Mach Number

on . Posted in Dimensionless Numbers

Mach number, abbreviated as Ma or M, a dimensionless number, is the ratio of the velocity of flow to the velocity of sound.  The speed of sound in this equation is dependent on the density of the medium that the sound is traveling through.  For example, the speed of sound through a solid object like a railroad track is much faster than the speed of sound through air at standard conditions.  The Mach number provides a measure of how fast an object is traveling compared to the speed at which pressure waves (sound waves) propagate through the medium.  It is often used in aerodynamics, aerospace engineering, and fluid dynamics to characterize the flow behavior and compressibility effects.

Mach number categorizes into different regimes based on the object's speed relative to the speed of sound

  • Subsonic ()  -  The object is traveling at a speed slower than the speed of sound.  Subsonic flows are characterized by smooth, continuous airflow around the object.
  • Transonic (0.8 < Ma < 1.2)  -  Transonic flows involve speeds close to the speed of sound.  As the object moves through the air, some parts of it may experience supersonic flow, while others remain subsonic.
  • Supersonic ()  -  In this regime, the object is traveling at a speed faster than the speed of sound.  Supersonic flows often result in shock waves forming around the object.
  • Hypersonic ()  -  Hypersonic flows involve extremely high speeds, several times the speed of sound.  At these speeds, the behavior of the flow becomes complex, with significant aerodynamic heating and other effects.
  • Mach 1 (-  At Mach 1, the object is traveling at the speed of sound.  This is the boundary between subsonic and supersonic flow.

The Mach number has significant implications for the aerodynamic behavior of objects and the formation of shock waves, which occur when an object moves faster than the speed of sound.  Understanding and accounting for the Mach number is critical in designing aircraft, rockets, and other high speed vehicles, as well as in the analysis of fluid flows in pipes and channels.


Mach number formula

\( Ma \;=\; v \;/\; a   \)     (Mach Number)

\( v \;=\; Ma  \; a  \)  

\( a \;=\; v \;/\; Ma   \)  

Solve for Ma

velocity, v
speed of sound, a

Solve for v

mach number, Ma
speed of sound, a

Solve for a

velocity, v
mach number, Ma

Symbol English Metric
\( Ma \) = Mach number \(dimensionless\)  
\( v \) = velocity, speed of object \(ft \;/\; sec\) \(m \;/\; s\)
\( a \) = speed of sound \(ft \;/\; sec\) \(m \;/\; s\)


Mach Number Conversion

Multiply By To Get
  9.646x107 feet per day
  4.0192x105 feet per hour
  66,986 feet per minute, fpm
  1,116 feet per second, fps
  1,225 kilometers per hour
  2.94x107 meters per day
  1.225x106 meters per hour
  20,417 meters per minute
  340.29 meters per second
  761 miles per hour, mph


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Tags: Velocity Air Aerodynamics