When the Mach number is less than unity, the flow is
Subsonic
In fluid dynamics, the Mach number is a crucial dimensionless quantity that represents the ratio of the flow speed past a boundary to the local speed of sound. It helps us understand whether a fluid flow is compressible and how it behaves.
Mach Number Defined
The Mach number, denoted as \(M\), is calculated using the formula:
\[M = \frac{V}{a}\]
Where:
- \(V\) is the flow velocity (speed of the object or fluid).
- \(a\) is the speed of sound in the medium where the flow is occurring.
Flow Regimes Based on Mach Number
The value of the Mach number helps classify different types of fluid flow, particularly in aerodynamics and gas dynamics. Here's a breakdown of the common flow regimes:
| Mach Number (\(M\)) | Flow Regime | Description |
|---|---|---|
| \(M < 1\) | Subsonic flow | The flow speed is less than the speed of sound. This means the object or fluid is moving slower than the sound waves it produces. Information (like pressure changes) can propagate ahead of the object. |
| \(M = 1\) | Sonic flow | The flow speed is exactly equal to the speed of sound. This is a critical point where significant changes in fluid properties occur, often leading to phenomena like choking in nozzles. |
| \(M > 1\) | Supersonic flow | The flow speed is greater than the speed of sound. In this regime, the object or fluid is moving faster than the sound waves it creates. Sound waves cannot propagate ahead, leading to the formation of shock waves. |
| \(M > 5\) (approximately) | Hypersonic flow | This is an extreme form of supersonic flow where the speeds are significantly higher than the speed of sound. Flows in this regime exhibit additional complex physical phenomena, such as extreme heating and chemical reactions in the fluid. |
Subsonic Flow Understanding
The question specifically asks about the scenario when the Mach number is less than unity, which means \(M < 1\). As explained above, when \(M < 1\), it means that the velocity of the flow is less than the speed of sound in that medium. This condition precisely defines subsonic flow.
For example, a typical commercial airplane flying at cruising altitude often operates in the subsonic flow regime, as its speed is less than the speed of sound at that altitude.
Important Questions from Dimensionless Number
Match the following and select the correct answer from the codes given below the lists
List I
List II
A.
Steam Nozzle
1.
Mach number
B.
Compressible flow
2.
Reaction turbine
C.
Surface Tension
3.
Biot number
D.
Heat conduction
4.
Nusselt number
5.
Supersaturation
6.
Weber number
The Reynold’s number, used for critical velocity for turbulent flow of fluids, is given by the relation
Reynolds number for non - circular cross-section is:
[V = mean velocity, ν = kinematic viscosity, P = ratio of cross-sectional area to the wetted perimeter]
A) \(V.\frac{{4P}}{v}\)
B) \(\frac{{V.P}}{v}\)
C) \(\frac{{V.2P}}{{4v}}\)
D) \(\frac{{V.P}}{{4v}}\)
The only possible dimensionless group that combines velocity ‘V’, body size ‘L’, fluid density ‘ρ’ & surface tension ‘σ’
- Which of the following is not a non-dimensional parameter?
