An orifice with a $1\mathrm{.}8-$in$-$diameter opening is used to measure the mass flow rate of water at and $=7\mathrm{.}536{10}^{-4}lb\frac{m}{f}t*s$ through a horizontal $4-$in$-$diameter pipe. A mercury manometer is used to measure the pressure difference across the orifice. If the differential height of the manometer is $5$ in$,$ determine the volume flow rate of water through the pipe, the average velocity, and the head loss caused by the orifice meter. Take the density of mercury to be $847lb\frac{m}{f}{t}^3.$

The volume flow rate of water through the pipe is $f\frac{t^3}{s}$

The average velocity is $q,f\frac{t}{s}.$

The head loss caused by the orifice meter is $$ ft $H_{2}O.$