$$ Spherical particles of density $2000$ kg$/$m$3$ and in the size range $20-100$ m are fed continuously into a stream of water $($density$,1000$ kg$/$m$3$ and viscosity, $0\mathrm{.}001$ Pa s$)$ flowing upwards in a vertical, large diameter pipe. What maximum water velocity is required to ensure that no particles of diameter greater than $50$ m are carried upwards with the water?