An Approximate Method of Determining the Slip Factor of the Radial Outward-Flow Impellers

Abstract

The flow through radial impellers is, in general, of such a complex nature that an exact solution is not obtainable, even if it is assumed that the flow to be inviscid, incompressible and irrotational so that the methods of potential theory may be employed. For a particular outward-flow impeller whose blades are of logarithmic spiral shape and of constant height, an accurate velocity distribution along the blades has been computed, under the assumption of the two-dimensional potential flow, by making use of the author's rigorous method (1)† of solving the problem. In the same case, an approximate velocity distribution is obtained following the procedures of a new method, described in detail in this paper, and it agrees fairly well with the aforementioned accurate one. Deducing out of this fact that the two results agree fairly well for the special case, it is assumed that the usefulness of the new approximate method of obtaining the velocity distribution may be extended to any radial outward-flow impeller in which the blades are of any shape and of varying heights. From thus determined approximate velocity distribution, the pressure distribution along the blades, then the torque exerted by the impeller on the fluid, and further the slip factor of the radial impeller, can be derived. The application of this approximate method for two centrifugal pump impellers and test data are presented, and the agreement of the results of the approximate method and the experiment is satisfactory.