The equations of motion for a turbulent boundary layer are formulated in an inverse manner and solved to provide the geometrical configuration of optimal two-dimensional diffusers with a distinct inviscid core. For each Reynolds number/diffusion length, optimality is inferred when the lowest exit freestream velocity is computed from the members of an assumed one-parameter family of skin friction decay functions. In addition to the unique inverse formulation and establishment of the appropriate skin friction distribution, an integral part of the analysis is the development of an invertable adverse pressure gradient skin friction law, which is used to solve for the channel-averaged streamwise pressure (inviscid core velocity) distribution. The diffuser configurations are presented graphically for various Reynolds numbers/lengths/blockages and exhibit a distinctive concave shape. The results are compared to three sets of experimental data which support the validity of the viscous flow analysis, the formulation of the governing equations, and the skin friction law which is proposed.

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