How 0.3 is defined . Why is this the limit? Is there a mathematical justification for this?
Becoz density variations up-to 10 % is thought to be constant.
As according to a relation d'density'/density ~Mach^2
So if mach is 0.3 density variation will b within 10% so that's why it's assumed.
Usually from speeds of Mach 0.4 upwards, we consider air to be compressible. The reason for this is, at speeds above this point, the air molecules ahead of the moving object will not "feel" or "sense" the oncoming object since its moving too fast. Thus the air particles ahead will crash with the moving object upon contact, being compressed and crushed against other molecules ahead.
At lower mach numbers, the air molecules will "sense" and "feel" the moving object before it reaches them and will move out of the way, thus acting as a incompressible fluid.
The mach 0.3 or mach 0.4 margin is for air, and generally this effect depends on the molecule's reaction time in the medium. Maybe lighter molecules like helium or hydrogen could withstand higher mach numbers before acting as a compressible fluid, as they have a lower inertia and can move faster.
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