It is desired to achieve complete recovery of bacterial cells from a fermentation broth with a tubular centrifuge on a pilot plant scale. The cells have been determined to be approximately spherical with a radius of $0\mathrm{.}5$m$.$ The speed of the centrifuge is $5000$ rpm$,$ the radius of the container $($R$0)$ is $5$cm$,$ the length of the container is $100$ cm$,$ and the outlet opening of the container has a radius $($R$1)$ of $2$ cm$.$ Estimate the maximum flow of fermentation broth $($Q$).$ Consider $=0\mathrm{.}001$ kg$/$m s$,\backslash$rho $=22\mathrm{.}5$ kg$/$m$3$