Across a centrifugal pump, the increase in energy per unit mass of liquid is gde

Question

Across a centrifugal pump, the increase in energy per unit mass of liquid is gdeltah, where g is the gravitational acceleration and deltah is the increase in head. This quantity gdeltah may be a function of the impeller diameter D, the rotational speed N, liquid density rho, and the flow rate Q. A centrifugal pump operating at 2,000 rpm is to be designed to handle a liquid hydrocarbon of specific gravity 0.95. To predict its performance, a half-scale model is to be tested, operating at 750 rpm, pumping a light oil of specific gravity 0.80. The scale model is found to deliver 400 gpm with a head increase of 20 ft. Assuming dynamical similarity, for the full-size pump Q = 8,533 gpm deltah = 569 ft

Explanation / Answer

use pump affinity laws. sorry cant do this my head only works in si units, no need to award karma you probably know this already q1 / q2 = (n1 / n2)(d1 / d2)^3 (1) where q = volume flow capacity (m3/s, gpm, cfm, ..) n = wheel velocity - revolution per minute - (rpm) d = wheel diameter dp1 / dp2 = (n1 / n2)^2 (d1 / d2)^2 (2) where dp = head or pressure (m, ft, Pa, psi, ..) P1 / P2 = (n1 / n2)^3 (d1 / d2)^3 (3) where P = power (W, bhp, ..)

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