Q$2)$ A pilot$-$scale filter with a cross$-$sectional area of $0\mathrm{.}25m^2,$ a depth of $1\mathrm{.}5$ m $,$ and a porosity of $0\mathrm{.}38$ is being operated at a flow rate of $60\frac{L}{m}in.$ The water temperature is $25C$ at which the viscosity is $0\mathrm{.}9{10}^{-2}\frac{g}{cm-s}$ and the density is $1\mathrm{.}00\frac{g}{c}{m}^3.$ Although the influent particle. distribution is heterodisperse, the filter was designed so that the single collector removal efficiencies according to the Yao model for $0\mathrm{.}1-m-$diameter particles by sedimentation and interception are ${}_g=1\mathrm{.}0{10}^{-6}$ and ${}_1=6\mathrm{.}0{10}^{-8}.$ There are no particles in the influent with $log{d}_p>2\mathrm{.}5$ or The particle diameter is in $m.$

A$)$ Compute the diameter of the collector grains and the density of the incoming particles.

B$)$ Plot $log{}_T$ versus $log{d}_p.$