A plate-and-frame filter press operating at a constant $\Delta P$ of $150 \mathrm{psi}$ is to be used to filter a sludge containing $2 \mathrm{lb}_{\mathrm{m}}$ of solids per $\mathrm{ft}^{3}$ of water. The filter must be disassembled and cleaned when the cake thickness builds up to $1 \mathrm{in}$. The frames have a projected area of $4 \mathrm{ft}^{2}$, and the downtime for cleaning is $10 \mathrm{~min} /$ frame. The properties of the sludge and cake were determined in a lab test operating at a constant flow rate of $0.2 \mathrm{gpm}$ of the filtrate and a filter area of $1 / 4 \mathrm{ft}^{2}$. The test results show that the pressure drop rises to 3 psi after $20 \mathrm{~s}$ and to 8 psi after $60 \mathrm{~s}$. Calculate the overall net filtration rate per frame in the filter in gpm of the filtrate, accounting for the downtime. The density of the cake was found to be $150 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}$.