Density Changes

We have calculated the density changes in air with altitude (standard atmosphere)

In compressible flow we are talking about changes of density of air with airspeed (at a given altitude). If we invoke the description of air as an ideal gas

Therefore from elementary calculus, the changes in density can be related to the changes in pressure and temperature as

Therefore, to solve problems in compressible flow, not only the momentum equation (for pressure) be included, but also the energy equation (for temperature).

The following relations om Thermodynamics will be useful

Additional Thermodynamics Information