Problem $06\mathrm{.}105-$ Water flows through a piping system to a reservoir

The system shown in the figure below consists of $1200$ m of $5$ cm cast$-$iron pipe, two $45\backslash$deg and four $90\backslash$deg flanged long$-$radius elbows, a

fully open flanged globe valve, and a sharp exit into a reservoir. If the elevation at point $1$ is $440$ m $,$ what gage pressure is required at

point $1$ to deliver $0\mathrm{.}005($m$^(3))/($s$)$ of water at $20\backslash$deg C into the reservoir? For water at $20\backslash$deg C$,$ take $\backslash$rho $=998$k$($g$)/($m$^(3))$and$\backslash$mu $=0\mathrm{.}001$k$($g$)/($m$)*$s$.$ For cast

iron, take $\backslash$epsi ~~$0\mathrm{.}26$mm$.$ Take $\backslash$pi $=(22)/(7).$ For the given flow, take f~~$0\mathrm{.}0315.$