Two reservoirs are connected through a $930$ m long, $0.3$ m diameter pipe, which has a gate valve. The pipe entrance is sharp (loss coefficient $=0.5$) and the valve is half-open (loss coefficient $=5.5$). The head difference between the two reservoirs is $20$ m. Assume the friction factor for the pipe as $0.03$ and $g=10\:m/s^2$. The discharge in the pipe accounting for all minor and major losses is ___________ $m^3/s$.