$[50$ points$]$ The figure below shows a branched pipe network with a water supply from a reservoir that must deliver $10cfs$ f water to node $C$ and $5cfs$ to node $D.$ The network consists of three $(3)$ pipes and one pump. The elevation of each node is shown below in the figure. Links AB$,$ BC$,$ and BD are $2000$ feet, $1250$ feet, and $475$ feet in length respectively. The diameters of pipes $AB,BC,$ and $BD$ are $24$ inches, $20$ inches, and $8$ inches, respectively. Based on the Darcy Weisbach equation, the expression for head loss $($in feet when $Q$ is in cfs$)$ in each pipe is given by $h_L=K{Q}^2$ where $K$ for each pipe is given as $K_{AB}=0\mathrm{.}0315,K_{BC}=0\mathrm{.}0489,$ and $K_{BD}=1\mathrm{.}816.$ Assume that minor losses are negligible. The pump head produced by the pump in Pipe AB is given by the formula below:

$[$:${}_p=-0\mathrm{.}1Q^2+100\}$

The supply pressure head at each node must be at least $65$ feet above the elevation. Determine the minimum elevation of the reservoir for the system to work properly.

$Z_A$

$Q=15cts$