Mach Number
Nov 23, 2022, 16:45 IST
A Mach number is the ratio of the velocity of flow after a specific limit of the speed of sound. Simply put, it is the ratio of the speed of a body to the speed of the sound in the medium.
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Formula of Mach Number
M = u/c
Where,
- M = Mach number
- u = Based on the limits, the local flow velocity
- c = The speed of sound in that medium
The speed of sound can be compared to the speed of Mach 1. So Mach 0.75 will be 75% of the speed of sound, also called subsonic, and Mach 1.65 will be 65% faster than the speed of light, also called supersonic.
The Mach number due to the local speed of sound depends on the surrounding media at a specific temperature and pressure. The flow can be determined as an incompressible flow using the Mach number. The medium can be either a liquid or a gas. The medium can flow while the boundary can be stable, or the boundary can move in a medium at rest.
The environment and the boundary can move at a certain speed, depending on their relative speed. The medium can be guided through several devices, such as wind tunnels, or immersed in the medium. The Mach number is called a dimensionless number because it is the ratio of two speeds.
The Mach number is known after the Austrian philosopher and physicist Ernst Mach. Since it is a dimensionless quantity and not a measurable unit, for example, the number given after the term Mach is Mach 4 and not 4 Mach.
Classification of Mach Number
A speed below the speed of sound is called subsonic. In contrast, a speed above the speed of sound is called supersonic, although scientists practicing aerodynamics mostly use these terms to describe a specific range of Mach values.
The various regimes of Mach values are-
| Regime | Subsonic | Transonic | Sonic | Supersonic | Hypersonic | Hypervelocity |
| Mach | <0.8 | 0.8–1.3 | 1.0 | 1.3–5.0 | 5.0–10.0 | >10.0 |
- Subsonic
A commercial aircraft with aerodynamic features such as a rounded nose and leading edges. Mach is below 0.8.
- Transonic
Aircraft that are built with curved wings. The Mach value is between 0.8-2.1.
- Supersonic
Built to be supersonic, the aircraft has a distinct design, full duck motion, thin aerofoil sections, and sharp edges. Mach levels are between 1.2 and 5.0.
- Hypersonic
These aircraft have distinctive features, such as cooled nickel-titanium skin and tiny wings. Mach values are between 5.0 and 10.0. The American X-15 aircraft set a world record in flight at Mach 6.72.
- High-hypersonic
Mach levels are between 10.0 -25.0. When flying at such enormous speeds, thermal controls become an integral part of the design. The heat of the surface must be considered beforehand.
- Re-entry speeds
Mach speed is greater than 25.0. It does not require wings and a blunt design.
Classification of Mach Regimes
| Regime | Speed | ||||
| (Mach) | (knots) | (mph) | (km/h) | (m/s) | |
| Re-entry speeds | >25.0 | >16,537 | >19,031 | >30,626 | >8,508 |
| High-hypersonic | 10.0–25.0 | 6,615–16,537 | 7,680–19,031 | 12,251–30,626 | 3,403–8,508 |
| Hypersonic | 5.0–10.0 | 3,308–6,615 | 3,806–7,680 | 6,126–12,251 | 1,702–3,403 |
| Supersonic | 1.3–5.0 | 794-3,308 | 915-3,806 | 1,470–6,126 | 410–1,702 |
| Transonic | 0.8–1.3 | 530–794 | 609–914 | 980–1,470 | 273–409 |
| Subsonic | <0.8 | <530 | <609 | <980 | <273 |
Frequently Asked Questions (FAQs)
Q1. What is relative density?
Ans. The ratio of the substance to the ratio of the water for solid and liquid and air for gas is known as relative density.
Q2. What is the unit of relative density?
Ans. It is a dimensionless quantity. So, it doesn’t have a unit.
Q3. What is Newtonian fluid?
Ans. It is a fluid with viscous stress proportional to the local strain.
Q4. When is a flow called supersonic?
Ans. The flow is known as supersonic when the Mach number is between 1 and 5.
Q5. Express 1 bar pressure in kPa.
Ans. 1bar = 100 kPa.
