[Physics Class Notes] on Mach Number Pdf for Exam

Concept of Mach Number

For explaining the concept in a simple manner; Mach number 1 speed is equated to the speed of sound. If Mach 0.75 denoted, it would be considered 75% of the sound speed, which is also known as subsonic. If Mach 1.65 is indicated, it will be regarded as 65% faster than the sound speed, also known as supersonic speed.   

The sound depends on the surrounding space at a specific pressure and temperature; also, we can determine whether the flow is incompressible with the help of the Mach Number.

The surrounding space can either be gas or liquid. 

The boundary will be stable, but the medium can be flowing, or the boundary can travel in a medium, meaning it is at a rest state. There can be a situation where both the medium and boundary are traveling with some speed.

The medium can be channeled through various devices like the wind tunnels or sometimes may immerse in the medium. As the ratio of two speeds expresses the number, Mach Number is considered as a dimensionless number.

Since it was worked upon by an Austrian Physicists and Philosopher by Ernst Mach, it has been named as Mach number. Since it is a dimensionless quantity and not a measurable unit, the word Mach is put before the number, like Mach 1 and not 1 Mach.

What is Mach Number in Physics?

Mach Number Definition – The ratio of the flow velocity after a certain limit of the sound speed is known as the Mach number. In simple terms, it is the ratio of the speed of the body to the sound’s speed in the surrounding medium.

Mach Number Formula

The Mach Number formula is:

M = v/c

Where,

[M_{a}] = [frac{v}{c}]

[M_{a}] → Mach Number

V → speed or velocity of an object.

c → speed or velocity of sound.

In simple terms, the speed of sound can be equated to Mach 1. Thus Mach 0.75 will be 75% speed of the sound, also known as subsonic speed, and Mach 1.65 will be 65% faster than the speed of sound, known as the supersonic speed.

The local speed of sound is dependent on the pressure and temperature of the surrounding medium. Mach number can also determine if the flow is incompressible. The medium can either be gar or liquid. There are many scenarios where the medium can be flowing, but the boundary is stable, or the medium and boundary are both traveling, meaning that medium is at rest. Even though the boundary and medium both are traveling at a certain speed, but their velocities concerning each other are what matters. The medium can be channeled through various devices like the wind tunnel or can be immersed in the medium. Since Mach number is the ratio of two speeds, it termed as a dimensionless quantity.  

Mach Number Classification

Below based on the ratio values, the Mach number is termed in various regimes.

Subsonic:

The aerodynamic features like the rounded noses or the leading edges found in the commercial aircraft. They have a mach speed below 0.8.

Transonic:

The aircraft with swept wings built have a mach speed value of 0.8 – 2.1.

Supersonic:

The aircraft has a definite design and a complete movement of thin aerofoil sections, canards, and sharp edges that can fly at supersonic speed with mach speed value between 1.2 and 5.0.

Hypersonic:

The aircraft that fly at Mach value of between 5.0 – 10.0 has many distinctive features like the small wings and nickel-titanium skin that is cooled. A world record was created by the U.S. plane X-15, which flew at a speed of Mach 6.72.

High-Hypersonic:

When flying at mach levels of 10.0 – 25.0, thermal controls become an important factor while designing as the hotness of the surface needs to be considered beforehand.

Re-Entry Speeds:

When the mach speed is above 25.0, its craft doesn’t require wings but a blunt design.

Classification of Mech Regime