MACH NUMBER

Velocity, it tells us at what magnitude and direction a moving object, similarly we need a term which we define us the speed of your aircraft, rocket, missile and all kind of air vehicle, its MACH NUMBER(M). As Mach number is directly related to the speed of sound

SPEED OF SOUND

The speed at which sound waves is travels through the air is called speed of sound. In aerodynamics speed of sound plays a very pivotal role

Speed of sound depends on

1.       Pressure

2.       Temperature

3.       Density

Let us assume that we are in a room with motionless air, density (r), Temperature (T), Pressure (P). Now if some sound is produced let as a firecracker sound. If u are standing in the middle of the room, the sound wave sweeps by you at velocity (a) m/s, ft. /s.

The sound wave is a thin region of disturbance in the air across temperature, pressure, density slightly changes, and this change in pressure activates your eardrums and helps us to hear. 

As the wave is passing in the room, there is a slight change in temperature, density, pressure, airspeed by the amount dT,dr,dp and da respectively. Thus the air behind the way is moving a+da

Let’s us apply the fundamental equation of gas flow, to get an equation for a

From the continuity equation  

A1 and A2 are an area of steam tube and there is a geometric reason for a change in an area

So A1=A2=A

Since drda is very small, hence we can ignore them

Form Euler’s equation

substitute equation 3 into 4 

On a physical basis, the flow through a sound wave involves no heat addition on the effect is negligible. Hence sound wave is isentropic

From isentropic flow

Equation 7 says that the ratio 

is the same constant value at every point

We can write

Substituting the value of c in equation 9 from equation 8

Substitute equation 10 into 6

For a perfect gas p=ρRT

Substituting this result into equation 11

Equation 12 is a very important result in aerodynamics it also tells us, the speed of sound in a perfect gas depends only on the temperature of the gas

The speed of sound leads to another, vital definition of Mach number

With the help of Mach number, we will define 5 different of aerodynamic flow

1.       Subsonic flow is a flow in which M<1

2.       Sonic flow is a flow in which M=1

3.       Supersonic flow is a flow in which M>1

4.       Transonic flow is a flow in which 0.8≤M≤1.2

5.       Hypersonic flow is a flow in which M>5