Need to find smallest diameter to be most efficient. Show all steps and how values are found

Two 32-inch pumps from the figure shown below are to be used in series at 1170 rpm to lift water through 500 ft of vertical cast-iron pipe. What should the pipe diameter be for most efficient operation? Neglect minor losses. For water at 20C, take p = 1.94 slug/ft and =2.09E-5 slug/ft.s. For cast iron, &0.00085 ft. Take = 22/7. Total head, ft n = 1170 r/min 800 NPSH 700 700 36-in dia. 1 600 32-in dia. 500 400 28-in dia. 300 1500 bhp 87% 88% 87% 3500 bhp 3000 bhp, 2500 bhp 2000 bhp 200 0 8 12 16 20 24 28 U.S. gallons per minute x 1000 50 30 20 NPSH, ft