Recent experiments at the Jet Propulsion Laboratory have the effect of compressibility on local skin friction Mach numbers up to 4.5. Friction coefficients were obtained at three stations on a flat plate, for both laminar turbulent boundary-layer flow, for Reynolds numbers from 4 X 10^5 to 1 X 10^7. The floating element technique used is to that of Liepmann and Dhawan.
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Donald Coles (1952) studied this question.