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Mach Number

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Quick
The Mach number is a dimensionless number abbreviated by Ma and sometimes by M. The Mach number is the ratio of the actual velocity of the fluid (or an object in still fluid) to the speed of sound in the same fluid at the same state.


Details

When analyzing rockets, spacecraft, and other systems that involve high-speed gas flows, the flow speed is often expressed in terms of the dimsionless Mach number defined as:

(Eq1)

Ma = V c

where c is the speed of sound whose value is 346 m/s in air at room temperature at sea level. A flow is called sonic when Ma = 1, subsonic when Ma < 1, supersonic when Ma > 1, and hypersonic when Ma >> 1.

The Mach number depends on the speed of sound, which depends on the state of the fluid. Therefore, the Mach number of an aircraft cruising at constant velocity in still air may be different at different locations.

Ma = 1	sonic
Ma < 1	subsonic
Ma > 1	supersonic
Ma >> 1	hypersonic
Ma ≅ 1	transonic

The Mach number is the dominant parameter in compressible flow analysis, with different effects depending on its magnitude. Aerodynamicists especially make a distinction between the various ranges of Mach number, and the following rough classifications are commonly used:

Ma < 0.3	Incompressible flow — density effects are negligible.
0.3 < Ma < 0.8	Subsonic flow — density effects are important but no shock waves appear.
0.8 < Ma < 1.2	Transonic flow — shock waves first appear, dividing subsonic and supersonic regions of the flow. Powered flight in the transonic region is difficult because of the mixed character of the flow field.
1.2 < Ma < 3.0	Supersonic flow — shock waves are present but there are no subsonic regions.
3.0 < Ma	Hypersonic flow — shock waves and other flow changes are especially strong.

The numerical values listed are only rough guides. These five categories of flow are appropriate to external high-speed aerodynamics. For internal (duct) flows, the most important question is simply whether the flow is subsonic (Ma < 1) or supersonic (Ma > 1), because the effect of area changes reverses. Supersonic flow effects may go against one's intuition.

Liquid flows are incompressible to a high level of accuracy, but the level of variation in density in gas flows and the consequent level of approximation made when modeling gas flows as incompressible depends on the Mach number. Gas flows can often be approximated as incompressible if the density changes are under about 5 percent, which is usually the case when Ma < 0.3. Therefore, the compressibility effects of air can be neglected at speeds under about 100 m/s. Note that the flow of a gas is not necessarily a compressible flow.

The speed of sound c is:

c = (kRT)^1/2

which is the local speed of sound for ideal gases.

A common rule of thumb is that for Mach numbers less than about 0.3, compressibility effects are practically negligible. Compressibility effects should be taken into consideration when the Mach number of the flow reaches about 0.3.

The reciprocal of the Mach number defines a shock wave.

The Mach number is important when considering compressible flow.

For air at standard conditions, a flow can thus be considred incompressible if the velocity is less than about 100 m/s (330 ft/s).