Yeast cells are to be collected by a centrifuge consisting of a number of cylinders rotated perpendiculars to the axis of rotation. During the course of centrifugation, the distance between the surface of liquid and the axis of rotation is $2\mathrm{.}5cm.$ The yeasts cells are assumed to be spherical with diameter of $9m$ and a density of $1000k\frac{g}{m^3}.$ The fluid has physical properties close to that of pure water. The centrifuge is to be operated at $600rpm.$ How much time does it take to have complete separation? Viscosity of the suspension is $1cp.$

Scale up of penicillin production is carried out from $5$ lit to $50,000$ lit keeping the volumetric mass transfer coefficient of oxygen constant. Properties of the fermentation medium and bubbles formed in small as well as in the large fermentor are assumed to be the same. The height of the lab scale fermentor is four times its diameter. The impeller diameter is $40\%$ of the tank diameter. The speed of agitator is $300rpm.$ If the power consumption per unit volume of both the fermentor is same, determine the size of large fermentor as well as the rotation speed of the agitator.

In a bioseparation process, auromycin crystals are to be separated from an acetone $($solvent$)$ solution. A small test filtration unit, which has a filtration area of $89c{m}^2,$ is used for the purpose. A pressure drop of $90\mathrm{.}32$ in$.Hg$ applied across the filter medium results the following data:

$\backslash$table$[[t($sec$),V($liters$)],[10,0\mathrm{.}500],[20,0\mathrm{.}707],[30,0\mathrm{.}866]]$

It is now planned to filter a much larger crop of auromycin crystals containing $8000$ liters of solvent by using a filter of $1\mathrm{.}5m^2$ area. If the properties of the test crop and the large crop are same and the cake of auromycin crystals formed over the filter is incompressible, determine the resistance of filter medium and the time required to filter the new crop at the same pressure drop?