Determine the curve-fit parameters of the pump performance curve based on the shutoff point and the best efficiency point.

At its best efficiency point ?= 0.87, a mixed-flow pump, with D = 16 in , delivers Q = 2500 cfm of water at H = 140 ft when operating at N = 1350 rpm. Calculate the specific speed of this pump. Estimate the required power input. Determine the curve-fit parameters of the pump performance curve based on the shutoff point and the best efficiency point. Scale the performance curve to estimate the flow, head, efficiency, and power input required to run the same pump at 820 rpm.