Velocity of Sound

In the beginning of this section, it was stated that gas dynamics deals with flows in which both compress­ibility and temperature changes are important. The term compressibility implies variation in density. In many cases, the variation in density is mainly due to pressure change. The rate of change of density with respect to pressure is closely connected with the velocity of propagation of small pressure disturbances, that is, with the velocity of sound “a.”

The velocity of sound may be expressed as:

In Equation (2.80), the ratio dp/dp is written as partial derivative at constant entropy because the variations in pressure and temperature are negligibly small, and consequently, the process is nearly reversible. More­over, the rapidity with which the process takes place, together with the negligibly small magnitude of the total temperature variation, makes the process nearly adiabatic. In the limit, for waves with infinitesimally small thickness, the process may be considered both reversible and adiabatic, and thus, isentropic.

It can be shown that, for an isentropic process of a perfect gas, the velocity of sound can be expressed as:

where T is absolute static temperature.

2.13.1 Mach Number

Mach number M is a dimensionless parameter, expressed as the ratio between the magnitudes of local flow velocity and local velocity of sound, that is:

Mach number plays a dominant role in the field of gas dynamics.