Algal cells are cultivated for bio$-$oil production. The broth contains algae of a wide range of diameters: $1-50$ mu m$.$ What range of cells can you trap if you centrifuge it in a tubular bowl centrifuge, which is $1\mathrm{.}2$ m high, with an outer radius of $15$ cm and has a distance to the liquid interface of $11$ cm$?$ The feed stream has a density of $1\mathrm{.}01$ g$/$cm$3$ and a viscosity of $1\mathrm{.}02$ cP$.$ The density of the cells is $1\mathrm{.}03$ g$/$cm$3.$The rotation speed is $6000$ r$/$min and productivity is $330$ liters$/$minute$.$

b$)$ If $100\%$ recovery is expected, determine the productivity of the centrifuge, if it is operated at the same speed?