Stewartson's compressibility correlation in three dimensions

Abstract

On the assumption of (a) zero heat transfer, (b) unit Prandtl number, (c) linear viscosity temperature relation, and (d) small cross-flow, a correlation between a compressible laminar boundary-layer flow and an incompressible flow with different external conditions is established.The correlation is applied to a known approximate method of solution for incompressible flow. For flow over a slender wing it is found that, so far as the effect on limiting streamlines—and hence on separation—is concerned, the fluid behaves as though it were incompressible but with pressure gradients multiplied by 1 + ½(γ − 1)M20 approximately, where M0 is the Mach number, supposed to be moderate in value. The effect on drag is also estimated.An attempt is made to assess the effect of variable Prandtl number Pr, and it is found that the above multiplying factor must be replaced by $1+\frac {1}{2}Pr^{\frac{1}{2}}(\gamma - 1)M^2_0$ but that variations in Prandtl number have little effect on the previous estimate of drag.