When Mach number is less than unity, the flow is called-
Sub-sonic flow
Understanding Flow Regimes Based on Mach Number
The flow of a fluid, such as air, is often classified based on its speed relative to the speed of sound in that fluid. The key parameter used for this classification is the Mach number.
What is Mach Number?
The Mach number (\(M\)) is a dimensionless quantity defined as the ratio of the speed of the fluid (\(V\)) to the speed of sound (\(a\)) in that fluid at the given conditions.
The formula for Mach number is:
\(M = \frac{V}{a}\)
Where:
- \(V\) is the velocity of the fluid flow.
- \(a\) is the speed of sound in the medium.
The speed of sound (\(a\)) varies with the properties of the medium, particularly its temperature.
Classifying Flow Types by Mach Number
Different ranges of the Mach number correspond to different flow regimes, characterized by distinct physical phenomena, especially concerning the compressibility of the fluid and the behavior of pressure waves (sound waves).
The main flow types based on Mach number are:
- Sub-sonic flow: When the Mach number is less than unity (\(M < 1\)). In this regime, the fluid speed is less than the speed of sound. Pressure disturbances can propagate upstream against the flow.
- Sonic flow: When the Mach number is equal to unity (\(M = 1\)). The fluid speed is exactly equal to the speed of sound. This condition is often reached at the throat of a converging-diverging nozzle.
- Super-sonic flow: When the Mach number is greater than unity (\(M > 1\)). The fluid speed is greater than the speed of sound. Pressure disturbances cannot propagate upstream; they form shock waves.
- Trans-sonic flow: Often defined as the regime where the flow contains both sub-sonic and super-sonic regions, typically around \(0.8 < M < 1.2\).
- Hyper-sonic flow: When the Mach number is significantly greater than unity, typically considered for \(M > 5\). This regime involves very high speeds and significant heating effects.
Applying to the Question: Mach Number Less Than Unity
The question asks about the flow type when the Mach number is less than unity. Based on our classification:
- \(M < 1\) corresponds to Sub-sonic flow.
- \(M = 1\) corresponds to Sonic flow.
- \(M > 1\) corresponds to Super-sonic flow.
- \(M > 5\) corresponds to Hyper-sonic flow.
Therefore, when the Mach number is less than unity, the flow is called Sub-sonic flow.
| Mach Number (M) | Flow Type | Characteristics |
|---|---|---|
| \(M < 1\) | Sub-sonic | Speed less than sound; pressure waves move upstream |
| \(M = 1\) | Sonic | Speed equals sound; critical condition |
| \(1 < M < \approx 5\) | Super-sonic | Speed greater than sound; shock waves form |
| \(M > \approx 5\) | Hyper-sonic | Very high speed; significant heating effects |
Conclusion
Based on the definition and classification of flow regimes by Mach number, a flow with a Mach number less than unity (\(M < 1\)) is known as Sub-sonic flow. This aligns with the provided options, identifying Sub-sonic flow as the correct classification.
Revision Table: Fluid Flow and Mach Number
| Concept | Definition/Relation |
|---|---|
| Mach Number (\(M\)) | Ratio of fluid speed to speed of sound (\(V/a\)) |
| Sub-sonic Flow | \(M < 1\) |
| Sonic Flow | \(M = 1\) |
| Super-sonic Flow | \(M > 1\) |
| Hyper-sonic Flow | \(M > \approx 5\) |
| Speed of Sound (\(a\)) | Speed at which small pressure disturbances travel in a medium; depends on medium properties (temp, composition) |
Additional Information: Speed of Sound and Compressibility
The concept of Mach number is closely related to the compressibility of a fluid. Compressibility refers to how much the volume or density of a fluid changes under pressure. For sub-sonic flows (\(M < 1\)), density changes due to pressure are relatively small, and often the fluid can be treated as incompressible, especially at very low Mach numbers.
As the Mach number increases, compressibility effects become more significant. At sonic and super-sonic speeds, density, pressure, and temperature can change dramatically, especially across shock waves in super-sonic flow. The speed of sound itself is related to the compressibility and density of the medium. For an ideal gas, the speed of sound is given by:
\(a = \sqrt{\gamma R T}\)
Where:
- \(\gamma\) is the ratio of specific heats
- \(R\) is the specific gas constant
- \(T\) is the absolute temperature
This formula shows that for a given gas, the speed of sound depends only on its temperature. Therefore, Mach number is often stated as the ratio of the flow speed to the local speed of sound, which varies with temperature in the flow field.
Important Questions from Dimensionless Number
Euler's dimensionless number relates the following:
- In fluid flow diagrams that plot the friction factor against the Reynolds number, such as the Moody chart, what crucial additional parameter is commonly represented by a series of curves?
The square root of the ratio of the inertia force due to flow to the elastic force of fluid is known as-
Euler number is related to
The gases are considered incompressible when Mach number is
