Based on the existing formulas and those proposed by the author for pump and pumping system performance (efficiency and NPSHc) conversion, a further mathematical derivation was introduced and a group of universal conversion formula was developed in the paper. The universal formulas were applicable for head, flow rate, efficiency and NPSHc. The head curves of both pump and pumping system were presented in a quadratic polynomial, and the head coefficients were calculated by using the least square method. The overall efficiency formula was detailed and the method for determining the constant involved the formula was introduced. Also, a universal NPSHc formula, which is applicable to any operating points, and where the shock loss effect is include, was provided in this paper. The approach for determining the coefficient in that formula was proposed as well. The universal formulas for head, flow rate, efficiency and NPSHc were derived according to flow similarity in pumps and by means of the affinity laws of pump, and presented with head coefficient, efficiency constant and NPSHc coefficient. All the formulas, their coefficients and constants were integrated into one formula, respectively; thus they were considered as universal ones, which are applicable to both model and prototype pumps. The universal formulas can be used to estimate pump and pumping system performance and carry out performance conversion from model to prototype.
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