With a tubular centrifuge we want to separate Adeno associated virus particles. It has been determined that the viruses are approximately spherical with a diameter of $0\mathrm{.}005m$ and have a density of $0\mathrm{.}5cm3.$ The speed of the centrifuge is $1000rpm,$ the bow diameter is $5cm,$ the bowlength is $50cm,$ and the outlet opening of the bow has a diameter of $2cm.$ Estimate the maximum flow rate of the fermentation broth that can be attained.