A viscous solution containing particles with a density of particle, $1461k\frac{g}{m^3}$ is to be clarified by centrifugation. The solution density is $801k\frac{g}{m^3}$ and its viscosity is $100$ centipoise. The tubular bowl centrifuge has a bowl with $r_2=0\mathrm{.}02225m,r_1=0\mathrm{.}00716m,$ and height $b=0\mathrm{.}1970m.$ Calculate the critical particle diameter, $D_{pc},$ of the largest particles in the exit stream if rotational speed, $N=23000RPM$ and flow rate $q=0\mathrm{.}002832\frac{m^3}{h}.$

$6$ Marks