Mach Number
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.
Different ranges of Mach numbers are associated with different flow regimes:
 Ma < 0.3: Subsonic flow, where the object is traveling at speeds lower than the speed of sound.
 0.3 < Ma < 1: Transonic flow, where the object is transitioning between subsonic and supersonic speeds.
 Ma > 1: Supersonic flow, where the object is traveling at speeds higher than the speed of sound.
 Ma >> 1: Hypersonic flow, where the object is traveling at extremely high speeds, typically many times the speed of sound.
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 

\(\large{ Ma = \frac{ v }{ a } }\)  
Mach Number  Solve for Ma\(\large{ Ma = \frac{ v }{ a } }\)
Mach Number  Solve for v\(\large{ v = Ma \; a }\)
Mach Number  Solve for a\(\large{ a = \frac{ v }{ Ma } }\)


Symbol  English  Metric 
\(\large{ Ma }\) = Mach number  \(\large{dimensionless}\)  
\(\large{ v }\) = velocity, speed of object  \(\large{\frac{ft}{sec}}\)  \(\large{\frac{m}{s}}\) 
\(\large{ a }\) = speed of sound  \(\large{\frac{ft}{sec}}\)  \(\large{\frac{m}{s}}\) 
Mach Number Conversion 

Multiply  By  To Get 
9.646x10^{7}  feet per day  
4.0192x10^{5}  feet per hour  
66,986  feet per minute, fpm  
1,116  feet per second, fps  
1,225  kilometers per hour  
2.94x10^{7}  meters per day  
1.225x10^{6}  meters per hour  
20,417  meters per minute  
340.29  meters per second  
761  miles per hour, mph 
Tags: Velocity Equations