# Mach Number

## What is Mach Number?

The Mach number is the ratio of flow velocity after a certain limit of the sounds speed. In simple words it is the the ratio of the speed of a body to the speed of sound in the surrounding medium.

Following is the table explaining other related concepts of fluid flow:

### Mach Number Formula

The formula of Mach Number is:

 M = u/c

In which,

• The Mach number is M,
• Based on the limits the local flow velocity is u,
• The speed of sound in that medium is c.

To explain it simply, the speed of sound can be equated to Mach 1 speed. Thus, Mach 0.75 will be 75% of the speed of sound that is also called subsonic and Mach 1.65 will be 65% faster than the speed of light which is also called supersonic.

The Mach number due to the local speed of sound is dependent on the surrounding mediums in specific temperature and pressure. A flow can be determined as an incompressible flow with the help of Mach number. The medium can either be a liquid or a gas. The medium can be flowing whereas the boundary may be stable or the boundary may be traveling in a medium which is at rest. The medium and boundary both may be traveling with certain speed but their velocities in respect to each other are what matters. The medium may be channeled through several devices such as wind tunnels or may be immersed in the medium. The Mach number is termed as a dimensionless number because it is a ratio of two speeds.

An Austrian philosopher and physicist Ernst Mach is after whom the Mach number is named. Due to it being a dimensionless quantity and not a measurable unit the number is put after the term Mach for instance, Mach 4 and not 4 Mach.

## Mach Number Classification

Speed below the speed of sound is termed as subsonic whereas speed above the speed of sound is termed as supersonic, although scientists practicing aerodynamics most of the time use these terms to describe a particular 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:

Commercial aircraft with aerodynamic features such as the rounded nose and leading edges. The mach is below 0.8.

### Transonic:

Aircraft that are built with swept wings. The mach value is between 0.8-2.1.

### Supersonic:

The aircraft created to go supersonic have a definite design it has complete movement of the canards, thin aerofoil sections, and sharp edges. The mach levels are between 1.2 and 5.0.

### Hypersonic:

These planes have several distinctive features such as nickel-titanium skin that is cooled and small wings. The mach values are between 5.0 and 10.0. The U.S. plane X-15 created the world record of flying at Mach 6.72.

### High- Hypersonic:

The mach levels are between 10.0 -25.0. When flying at such huge speeds thermal controls becomes an integral portion of the design. The hotness of the surface must be considered beforehand.

### Re-entry speeds:

The Mach speed is above 25.0. This 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

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## Mach Number Important Questions

Q1. What is Mach number significant for?

Ans: The flow in the air is having higher speeds than the sound and that is the significanence of Mach number.

Q2. Name the flows for which Bernoulli’s equation is applicable.

Ans: Following is the list of flows for which Bernoulli’s equation:

• Rotational flow
• Turbulent flow

Q3. What is the relative density of mercury?

Ans: The relative density of mercury is 13.6.

Q4. What is relative density?

Ans: Relative density is defined as the ratio of a substance to the ratio of water for liquid and solid and air for gas.

Q5. What is the unit of relative density?

Ans: Relative density is a dimensionless quantity. Therefore, it doesn’t have a unit.

Q6. What is Newtonian fluid?

Ans: Newtonian fluid is defined as the fluid that has viscous stress proportional to the local strain.

Q7. When is a flow called supersonic?

Ans: When the Mach number is between 1 to 5, the flow is known as supersonic.

Q8. Express 1 bar pressure in kPa.

Ans: 1bar=100 kPa.

Q9. What is Reynold’s number?

Ans: Reynold’s number is defined as the ratio of inertia force to viscous force.

Q10. What is Reynold’s number for laminar flow?

Ans: Reynold’s number for laminar flow is less than 2300.

#### Practise This Question

The Poisson's ratio cannot have the value