Leutolin is produced in a cylindrical stirred tank bioreactor. Lab scale tank diameter $=12$ cm$,$ lab scale impeller speed $=600$ rpm$,$ Htank$/$Dtank $=1\mathrm{.}0,$ Dimpeller$/$Dtank $=0\mathrm{.}33,$ liquid density $=1000$ kg$/$m$3,$ viscosity $=1\mathrm{.}0$ cP$.$ The tank is scaled to $10,000$ L$.$ a$.$ Estimate the impeller and tank diameters $($in m$)$ for the $10,000$ L tank$.$ b$.$ Estimate the rotational speed $($in rps$)$ for the $10,000$ L tank when scale$-$up is done using the constant power per unit volume approach. c$.$ Estimate the power required $($in Watts$)$ to operate the $10,000$ L tank$.$ Disk turbine impeller is used in both scales.

Show all the steps and calculations, the answers should match these:Start by estimating scale factor and then dimensions and rotational speed in the large tank. $$ Estimate Re$,$ then P$.$ Answers: $($a$)$ Dtank $=2\mathrm{.}31$ m$,$ Dimpeller $=0\mathrm{.}76$ m$,($b$)$ n $=1\mathrm{.}39$ rps$,($c$)$ P $=4086$ W$.$