A pumped water system is equipped with a pump, a valve and a long pipe to carry water from a lower tank to a higher tank. The pump characteristic is given by:Hp $=1200-8$ x $10^4$V$2$ The length and diameter of the pipe are $147$ m and $0\mathrm{.}18$ m$,$ respectively. The static head between the two tanks is $28$ m$.$ The friction factor for the turbulent flow in the pipe is $0\mathrm{.}02.$ The valve loss coefficient is $9.$ Ignoring all other minor losses, calculate the volume flow rate when the valve is wide open.Write your answer to three decimal places.