In the multi$-$reservoir system shown in Figure $(1)$ below, $EA=110ft,EB=130ft,$ and $Ec=150ft.$ All pipes have a Darcy$-$Weisbach friction factor of $0\mathrm{.}02.$ Pipe $1$ is $11,000ft$ long and has a diameter of $2\mathrm{.}5$ ft $.$ Pipe $2$ is $16,000ft$ long and has a diameter of $2\mathrm{.}5$ ft $.$ Pipe $3$ is is $6,000ft$ long and has a diameter of $3ft.$ The pump characteristics are given in the following table and plotted in Figure $(2).$ Determine the discharge in each pipe.

$$iguie $(1)$

Table: Pump characteristic curve

$\backslash$table$[[$Q$,$ cfs$,0,10,20,30,40,50,60],[Hp,ft,80,78\mathrm{.}5,74,66\mathrm{.}5,56,42\mathrm{.}5,26]]$

Figure $(2)$