Relationship between Mach number and Reynolds number

In summary, Mach number and Reynolds number are both nondimensional numbers that involve velocity, but they do not have a direct relationship other than both featuring velocity. The classification of a fluid's viscosity is typically based on its dynamic viscosity. When discussing hypersonic flow, there may be significant viscous effects, but the relationship between Mach number and Reynolds number does not directly indicate this. Additionally, the relationship between Mach number and Reynolds number is dependent on the speed of sound, making it difficult to directly compare the two.
  • #1
charlies1902
162
0
Is there any correlation between Mach number and Reynolds number?
Both of these nondimensional numbers involve speed, but they don't seem all that related other than that.
For high speed flow, we have high Mach number. Is it incorrect to say that "generally" high speed flow is turbulent?
 
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  • #2
There is no relationship other than both of them feature the velocity.

It is incorrect to say that generally high speed flows are turbulent. In fact, the effect of compressibility is stabilizing to a boundary layer.
 
  • #3
Also, what if you have high speed flow of a very viscous fluid?
 
  • #4
boneh3ad said:
There is no relationship other than both of them feature the velocity.

It is incorrect to say that generally high speed flows are turbulent. In fact, the effect of compressibility is stabilizing to a boundary layer.
When we classify how "viscous" a fluid is, do we typically look at the dynamic or kinematic viscosity?

Water is regarded as more viscous than air. It's dynamic viscosity is higher than air, but it's kinematic viscosity is smaller. So I guess we look at dynamic viscosity?
 
  • #5
charlies1902 said:
When we classify how "viscous" a fluid is, do we typically look at the dynamic or kinematic viscosity?

Water is regarded as more viscous than air. It's dynamic viscosity is higher than air, but it's kinematic viscosity is smaller. So I guess we look at dynamic viscosity?
When we talk about how viscous a fluid is, we are taking about its dynamic viscosity.

Chet
 
  • #6
Kinematic viscosity is really more of a mathematical tool than anything else.
 
  • #7
Chestermiller said:
Also, what if you have high speed flow of a very viscous fluid?
I'd like to know this as well.

If we're talking about hypersonic flow, what does mean in regards to viscous effects?
 
  • #8
charlies1902 said:
I'd like to know this as well.

If we're talking about hypersonic flow, what does mean in regards to viscous effects?
$$Re=\frac{\rho v D}{\mu}=\frac{\rho c D}{\mu}\frac{v}{c}=Ma\frac{\rho c D}{\mu}$$
 
  • #9
Chestermiller said:
$$Re=\frac{\rho v D}{\mu}=\frac{\rho c D}{\mu}\frac{v}{c}=Ma\frac{\rho c D}{\mu}$$
Hmmm, but does this relation tells us much?
Can we directly say that that Reynolds number scales with Mach number?
I don't think so because there's that extra speed of sound term in the numerator.
 
  • #10
charlies1902 said:
Hmmm, but does this relation tells us much?
Can we directly say that that Reynolds number scales with Mach number?
I don't think so because there's that extra speed of sound term in the numerator.
Why don't you just run some calculations for some sample situations, and see what the Mach number and Reynolds number come out to be. Then you won't need to speculate.

Chet
 
  • #11
You can say that it is directly proportional to Mach number for a constant speed of sound. Of course this doesn't mean much as it is equivalent to saying that Reynolds number is directly proportional to velocity, which is true by definition.

What exactly is your question about "what does it mean in regards to viscous effects"? I'm not sure I follow what you are trying to ask so I'm not quite sure how to respond.
 

Related to Relationship between Mach number and Reynolds number

1. What is the relationship between Mach number and Reynolds number?

The Mach number is a dimensionless quantity that represents the speed of an object (such as an aircraft) relative to the speed of sound in the surrounding medium. The Reynolds number is also a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a fluid flow. The relationship between Mach number and Reynolds number is that as the Mach number increases, the Reynolds number also increases, indicating a transition from laminar to turbulent flow.

2. How do Mach number and Reynolds number affect aerodynamics?

Mach number and Reynolds number have a significant impact on aerodynamics. As Mach number increases, shock waves and compressibility effects become more prominent, which can create higher drag and affect the overall performance of an aircraft. Additionally, as Reynolds number increases, the flow may transition from laminar to turbulent, which can also impact the aerodynamic characteristics of an object.

3. Is there an ideal Mach number or Reynolds number for aerodynamics?

There is no specific ideal Mach or Reynolds number for aerodynamics. The optimal values depend on the specific application and design goals. For example, supersonic aircraft typically have higher Mach numbers, while subsonic aircraft operate at lower Mach numbers. Similarly, the Reynolds number may vary depending on the size and shape of the object in question.

4. How does Mach number and Reynolds number impact the design of aircraft?

The relationship between Mach number and Reynolds number is an important consideration in aircraft design. High Mach numbers may require specialized materials and designs to withstand the effects of compressibility. On the other hand, high Reynolds numbers may require the use of turbulence models and other design considerations to account for the effects of turbulence on the aircraft's performance.

5. Can Mach number and Reynolds number be used to predict flow behavior?

Yes, Mach number and Reynolds number are important parameters in predicting flow behavior. In general, higher Mach numbers and Reynolds numbers indicate more complex and turbulent flow behavior. However, other factors such as geometry, surface roughness, and fluid properties also play a role in determining flow behavior, so these parameters should be considered in conjunction with Mach and Reynolds numbers.

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