The study reports on a generalization of Reichardt's hypothesis by Alexander, Baron and Comings to develop a unified treatment for the synthesis of diffusion patterns for mass, heat and momentum. The technique was applied for co-planar and co-axial flows, to a study of the effects of initial flux distribution and outlet shape on diffusion patterns; and to shallow submerged outlets. Four simple approximations to the P-function, involving only exponential and error functions, were found to represent flux distributions downstream from a circular jet of finite size at all points between the nozzle and infinity. The results may be applied in the study and design of discharge outlets, syphon spillways, hydraulic breakwaters and diffusion of tracers in streams and penstocks.