$5\mathrm{.}7\mathrm{.}2.$ In Figure P$5\mathrm{.}7\mathrm{.}2,$ each pipe has the following properties: $D=3ft,L=5,000ft,$ and $f=0\mathrm{.}02.$ The two pumps are identical; the pump characteristics are shown in the following table. The water surface elevations are $80\mathrm{.}0$ ft in reservoir A and $94\mathrm{.}0$ ft in reservoir D $.$ The discharge in pipe BC is $20$ cfs in the direction from B to C $.$ Determine $($a$)$ the discharge in AB and BD $,($b$)$ the water surface elevation in reservoir C $,$ and $($c$)$ the head added to the flow by each pump.

Figure P$5\mathrm{.}7\mathrm{.}2$