Review of status of potential flow calculations in redially bladed pump impellers

The incompressible and inviscid flow in two-dimensional, radial-flow, pump impellers fitted with straight radial blades is reanalyzed analytically with the aid of the theory of functions of a complex variable, in particular by using the method of conformal mapping. The fluid velocity along the impeller blades is newly solved in closed-form by a Fourier series, with the Fourier coefficients being given by the hypergeometric function or (Gauss) series. Previously unpublished expressions in closed-form and illustrating graphs are presented for slip factors, the condition of shockless entry, and the volume flow rate minimally required for efficient operation. An (illustrative) extension of the classical, one-dimensional, Eulerian expression for developed head of radially bladed pump impellers is discussed, quantifying the effect of finite blade numbers.