A computational study has been performed to investigate the effects of blade row interaction on the performance of radial turbomachines, which was motivated by the need to improve our understanding of the blade row interaction phenomena for further improvement in the performance. High-speed centrifugal compressor stages with three settings of radial gap are configured and simulated using a three-dimensional Navier-Stokes flow method in order to investigate the impact of blade row interaction on stage efficiency. The performance predictions show that the efficiency deteriorates if the gap between blade rows is reduced to intensify blade row interaction, which is in contradiction to the general trend for stage axial compressors, hi the compressors tested, the wake chopping by diffuser vanes, which usually benefits efficiency in axial compressor stages, causes unfavourable wake compression through the diffuser passages to deteriorate the efficiency. Similarly, hydraulic turbine stages with three settings of radial gap are simulated numerically. A new three-dimensional Navier-Stokes flow method based upon the dual-time stepping technique combined with the pseudo-compressibility method has been developed for hydraulic flow simulations. This method is validated extensively with several test cases where analytical and experimental data are available, including a centrifugal pump case with blade row interaction. Some numerical tests are conducted to examine the dependency of the flow solutions on several numerical parameters, which serve to justify the sensitivity of the solutions. Then, the method is applied to performance predictions of the hydraulic turbine stages. The numerical performance predictions for the turbines show that, by reducing the radial gap, the loss generation in the nozzle increases, which has a decisive influence on stage efficiency. The blade surface boundary layer loss and wake flow mixing loss, enhanced with a higher level of flow velocity around blading and the potential flow disturbances, are responsible for the observed trend.