Mach Number: Definition, Formula, Types and Classification

Mach Number Overview

The compressibility characteristics of fluid flow are measured by the Mach number; at a given Mach number, regardless of other variables, the fluid (air) behaves similarly when under the influence of compressibility. The International Standard Atmosphere predicts that the speed of sound is 340.3 meters per second (1,116.5 ft/s; 761.23 mph; 661.49 kn) in dry air at mean sea level with a standard temperature of 15 °C (59 °F). Since atmospheric temperature typically decreases with increasing altitude between sea level and 11,000 meters (36,089 ft), the speed of sound also tends to decrease as altitude increases. The speed of sound is not a constant; in a gas, it increases proportionally to the square root of the absolute temperature.

What is Mach number?

The ratio of flow velocity after the sound speed reaches a certain limit is known as the Mach number. Simply put, it is the ratio of a body's speed to the speed of sound in the medium around it.

Mach Number Formula

The Mach number formula is-

M = u/c, where:

1. The local Mach number is M.
2. u is the local flow velocity with respect to the boundaries, which may be internal (such as an object submerged in the flow) or external (such as a channel), and
3. c, the speed of sound in a medium, depends on the thermodynamic temperature squared for air.
4. Mach 1 is, to put it simply, the same as the speed of sound.
5. So, Mach 0.75 will be 75% of the speed of sound, or subsonic speed, and Mach 1.65 will be 65% of the speed of sound, or supersonic speed.
6. The local sound speed is influenced by the surrounding medium's pressure and temperature.
7. It is also possible to determine whether a flow is compressible using the Mach number.
8. The media can be a gas or a liquid.
9. Various situations exist where the medium is flowing but the boundary is stable, or where the medium and boundary are both moving but the boundary is stationary.
10. It is the relative velocities between the border and the medium that matter, even though both are moving at the same speed.
11. The medium can either be immersed in it or routed through a variety of apparatuses, such as a wind tunnel.
12. Since Mach number is the ratio of two speeds, it is a dimensionless quantity.

Read more about What is Friction?

Mach Number Classification

Although scientists who practice aerodynamics most of the time use these terms to describe a specific range of Mach values, speed below the speed of sound is referred to as subsonic, and speed above the speed of sound is referred to as supersonic.

The various Mach value regimes include:

1. Subsonic: A commercial aircraft with aerodynamic characteristics like a rounded nose and leading edges.The Mach number is below 0.8.
2. Transonic: Wings that are swept back during construction. The Mach value is between 0.8-2.1.
3. Supersonic: The aircraft built to travel at supersonic speeds have a distinct design, including canards that can fully extend and retract, thin aerofoil sections, and sharp edges. The Mach numbers range from 1.2 to 5.0.
4. Hypersonic: These aircraft stand out thanks to their small wings and cooled nickel-titanium skin. The Mach numbers range from 5.0 to 10.0. The American X-15 aircraft set the world record for fastest flight at Mach 6.72.
5. High-Hypersonic: The Mach ranges from 10.0 to 25. Thermal controls become an essential component of the design when flying at such incredible speeds. The surface's heat must be taken into account in advance.
6. Re-entry velocities: The Mach number is greater than 25. This does not call for blunt edges and wings.

Concept behind Mach Number

1. To make the subject simpler, the speed of sound is equivalent to Mach 1.
2. If Mach 0.75 is used, it indicates a speed that is 75% of the sound speed, also known as subsonic.
3. If Mach 1.65 is mentioned, it means that the speed is supersonic speed, which is defined as a speed that is 65 percent faster than the speed of sound.
4. The environment's temperature and pressure have an impact on the sound.
5. The surrounding area could be either a liquid or a gas.
6. Although the medium may flow or the boundary may travel in a medium, in which case it will be at rest, the border will be stable.
7. It's possible that the border and the medium are shifting simultaneously.
8. The medium can occasionally be immersed or funneled through various apparatuses like wind tunnels.
9. Mach Number is a dimensionless number because it is expressed as the ratio of two speeds.
10. It is preceded by the term Mach, as in Mach 1 rather than 1 Mach, because it is a dimensionless quantity and not a measured unit. 

Classification of Mach Number Regimes

For supersonic and hypersonic flows, small disturbances spread downwind within a cone. The trigonometric sine of the cone angle b, which is equal to the inverse of the Mach number M, is the source of the Mach angle's name.

Significance of Mach Number

When comparing the speed of any object with the speed of sound, the Mach number is a crucial factor. It is a parameter used to indicate how fast a flying object is moving through the air. It is widely used in fluid dynamics. To fully understand how airplanes and rockets move, the Mach number is extensively studied. It is a dimensionless quantity that, by definition, expresses the proportion of an object's velocity to the speed of sound.

Typically, the letter "M" is used to denote the Mach number.

Mach number is equal to (frac)(speed of sound/speed of object).

((M=frac{v}{c})

Where v is the object's velocity in relation to an internal or external boundary in a medium

and c equals the local medium's speed of sound.

The air molecules closest to an airplane's body are disturbed when it is in the air. When an airplane is moving at a higher speed, the air around it is compressed. By evaluating the Mach number, we can determine whether or not the fluid is compressible. Because it is the ratio of two velocities with the same dimensions, the Mach number has no dimensions.

Conclusion

1. The ratio of flow velocity when a specific limit of sound speed has been reached is known as the Mach number. It is, to put it simply, the ratio of the body's speed to the speed of sound in the medium in which it is traveling. 
2. A certain Mach number causes the fluid (air), regardless of other factors, to behave similarly under the influence of compressibility. This is known as the compressibility property of fluid flow.
3. It is generally used to determine how close a flow may be treated as an incompressible flow with a given approximation.
4. Mach number is a similarity parameter in many equations for compressible flows, shock waves, and expansions.
5. The type of gas and its temperature determine the gas's kind of speed of sound, which determines the gas's Mach number.