Two water pumps are arranged in series. The performance data for both pumps follow the parabolic curve

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Two water pumps are arranged in series. The performance data for both pumps follow the parabolic curve fit Havailable = 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?

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