This article presents the application of a RANS algorithm based on a pressure correction method for incompressible flow simulations of low-speed rotating machines. A numerical scheme is developed by extending a flow analysis in a stationary frame to a rotating frame for turbomachinery applications. The numerical scheme is explained with emphasis on the effect of rotation on the flow fields and turbulence modeling. The results of the numerical calculations for flow through an enclosed turbomachine and an extended turbomachine are compared with the experimental data to judge them on realistic flow patterns. The numerical solutions have shown reasonable agreement with the experimental data which demonstrates the merits and robustness of this numerical scheme.