A Fundamental Derivative in Gasdynamics

The quantity which is here called the fundamental derivative has been defined as the nondimensional form $\mathrm{\Gamma \equiv }\frac{1}{2}{\rho }^3{c}^4{\mathrm{(\partial }}^2{\mathrm{{\rm Y}/\partial P}}^2{)}_s$ . The relation of $\Gamma$ to other thermodynamic variables is discussed. It is already known that the existence of conventional compression shocks requires $\text{Γ>0}$ . It is shown that other dynamic behavior of compressible fluids is fixed by the sign of $\Gamma$ . Particular emphasis is given to phenomena corresponding to negative $\Gamma$ . These phenomena include the area variation of a transonic passage, the form of a Prandtl‐Meyer wave, the behavior of adiabatic flow with friction, and nonlinear wave propagation. Formulas and numerical values are given for $\Gamma$ in various substances.