Table of Contents
Definition of Mach Number:
The velocity of an object in a medium divided by the sound velocity in that medium is called Mach Number. Mach Number is indicated by “M”. There is no dimension of Mach Number because it is the ratio of two velocity.
Mach number (M) = [object velocity(u)] / [sound velocity(c)]
Importance of Mach Number:
Mach Number is very important in fluid mechanics. Normally it is used to compare speed of flow with respect to speed of sound. Mach Number is very crucial in research and development. Compressibility of a fluid can ber determined by Mach Number.
It is a dimensionless quantity because it is calculated by deviding two velocity. In case of flow is quasi-steady and isothermal with M <0.2–0.3, the compressibility effect is
small and the fluid can be treated as incompressible.
Ernst Mach, the Austrian philosopher invented the Mach Number. As we knows that it is a dimensionless quantity and not a measurable unit, the number is placed after the term Mach, such as Mach 4 instead of 4 Mach.
Applications of Mach Number:
- Mach Number is used to determine the compressibility of the fluid.
- Mach Number is used to determine the sonic condition of fluid while determining the probability of acoustic induced vibration.
- Mach Number is used to study the motion of rockets air planes, etc.
- Mach Number is very helpful to study flow through nozzles.
- Mach Number is used to study the behaviour of shock waves.
Affect of Mach Number on Compressibility of Fluids:
An ideal fluid is incompressible. But in reality there is no fluid which is perfectly incompressible. Expansion and compression are two important properties of a fluid. There are no effects of pressure and temperature on incompressible fluids. Compressible fluids can expand or compressed due to temperature or pressure. In an incompressible fluid there is no affects on density. Incompressible fluids shows change in density due to temperature and pressure.
Various types of fluids behave similar at a specific Mach Number. If we have two diffrent types of fluid, these two fluids can behave similarly at a particular Mach Number. So we can say, Mach Number plays important role in fluid mechanics.
Relation Between Sonic Velocity and Mach Number:
When pressure increased beyond the certain point the adjacent molecules undergo a small change in position. Motion is infinitely quick for incompressible fluids. In reality, most of the fluids are compressible upto certain limit. This limit can be negligible for most of the fluids.
For ideal gas:
c=√(γRT)
As the pressure at a point is increased the adjacent molecules undergo a small change in
position. If the fluid is incompressible then the motion is infinitely quick. Most fluids are, to
some degree compressible, therefore this time is finite. If there is a sudden change, or the
fluid is moving quickly then this time is important.
Velocity of the gas is a function of sonic velocity.
M= u/c
Where M is the Mach Number;
When M < 1 Subsonic
M = 1 Sonic
M > 1 Supersonic
c = Sonic velocity (m/s)
γ = Specific heat ratio
R = Specific gas constant ( J / mol . K)
T = Temperature of the fluid (K)
Explanation of Mach Number Formula
Mach Number is the ratio of two velocity.
Formula of Mach Number is given by:
Mach Number, M=u/c
Velocity if fluid = u
Velocity of sound = c
M = Mach Number
Based on the Mach Number, It can be decided that weather the
fluid is incompressible or not. The medium in which fluid flow can be liquid or gas. This formula works when boundries are stable.
Classification of Flow Based on Mach Number:
5 types of flow based on Mach Number:
- Incompressible flow
- Subsonic flow
- Transonic flow
- Supersonic flow
- Hypersonic flow
Let’s know more about these types if flow.
1. Incompressible flow
M= 0
In this type of flow, density of the fluid does not change. Volume of the fluid remain same even application of pressure.
2. Subsonic flow
0 <M<1
In subsonic flow, Mach Number remain between 0 and 1. No shock waves are produced in the fluid. If M <0.3, subsonic flow is considered as Incompressible flow.
3. Transonic flow
0.8 <M<1.2
The Mach Number of transonic flow varies between 0.8 to 1.2. Low intensity shock wave may be generated. It is very difficult to analyse transonic current because the governing equations are non-linear and it is often impossible to separate the non-viscous and viscous aspects of the flow.
4. Supersonic flow
1<M<3
Mach Number of supersonic flow varies between 1 to 3. It is easy to analyse supersonic flow. In the supersonic flow, information propagates along specific directions called
properties, and determining these directions greatly simplifies the calculation of the flow field.
5. Hypersonic flow:
M> 3
Mach Number of the hypersonic flow is greater than 3. In this type if flow velocity is very high and friction or shock waves can result in sufficiently large temperature rises in the liquid due to molecular dissociation and other chemical effects.