Refer to figure.
The local Mach numbers determine the subdivision of flow regimes into:

• Subsonic: All local Mach numbers are less than M 1.0. The subsonic regime is further subdivided, at M_FS 0.4, into low and high subsonic (compressible and incompressible flow). Compressibility effects are negligible below M_FS 0.4, but become significant above this.
• Transonic: Some local Mach numbers are greater than M 1.0 and some are less.
• Supersonic: All local Mach numbers are greater than M 1.0.

The terms compressibility and incompressibility describe the ability of molecules in a fluid to be compacted or compressed (made more dense) and their ability to bounce back to their original density, in other words, their "springiness."

An incompressible fluid cannot be compressed and has relatively constant density throughout. Liquid is an incompressible fluid. A gaseous fluid such as air, on the other hand, can be either compressible or incompressible.

Generally, for theoretical and experimental purposes, gases are assumed to be incompressible when they are moving at low speeds (under approximately M 0.4). The motion of the object traveling through the air at such speed does not affect the density of the air. This assumption has been useful in aerodynamics when studying the behavior of air in relation to airfoils and other objects moving through the air at slower speeds.