You want to use a plate-and-frame filter to filter an aqueous slurry at a rate of $1.8 \mathrm{~m}^{3} / 8 \mathrm{~h}$ day. The filter frames are square, with a length on each side of $0.45 \mathrm{~m}$. The "downtime" for the filter press is $300 \mathrm{~s}$ plus an additional $100 \mathrm{~s}$ per frame for cleaning. The filter operates with a positive displacement pump, and the maximum operation pressure differential for the filter is $45 \mathrm{psi}$, which is reached after $200 \mathrm{~s}$ of operation.

(a) How many frames must be used in this filter to achieve the required capacity?

(b) At what flow rate (in gpm) should the pump be operated?

The following lab data were taken with the slurry at a constant $\Delta P$ of 10 psi and a $0.05 \mathrm{~m}^{2}$ sample of the filter medium:

After $300 \mathrm{~s}$, the total volume of the filtrate was $400 \mathrm{cc}$.

After $900 \mathrm{~s}$, the total volume of the filtrate was $800 \mathrm{cc}$.