For the application at hand, the flow rate of Prob. 14–36 is not adequate. At least 9 Lpm is required. Repeat Prob. 14–36 for a more powerful pump with H₀ = 8.13 m and a = 0.0297 m/(Lpm)². Calculate the percentage improvement in flow rate compared to the original pump. Is this pump able to deliver the required flow rate?

Data from Problem 14–36

The performance data of a water pump follow the curve fit H_available = H₀ – aV̇², where the pump’s shutoff head H₀ = 7.46 m, coefficient a = 0.0453 m/(Lpm)², the units of pump head H are meters, and the units of V̇ are liters per minute (Lpm). The pump is used to pump water from one large reservoir to another large reservoir at a higher elevation. The free surfaces of both reservoirs are exposed to atmospheric pressure. The system curve simplifies to H_required = (z₂ – z₁) + bV̇², where elevation difference z₂ – z₁ = 3.52 m, and coefficient b = 0.0261 m/(Lpm)². Calculate the operating point of the pump (V̇_operating and H_operating) in appropriate units (Lpm and meters, respectively).