A slurry containing $1 \mathrm{lb}_{\mathrm{m}}$ of solids per gallon of water is to be filtered in a plate-and-frame filter having a total filtering area of $60 \mathrm{ft}^{2}$. The slurry is fed to the filter by a centrifugal pump, which develops a head of 20 psig. How long would it take to build up a layer of filter cake $4 \mathrm{in}$. thick on the filter medium? Laboratory data were taken on the slurry using a positive displacement pump operating at $5 \mathrm{gpm}$ and $1 \mathrm{ft}^{2}$ of the filter medium. It was found that the pressure drop increased linearly with time from an initial value of $0.2 \mathrm{psi}$, reaching a value of $50 \mathrm{psi}$ after $1 \mathrm{~min}$. The density of the dry filter cake was found to be $0.85 \mathrm{~g} / \mathrm{cm}^{3}$.