Filtration of $300ml$ of fermentation broth was carried out in a laboratory$-$sized filter a $($area $10c{m}^2)$ with a pressure drop of $10$ psi. The filtration took $20$min. Based on previous studies, the filter cake obtained from Penicillium chrysogenum was compressible with the exponent $\text{'}s\text{'}$ in the equation for calculation of filter area equal to $0\mathrm{.}5.$

What size of filter is required to carry out filtration of $1m3$ broth from a pilot plant in $2$ hours and at a pressure drop of $20$ psi?

What is the percentage increase in filter area if the pressure drop is reduced to $10$ psi?