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Mach Number Formula

Mach number is an important coefficient term that we use in motion in the air. It is the number as the ratio of flow velocity after a certain limit of the sounds speed. In other words, it is the ratio of the speed of some object to the speed of sound in the surrounding medium. So, Mach number is useful to compare the speed of an object with the speed of sound. In various fast speed aircraft and airplanes, Mach number is useful for many calculations and comparisons. In this article, we will learn the Mach number formula with examples. Let us learn it!

Concept of Mach Number

To explain its concept simply, the speed of sound can be equated to Mach Number 1 speed. Thus, Mach 0.75 will be 75% of the speed of sound, which is also called as subsonic. Also, Mach number 1.65 will be 65% faster than the speed of sound which is called supersonic speed.

The Mach number due to the local speed of sound is normally dependent on the surrounding mediums at some specific temperature and pressure. This flow can be determined as an incompressible flow with the help of this important number.

Here, the medium can either be a liquid or a gas. The medium can be flowing whereas the boundary may be a stable one. Or also the boundary may be traveling in a medium that is at rest state. Sometimes the medium and boundary both may be traveling with some speed.

The medium may be channeled through various devices such as wind tunnels or sometimes even may be immersed in the medium. The Mach number is referred to as a dimensionless number because it is expressed as the ratio of two speeds.

An Austrian philosopher and physicist Ernst Mach has worked on it. Therefore it is named Mach number. Due to it being a dimensionless quantity but not a measurable unit the number is put after the term Mach only, like Mach 4 and not 4 Mach.

Mach number Formula

Mach Number Classification

The various regimes of Mach values are given based on the ratio values. These are:

  • Subsonic: Commercial aircraft with aerodynamic features such as the rounded nose and leading edges have Mach number below 0.8.
  • Transonic: Aircraft that are built with swept wings has Mach number is between 0.8 – 2.1.
  • Supersonic: The aircraft created to go supersonic have a specific design with sharp edges has the Mach number is between 1.2 and 5.0.
  • Hypersonic: These planes have many distinctive features and have Mach values between 5.0 and 10.0.
  • High-Hypersonic: The Mach levels are between 10.0 – 25.0 for these.

The Formula for Mach Number

The Mach Number Formula is as: \(M = \frac {v} {c}\)

M The Mach number
V Based on the limits of values local flow velocity
c The speed of sound in the given medium

Solved Examples for Mach Number Formula

Q.1: Speed of some object given as 240 m per second at a normal temperature of 20 degrees. Then compute the Mach number for this object.

Solution: Given,

V = 240 m per second

And we c = 340 m per second at a normal temperature of 20 degrees.

Fomula is:

\(M  = \frac {v} {c}\\\)

\(= \frac {240} {340} \\\)

= 0.70

Thus Mach number is 0.70.

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