### Abstract

A mathematical model for computing the radial profiles of the axial and circumferential velocity components, respectively, of the swirling flow exiting the runner of hydraulic turbines is extended for the 2D case in the incompressible, inviscid, axisymmetrical, and steady swirling flow case. The resulting numerical algorithm provides numerical results in good agreement with available data for both axial and circumferential velocity profiles measured on a model Francis turbine at several operating regimes.