You have to use a disk$-$stack centrifuge for the clarification of your $50$ g L$-1$ wet mass yeast culture broth $($dynamic viscosity$=2\mathrm{.}0$ mPa s$).$ However, the process development has to be carried out in a fixed$-$angle centrifuge with b$=45\backslash$deg $,$ r$1=0\mathrm{.}030$ m and r$2=0\mathrm{.}135$ m$.$ Given that delta p is $0\mathrm{.}1$ kg m$-3$ for the ~$5$m$-$sized cells and z $($zeta$,$ relative g number$)$ is $5,000,$ what is the maximum sedimentation time t assuming free sedimentation? How fair is it to assume free sedimentation given the feed properties? Assuming that you need to process about $12$ m$3$ broth in $3$ hours at large scale, what is the sigma factor of the large scale centrifuge you require? Which centrifuge type would you choose and why? Given that z remains the same at large scale and r$1$ and r$2$ double, which number of disks would a disk$-$stack centrifuge require to handle the separation task $($assume that the effective radius of the centrifuge is $($r$2-$ r$1)/2+$ r$1)?$ How could you improve the settling velocity assuming that z is fixed?