Design a flotation system whose influent flow is $30$ m$3/$h$,$ containing suspended solids at a concentration equal to $300$ mg$/$L$.$ The optimal A$/$S ratio found on a pilot scale is $0\mathrm{.}02$ kg of air$/$kg of solids and the operating temperature is $30$C$.$ Adopt f $=0\mathrm{.}5($more conservative$).$ Calculate: $($a$)$ for a system without recirculation, $($b$)$ for better quality effluent, with recirculation.