An orifice with a $4\mathrm{.}6-$cm$-$diameter opening is used to measure the mass flow rate of water at $25$C through a horizontal $10-$cm$-$diameter pipe. A mercury manometer is used to measure the pressure difference across the orifice. If the differential height of the manometer is $20$ cm$,$ determine the volume flow rate of water through the pipe, the average velocity, and the head loss caused by the orifice meter in m of H$2$O$.$