Mach Number and its Significance

Mach number.

Mach number is a dimensional less number. It is the ratio of fluid to the velocity of the sound in that fluid. It was named after the Ernst Mach he is the person behind the Mach number. If the Mach number is related to the object especially aircraft the Mach number is defined as, the ratio of the velocity of the object relative to the fluid and the velocity of sound in that fluid. 

Mach number is used to analyze fluid flow dynamics problem where the compressibility is a significant factor. 

Mathematically it is expressed as –

M= speed of object /speed of sound

M= V/C

Where,

M= Mach number

V= speed of the aircraft

C= speed of the sound

Subsonic

If the Mach number less than one (M<1): In this case, the speed of the object is less than the sound speed.

Supersonic.

If the Mach number more than one (M>1): In the supersonic speed, the object speed is more than the sound speed.

Transonic

If the Mach number is equal to one (M=1):

In transonic speed, the speed of the object is nearly equal to the speed of the sound.

Hypersonic speed (M>>1):

When the speed of the object is much higher than the speed of the sound in the same medium is called hypersonic speed.

The significance of Mach number

The Mach number is used to describe the speed of aircraft in terms of the speed of sound. If the aircraft speed is equal to the speed of sound then the Mach number would be 1.

Example problem,

An aircraft flies at speed 700 mph at an altitude of 36000 ft. The surrounding temperature is -60 ^oF.

The speed of the aircraft can be calculated as-

v = (700 miles/hr) (5280 ft/miles) / (3600 sec/hr)

    = 1026.67 ft/sec

The Mach number can be calculated as-

M = (1026.67 ft/s) / (980 ft/s)

= 1.047 >1

 The aircraft is flying at supersonic speed.