A theoretical method for calculating the radial pressure distribution for laminar viscous flow in a narrowly spaced radial diffuser having arbitrarily shaped walls deviating only moderately from a plane surface is developed. The analysis as it stands is also directly applicable to turbulent flow in the initial inlet region of a diffuser. Additional work is necessary to obtain a complete turbulent-flow analysis. Pressure distributions calculated by the laminar-flow theory show reasonably good agreement with the limited experimental pressure distributions available at the time of the analysis. Fairly good agreement also is obtained for the performance of a disk-valve element.