Consider the following pipe network:

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Consider the simple pipe network shown above. The head $H_5$ at the reservoir is $100\mathrm{.}0[$m$].$ The demand at junction $4$ is $0\mathrm{.}280[$cms$].$ The lengths of the pipes are $x_1=223\mathrm{.}0[m],x_2=324\mathrm{.}0[m],x_3=269\mathrm{.}0[m],x_4=486\mathrm{.}0[m],x_5=318\mathrm{.}0[m],x_6=431\mathrm{.}0[m].$ The diameters of the pipes are $D_1=0\mathrm{.}235[m],D_2=0\mathrm{.}219[m],D_3=0\mathrm{.}31[m],D_4=0\mathrm{.}132[m],D_5=0\mathrm{.}303[m],D_6=0\mathrm{.}159[m].$ Assume that the Hazen$-$Williams coefficient for all pipes is $C_{HW}=100$ and neglect minor losses. The bottom elevations of all junctions are $0[$m$].$ What is the magnitude of the flow rate in pipe $4$ in $[$cms$]?$

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