Numerical computation of the flowfield inside a pump is herein used as a numerical laboratory, subject to the limitations of modeling assumptions and to experimental verification. A numerical computation of the flow inside a real industrial centrifugal pump is performed that includes a very sophisticated geometry. Conversely to other computations, in this test case no simplification of the geometry was introduced. Numerical computations are obtained using Spalart-Allmaras turbulence model. A detailed analysis of the turbulent flowstructure is performed for the design point and two off design conditions. Additional computations were performed in order to compare the numerical and experimental pump characteristics; these were obtained under normalized testing conditions. Further computations are presented for the pump working in reverse turbine mode (PAT). Detailed analyses of the flow allow a comparison of the internal flow losses when the pump is operating in direct and reverse mode. This is also useful to help in the selection of an adequate pump geometry that can work in both modes with best efficiency.