Mach number

Significance of the Mach number

It measures the relationship between the forces related to the movement and the compressibility of the fluid.

The propagation velocity or speed of sound, noted has , represents the propagation velocity of any shock produced in the medium. In the air at the usual temperatures, it is worth approximately 340 m.s^-1 or 1224 km.h^-1. This speed varies however according to altitude and from the temperature.

Generally, except obstacle, this shock is propagated in the same way in all the directions. Thus, it is found at the end of one second distributed on a sphere of 340 meters ray. The surface of a sphere being proportional to the square of its ray, the intensity of the disturbance decrease very quickly with the distance: it is the main cause of the attenuation of a sound, much more important than viscosity.

In what follows, a plane moving uniform at the speed V will be compared to a point.

Subsonic flow

If V < has (My < 1) the plane, which has a speed lower than that of the increase in the spheres of disturbance than it creates at every moment, is permanently inside those which were created previously. It is the phenomenon of which everyone with the experiment: the fixed observer feels the very weak sound of the first very dilated spheres, then the intensity increases until the plane is closest and decreases until the extinction. Moreover, the displacement of the point of emission of the spheres of disturbance gives rise to the effect Doppler.

Sonic flow

If My = 1, the plane sticks permanently in front of all the spheres created previously which thus find all tangent in a plan perpendicular to the movement of the plane. The superposition of a multitude of small disturbances creates a large disturbance which increases the resistance of the air considerably: it is the Mur of the sound.

Supersonic flow

When My > 1, the plane leaves on the contrary all the spheres of disturbance behind him. A simple reasoning shows that they all are tangent with a cone called cone of Mach.

Out of the cone of Mach, in front of the plane, it is absolute silence because no disturbance still reached the observer. The observer located in the cone hears a sound which decrease as into subsonic. On the cone, the bang corresponds to the superposition of the small disturbances.

Practical data

The considerations which precede give an idea of the importance of the Mach number but reality is definitely more complicated. One generally distinguishes the beaches following speeds:

My < 0,8: one speaks about flow Subsonique,
0,8 < My < 1,2: one speaks about flow Transsonique,
1,2 < My < 5: one speaks about flow Supersonique,
5 < My : one speaks about flow Hypersonique.

One can neglect the compressibility of the air for the Mach numbers lower than approximately 0,3. The definite sonic case previously like border between the subsonic one and the supersonic one do not have physical reality: it is replaced by a zone of transition rather broad, known as transonic, in which the phenomena are particularly complicated. Into supersonic, the cone of Mach, obtained by considering a specific obstacle, is only one simplified image of the shock wave (or the two shock waves which creates the double bang) in the vicinity of a real obstacle. The hypersonic mode is the field where appear physicochemical phenomena.

See too

Number without dimension
Reynolds number (intervening in the classification of the modes of flows).
Swiftness of the sound
Wall of the sound

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