Non-dissipative, inviscid, compressible flow
We consider a simple fluid such as air or water. This fluid is described by a number of thermodynamical fields, such as pressure, density, etc., as well as a velocity field u. A variable is called specific when it gives a quantity per unit mass. For instance, let E be the internal energy of a finite volume V of fluid. Let M = ρV be the mass of this volume of fluid. Then e = E/M is the specific internal energy. Table C.1 lists all the thermodynamic variables used in this appendix.
In addition to thermodynamic variables there are variables describing the external actions on the fluid. The effect of gravity, for instance may be represented by the acceleration f = g. The heating rate per unit mass q represents sources of heat, for instance from radiation. There may be heat and momentum exchanges inside the fluid, by heat conduction or viscous forces. These are not taken into account in the non-dissipative description.
For a one-component gas, there are only two independent thermodynamic variables. As a special choice, one may choose ρ, T as independent variables and express all quantities such as p, e, h, etc., in terms of ρ and T, but other choices are possible as well. These relations are linked through equations of state. For instance p = p(ρ, T) is the standard form for an equation of state.