Page:THEORY OF SHOCK WAVES AND INTRODUCTION TO GAS DYNAMICS.pdf/8

formula, to $\rho uc$, where $c$ is the speed of sound, $u$ to the speed of motion and p$\rho$ is gas density. Gas pressure is approximately equal to $\rho c^{2}$.

If we juxtapose the expressions, we see that at subsonic velocities the pressure differentials are small as compared with pressure proper and, consequently, we may therefore, as a rule, ignore the compressibility of the medium.

Following is a definition of the scope of gas dynamics. Gas dynamics is the science of motion at great pressure differentials and high velocities, velocity being measured in terms of the speed of sound.

In similarity theory we have the following ratio between motion and speed of sound:

$u/c=M$

where $M$ is known as the Mach number.

Gas dynamics studies motion and $M$ values close to unity. If $M$ is considerably smaller than 1, the general equation of gas dynamics becomes those of hydrodynamics of an incompressible liquid.

It will be assumed in the following that laws of hydrodynamics of an incompressible liquid are known, and we shall therefore not dwell on the derivation of the corresponding formulas.

To take account of compressibility means that one also has to take account of the change in the state of the medium. In hydrodynamics the action of dissipative forces (viscosity) leads to a release of heat In the liquid and to a change in its temperature, but it does not lead to a change in volume: the changes within the liquid have no inverse effect on the nature of the flow and have little importance for the phenomena investigated in hydrodynamics.

In gas dynamics, instead, we shall continuously deal with changes in the state of medium in the flow proper. This aspect of gas dynamics requires that any and all phenomena be also investigated from a thermal dynamics point of view; thus, thermodynamics is totally indispensable for the study of gas dynamics.