The same two water pumps of Prob. 14–71 are arranged in parallel. Calculate the shutoff head and free delivery of the two pumps working together in parallel. At what combined net head should pump 1 be shut off and bypassed? Explain.

Data from Problem 71

Two water pumps are arranged in series. The performance data for both pumps follow the parabolic curve fit H_available = H₀ – aV̇². For pump 1, H₀ = 6.33 m and coefficient a = 0.0633 m/Lpm²; for pump 2, H₀ = 9.25 m and coefficient a = 0.0472 m/Lpm². In either case, the units of net pump head H are m, and the units of capacity V̇ are Lpm. Calculate the combined shutoff head and free delivery of the two pumps working together in series. At what volume flow rate should pump 1 be shut off and bypassed?