mathrm{Hg}$ with $30 %$ of its surface submerged and rotates at a rate of $5 \mathrm{~min} / \mathrm{rev}$. If the drum length is equal to its diameter, how big should it be?

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