A pump with the pump performance curve shown below is used for water distribution for firefighting efforts (on Earth). The water travels through a L = 1000 ft length of D = 2 in diameter pipe connected to the pump. Water enters the pipe at atmospheric pressure and must be delivered at greater than p = 10 psig to a destination Z = 15 ft above the inlet at a volume flow rate of Q = 1500 gal. The pipe can be assumed to have a friction factor of f = 0.01, and min the only relevant minor loss comes from a variable control valve. H (ft) 180 160 140 120 100 80 60 40 20 0 0 at Q Performance Curves for Pump at various Speeds X = 1500 500 1000 1500 min' X 2000 Q (gal/min) x 2500 X 3000 X X Fig. D.S Data -1000 rpm 1200 rpm -1400 rpm 1600 rpm a) Calculate the head loss due to major losses for this system b) Assuming the pump can only be operated at the speeds shown above, what is the minimum rpm which satisfies the above requirements? c) Operating at the speed found in part b, what is the actual pressure at the outlet of the 3500 4000 system? d) What must the loss coefficient of the control valve be set to, to ensure the pump operates when running at the speed found in part b? 4500