In a fire fighting system, a pipeline with a pump leads to a nozzle as shown in Fig. S$5\mathrm{.}11.$ Find the flow rate when the pump develops a head of $80ft,$ given that we may express the friction head loss in the $6-$indiameter pipe by $h_f=5\frac{V_6^2}{2}g,$ and the friction head loss in the $4-$in$-$diameter pipe by $h_f=12\frac{V_4^2}{2}g.($a$)$ Sketch the energy line and hydraulic grade line. $($b$)$ Find the pressure head at the suction side of the pump. Find $($c$)$ the power delivered to the water by the pump, and $(d)$ the power of the jet.