An analysis of the incompressible turbulent boundary layer, developing under the combined effects of mass transfer and pressure gradient, is presented in this paper. A strip-integral method is employed whereby two of the three governing equations are obtained by integrating the combined momentum and continuity equation to 50 percent and 100 percent, respectively, of the boundary-layer height. The latter equation is the usual momentum-integral equation; the former equation requires specification of shear. Accordingly, Clauser's equilibrium eddy-viscosity law is assumed valid at this point. The third and final equation is obtained by specifying that Stevenson's velocity profiles apply throughout the domain of interest, from which a skin-friction law can be derived. Comparisons of the numerical results with the experiments of McQuaid, which include combined effects of variable pressure gradient and mass transfer, show good agreement.

A generalized form of the Coles compressibility transformation is utilized to analyze compressible turbulent boundary-layer flows. The generalization in the transformation is distinguished by specifying a stretching parameter that depends upon both space variables rather than on only the streamwise coordinate. This modification is shown to eliminate the distortion observed in the wake region of the transformed velocity profiles. For zero pressure gradient flows, predictions based upon the analysis are consistently superior with predictions due to Spalding-Chi and Baronti-Libby. A wide range of experimental data have been examined with Mach numbers ranging as high as 8, wall to free stream total temperature ratios as low as 0.25 and momentum thickness Reynolds numbers up to approximately one million.