The performance of a centrifugal pump or compressor system has often been investigated on an overall basis for a wide range of operations and these investigations have, in the past, resulted in some remarkable technical advances. Detailed and penetrating studies of both the rotor and the components up and downstream are essential to obtain a knowledge of the critical areas and to increase further the efficiency of the system. In this study one problem area, the flow in radial diffusers in the absence of unsteady flow, is isolated and an extensive analytical and experimental study concerning this has been undertaken. In the absence of wakes from the impeller or other unsteady flow phenomena, the formation of a boundary layer on the side walls of the diffuser is the main cause of a loss in diffuser efficiency. The boundary layers which are three dimensional in character are investigated for several inlet conditions, and the theoretical results are compared with those of the experiments; the agreement is good. The analysis is extended for a three-dimensional compressible boundary layer.