H$4.$ Scale up of a Disk Centrifuge based on Laboratory Data: In a laboratory centrifuge, a cell suspension with density $1\frac{g}{c}{m}^3$ and viscosity $8\mathrm{.}8cP$ containing E$.$ coli cells of diameter $0\mathrm{.}95m($density $1\mathrm{.}150\frac{g}{c}{m}^3)$ was centrifuged. Determine the maximum flow rate for the clarification of a suspension of E$.$ coli cells by a plant scale disk centrifuge based on the laboratory data if you want to keep the $vg$ same as from the laboratory experiment. The plant centrifuge has a bowl diameter of $25\mathrm{.}4cm$ and maximum dimensionless acceleration $({}^2\frac{R}{g})14200.$ You also know that $=45,R_1=8cm$ and number of disks $=120.$