Mach Number

We all know that an aeroplane is much fast compared to other modes of transport. Have you ever wonder how fast an aeroplane can fly? But what happens if aeroplanes fly in much higher speed than sound. The aeroplanes suffer shock wave that affects the blade of the aeroplane. Mach number plays a very important role to study these matters. We can compare the speed of an object with the speed of sound by the help of the Mach number. It is also a tool to determine if a flow is incompressible or not.

Mach Number

Significance of Mach number

Mach number is an important quantity to compare the speed of any object with a speed of sound. It is a parameter to denote the speed of a flying object in air medium. In fluid dynamics, it has very vast use. Mach number is heavily studied to have a proper idea on the motion of aeroplanes and rockets. By definition, it is a dimensionless quantity expressing the ratio of the velocity of an object in a medium to speed of sound.

Generally, the Mach number is represented with the symbol ‘M’.

Mach Number= $$\frac{Speed of object}{Speed of sound}$$

$$M=\frac{v}{c}$$

Where v= Speed of the object in a medium with respect to some boundary either internal or external.

And c =Speed of sound in the local medium.

When an aeroplane is flying in the sky the air particles nearest to the body of aeroplane get disturbed. If the aeroplane has a higher velocity it provides a compressing effect on the surrounding air. Hereby judging the Mach number we can say that the fluid is compressible or not. Mach number has no dimensions because it is the ratio of two velocities having the same dimensions.

Various Types of Flow

According to the variation of Mach number fluid flow is classified.

Subsonic: For these type of flow the Mach number remains below 0.8. Commercial aeroplanes flowing in this range have a round nose and leading edges.

Sonic: For sonic flow, the Mach number is one. That is for these type of flow the velocity of an object is equal to the velocity of sound in the local medium.

Supersonic: When the object flow with greater velocity than the sound it is said to have supersonic velocity. It has a Mack number greater than one. Aeroplanes have proper designs to undergo supersonic speed.

Hypersonic: When the speed of an object is much higher than the speed of sound the flow is called hypersonic. The range of Mach number is five to ten in this case.

The design of aircraft is done according to the Mach number to get the best result. Also, we know that sound moves in the form of waves. In air medium, the movement of these waves depends on various factors such as temperature and pressure of the air.

We know that when a fluid flows over a solid surface, a thin membrane of fluid sticks to the surface and acquires the same velocity of the surface.

Q.1 What is a sonic boom?

Answer: When an aeroplane flies with more speed than the sound that is supersonic a shock wave is produced. In this condition major changes in temperature, pressure takes place.This shock effect is heard by the people in the ground similar to a clap sound.

Q.2 Discuss incompressible fluid with the help of Mach number?

Answer: Incompressible fluid is those fluids whose density remains the same. Even if we change the pressure the volume remains constant. In reality, the change in volume with change in pressure is very small. Fluids are considered incompressible when the temperature is constant. From Bernoulli’s theorem, we know that change in pressure is related to change in velocity. Change in velocity is related to Mach number. If Mach number is very high then the fluid is considered compressible, and if Mach number is low then for change in pressure the volume remains constant making the flow incompressible. For mechanical approximation, if Mach number is less than 0.3 then it is incompressible flow.

Q.3 How Mach number changes with change in medium and height?

Answer: Let us assume an aeroplane is flying with the speed of sound in air medium. Now as the height changes the speed of sound also changes in that particular height resulting change in Mach number. So the aeroplane has to adjust itself with the relative change in the speed of sound.

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