Suppose you are looking into purchasing a water pump with the performance data shown in Table P14–35. Your supervisor asks for some more information about the pump. 

(a) Estimate the shutoff head H₀ and the free delivery V̇_max of the pump. [Perform a least-squares curve fit (regression analysis) of H_available versus V̇², and calculate the best-fit values of coefficients H₀ and a that translate the tabulated data of Table P14–35 into the parabolic expression, H_available = H₀ – aV̇². From these coefficients, estimate the free delivery of the pump.] 

(b) The application requires 57.0 Lpm of flow at a pressure rise across the pump of 5.8 psi. Is this pump capable of meeting the requirements? Explain. 

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TABLE P14-35 V, Lpm 20 30 40 50 H, m 21 18.4 14 7.6