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Mach number is the coefficient phrase used to describe motion in the air. In fluid dynamics, the Mach number expresses the ratio of flow velocity past a boundary to local sound speed. The Mach number is crucial in the study of approximations that can be used to treat a flow as an incompressible flow. Mach number can also be used to compare the speed of an object to the speed of sound. Considering the numerous fast-speed aircraft and airplanes, Mach Number is important for many computations and comparisons. It is named after Ernst Mach, an Austrian philosopher, and scientist.
| Table of Contents |
Key Takeaways- Mach Number, Subsonic, Sonic, Supersonic, Hypersonic, Re-entry Speed, u/c, Flow Velocity
What is Mach Number?
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Mach number is the ratio of flow velocity after a given limit of sound speed. It is the ratio of a body's speed to the speed of sound in the surrounding medium, in the simplest form. In fluid mechanics, Mach number is the ratio of a fluid's velocity to the velocity of sound in that fluid. The word Mach is placed before the number since it is a dimensionless quantity and not a measuring unit. Mach number is equal to the velocity of the object relative to the fluid divided by the velocity of sound in that fluid in the case of an object traveling through a fluid, such as an aircraft in flight.
Mach number
By comparing the object’s speed to the speed of sound, Mach number determines the object's speed. Mach Number is important for numerous computations and comparisons when evaluating various fast-speed aircraft and airplanes. Subsonic flow is indicated by Mach numbers less than one; supersonic flow is indicated by Mach values greater than one.
Read More:
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| Shearing Stress | Fluid Friction | Mechanical Properties of Fluids |
| Hydraulic Lift | Barometer | Reynolds Number |
| Fluid Pressure | Hydrostatic Paradox | Viscosity |
Concept behind Mach Number
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- The speed of sound is equivalent to Mach number 1 in order to simplify the subject.
- If Mach 0.75 is used, it means that it is 75 percent of the sound speed, which is also referred to as subsonic.
- If Mach 1.65 is specified, it means that the speed is 65 percent faster than the speed of sound, generally known as supersonic speed.
- The sound depends on the surrounding space at a certain temperature & pressure.
- It is possible for the surrounding space to be either gas or liquid.
- The border will be stable, but the medium may flow or the boundary may travel in a medium, in which case it will be at rest.
- It's possible that both the medium and the border are moving at the same time.
- The medium can be funneled through various devices such as wind tunnels, or the medium can be immersed at times.
- Because it is stated as the ratio of two speeds, Mach Number is a dimensionless number.
- Because it is a dimensionless quantity and not a measured unit, it is preceded by the term Mach, as in Mach 1 rather than 1 Mach.
Critical Mach number
Mach Number Formula
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The formula for Mach Number is-
| M or Ma = u/c |
where,
M or Ma is the Mach Number,
u is the local flow velocity according to the limits,
c is the speed of the sound given on that particular medium.
- The speed of sound is equal to Mach 1 in simple words.
- As a result, Mach 0.75 will be 75 percent of the speed of sound, or subsonic speed, while Mach 1.65 will be 65 percent of the speed of sound or supersonic speed.
- The pressure and temperature of the surrounding medium affect the local speed of sound.
- Mach number can also be used to determine whether or not the flow is compressible.
- Gas or liquid can be used as the media.
- There are a variety of circumstances in which the medium is flowing but the boundary is stable, or where the medium and boundary are both moving but the medium is at rest.
- Even while the border and the medium are both moving at a given pace, it is their relative velocities that count.
- The medium can be routed through a variety of devices, such as a wind tunnel, or it can be immersed in it.
- Mach number is a dimensionless quantity because it is the ratio of two speeds.
Classification of Mach Number
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Although scientists practicing aerodynamics most of the time use these terminologies to represent a certain range of Mach values, speed below the speed of sound is referred to as subsonic, and speed above the speed of sound is referred to as supersonic. Fluid flow is categorized based on the fluctuation in Mach number.
- Subsonic: The Mach value for this type of flow is less than 0.8. The leading edges and noses of commercial aircraft in this category are spherical.
- Sonic: Sonic flow has a Mach number of one. In these types of flows, an object's velocity is equal to the velocity of sound in the local medium.
- Supersonic: The term "supersonic velocity" refers to an object moving faster than the speed of sound. It has a higher Mach number than one. Airplanes are designed in such a way that they can travel at supersonic speeds.
- Hypersonic: Hypersonic flow occurs when the speed of an object is substantially faster than the speed of sound. In this example, the Mach number ranges from five to ten.
- High-Hypersonic: Thermal controls become a significant aspect in design while flying at Mach levels of 10.0–25.0, as the hotness of the surface must be considered beforehand.
- Re-Entry Speeds: When Mach speed is greater than 25.0, the craft does not need wings and instead has a blunt shape.
Mach number and airplanes
To achieve the best results, aircraft are designed according to Mach number. In addition, we know that sound travels in waves. The traveling of these waves in an air medium is influenced by many elements such as air temperature and pressure. The Mach number is determined by the speed of sound in the gas, which is determined by the type of gas and its temperature.
In many equations for compressible flows, shock waves, and expansions, the Mach number appears as a similarity parameter. When conducting wind tunnel testing, the Mach number must be precisely matched between the experiment and the flight conditions. It's entirely erroneous to calculate a drag coefficient at a low speed (say 200 mph) and then apply it at twice the speed of sound (about 1400 mph, Mach = 2.0). The difference in physics between these two examples is due to the compressibility of air.
Mach Regimes
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Small disturbances are propagated downstream within a cone for supersonic and hypersonic flows. Mach angle is named after the trigonometric sine of the cone angle b, which is equal to the inverse of the Mach number M.
| sin (b) = 1/M |
A supersonic flow has no upstream influence; disruptions are only conveyed downstream.
Significance of Mach Number
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- Mach number provides information on a wide range of flow parameters.
- Mach number is a crucial metric for comparing the speed of any item to the speed of sound.
- It is a measurement for estimating the speed of a flying item in a fluid medium.
- It has multiple applications in fluid dynamics.
- Mach number is extensively studied in order to gain a thorough understanding of the motion of planes and rockets.
- When an airplane is flying through the sky, the air particles closest to the plane's body are disrupted.
- When an airplane travels at a faster speed, it compresses the air around it.
- By judging the Mach number, we can determine whether or not the fluid is compressible.
Read More:
| Learn More about Mach Number Related Concepts | ||
|---|---|---|
| Derivation of Continuity Equation | Fluid Flow | Value of R in atm |
| Critical Velocity | Buoyant Force | Density |
| Surface Tension | Stokes’ Law | Venturi-meter |
| Bernoulli’s principle | Hydraulic Machines | Hydrostatic Pressure |
| Pascal’s Law | Surface Energy | sphygmomanometer |
Things to Remember
- Mach number is the ratio of flow velocity when a given limit of sound speed has been reached. Simply put, it's the ratio of the body's speed to the speed of sound in the surrounding medium.
- Mach number is a measure of the compressibility properties of fluid flow: regardless of other variables, the fluid (air) behaves similarly under the effect of compressibility at a certain Mach number.
- It is generally used to determine how close a flow may be treated as an incompressible flow with a given approximation.
- In many equations for compressible flows, shock waves, and expansions, Mach number appears as a similarity parameter.
- Mach number is determined by the speed of sound in the gas, which is determined by the kind of gas and temperature of the gas.
Sample Questions
Ques. In a transonic flow, what is Mach number? (2 marks)
Ans. The flight Mach number approaches one, M = 1, when the object approaches the speed of sound, and the flow is described as transonic. The local speed of the object exceeds the speed of sound in some regions.
Ques. What is sonic boom? (2 marks)
Ans: A shock wave is created when an airplane flies faster than the speed of sound, which is supersonic. Major temperature and pressure shifts occur in this situation.
People on the ground hear a clap sound as a result of the shock effect. This is known as the sonic boom.
Ques. How does the Mach number change when the medium and height change? (3 marks)
Ans: Assume a plane is flying at the speed of sound in a medium of air. As the height changes, the speed of sound changes as well, resulting in a change in the Mach number.
As a result, the plane must adjust to the relative change in sound speed.
Ques. Define the importance of Mach Number. (3 marks)
Ans: The Mach number is a crucial parameter for comparing the speed of any item to the speed of sound.
- It's a measurement for expressing the speed of a flying object in a fluid medium.
- It has a lot of applications in fluid dynamics.
- Mach number is extensively studied in order to gain a thorough understanding of the motion of planes and rockets.
Ques. What is Mach number used for? (3 marks)
Ans: Mach numbers have many applications such as:
- Mach numbers are used for the assumptions on compressibility.
- It is used to evaluate the noise produced by aircraft and equipment.
- The Mach number is used to describe high-speed objects and high-speed fluid movement inside tunnels or nozzles.
Ques. What is the significance of Mach number in aviation? (3 marks)
Ans: Mach number describes the speed of sound and the point at which the airflow surrounding an airplane becomes incompressible, and it is constant regardless of height. This is due to the fact that the Mach number describes the speed of sound, which varies depending on the density of the medium through which it travels. As a result, the Mach number M or Ma can be used to describe flight regimes with varying compressibility effects.
Ques. With the help of Mach number, discuss incompressible fluids. (5 marks)
Ans: Incompressible fluids have the same density no matter how much they are compressed. Even if the pressure is changed, the volume remains constant. In fact, the volume change due to pressure changes is negligible. Fluids are said to be incompressible when the temperature remains constant. We know that change in pressure is proportional to change in velocity because of Bernoulli's theorem.
Mach number is connected to the change in velocity. If the Mach number is high, the fluid is compressible; if Mach number is low, the volume remains constant with changes in pressure, rendering the flow incompressible. In mechanical terms, if Mach number is less than 0.3, the flow is incompressible.
Ques. An airplane traveling at 1800 km/hr in the air with a pressure of 1 bar and a temperature of 10°. Calculate the Mach number. Given k =1.4 and R= 287 J/Kg.K (3 marks)
Ans: Temperature (t) = 10°
T = 10 + 273 = 283 K
Speed V = 1800 km/hr = 500m/s
Velocity, C = KRT = √1.4 × 287× 283 = 337.20 m/s.
Mach number will be = V/C = 500/337.20 = 1.48
Ques. A body traveling through fluid has a Mach number of 0.5. If the speed of sound is 345 m/s, what is the fluid's velocity? (2 marks)
Ans: Given Mach Number = 0.5
Speed of sound = 345 m/s
As the formula for Mach Number will be = M = V/C
0.5 = V/345
⇒ V = 0.5 * 345 = 172.5 m/s (Ans.)
Ques. If the Mach angle is 30°, calculate the bullet's velocity. Given that the ambient temperature is 22?, k =1.4 and R= 287 J/Kg.K (3 marks)
Ans: C = KRT = √1.4×287×295 = 344.52 m/s
As the formula for Mach angle will be =sin α =1/m
sin 30° = ½ = 0.5
M =2
So the velocity V will be = m*c= 2*344.5
= 689.04m/s (Ans.)
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