Mach Number

# It is defined as the ratio of local velocity of fluid to the acoustic or sound velocity.

It is a dimensionless number designated by M.

It is expressed as, M = C/a Where, C = Velocity of fluid (air),
   a = Velocity of sound.

# Mach number can also be expressed as the square root of the ratio of inertia force
of flow to the elastic force.

M² = (Inertia force of flow)/(Elastic force of fluid)

Different Regimes of Compressible flow

Subsonic Flow:
If the flow of fluid with a mach number less than 1, (i.e., C<a) then the flow is called
a subsonic flow. It is characterized by smooth streamlines.

Sonic Flow:

It the fluid flows with Mach number is equal to unity, (i.e., C=a) then the flow is
considered as sonic flow.

Supersonic flow:

If the Mach number is greater than 1 (i.e., C>a) then the flow is called
supersonic flow. It is observed with an oblique shock.

Hypersonic flow:

It the mach number of the flowing fluid is very high, (i.e., M>5) then the flow
is a hypersonic flow. This flow is observed with severe shock in the flow field. 

Note :
M > 5 --> Hypersonic flow

M > 1 --> Supersonic flow

M = 1 --> Sonic flow

M < 1  --> Subsonic flow