Mach Number

Mach Number

What is Mach Number?

The Mach number is the ratio of flow velocity after a certain limit of the sounds speed. The formula that represents it 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– Classified:

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:

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.

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Practise This Question

A beam of light consisting of red, green and blue colours is incident on a right angled prism. The refractive indices of the material of the prism for the above red, green and blue wavelength are 1.39, 1.44 and 1.47
respectively. The prism will