The centrifugal separation of a biomass of $80m$ sized cells of density $1\mathrm{.}04k\frac{g}{m^3}$ was carried out in a tubular centrifuge having a diameter of $15cm$ and rotating at $1200rpm.$

$($a$)$ Calculate the residence time if the distance between the liquid surface and the axis of rotation was $0\mathrm{.}8cm,$ the liquid density and the liquid viscosity were $1\mathrm{.}0k\frac{g}{m^3}$ and $0\mathrm{.}013\frac{g}{c}m.sec$ respectively.

$($b$)$ What would be the volumetric capacity $(Q)$ of the centrifuge if its length was $40cm?$

$($c$)$ Calculate the $$ factor

$($d$)$ What will be the time required for centrifuging ${10}^{6}c{m}^3$ of broth?

$(6$ marks$)$

$t_r=\frac{18}{{}^2({}_s-)d^2}ln(\frac{R_0}{R_1}),Q=\frac{{}^2({}_s-)d^2}{18ln(\frac{R_0}{R_1})}[l(R_0^2-R_1^2)],=\frac{2l{r}^2{}^2}{g}$

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