Derivation of the free-jet Mach-disk location using the entropy-balance principle

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Abstract
The molar‐entropy change of a gas expansion in a free jet is analyzed. Relating the entropy change along the expansion process to the entropy change evaluated using the thermodynamic properties of the initial and final states, one finds that the Mach‐disk location is proportional to the square root of the pressure ratio p0/p∞ in agreement with the empirical expression given by Ashkenas and Sherman. The analysis shows further that the Mach‐disk location is independent of the temperature ratio T0/T∞, and is only a weak function of the specific heat ratio γ.