Relationship between Mach number and Reynolds number

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Discussion Overview

The discussion explores the relationship between Mach number and Reynolds number, focusing on their definitions, implications in fluid dynamics, and the effects of viscosity in high-speed flows. Participants examine whether there is a correlation between these two nondimensional numbers and the conditions under which high-speed flows may be turbulent.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that there is no direct relationship between Mach number and Reynolds number, noting that both involve velocity but serve different purposes in fluid dynamics.
  • It is proposed that it is incorrect to generalize that high-speed flows are turbulent, with one participant suggesting that compressibility can stabilize a boundary layer.
  • Questions are raised about the classification of fluid viscosity, specifically whether dynamic or kinematic viscosity is more relevant, with a consensus that dynamic viscosity is typically considered.
  • Participants inquire about the implications of high-speed flow of very viscous fluids and how this relates to viscous effects in hypersonic flow.
  • Mathematical expressions are presented to relate Reynolds number and Mach number, but some participants express skepticism about the usefulness of these relations, particularly due to the presence of the speed of sound term.
  • One participant suggests that Reynolds number can be considered directly proportional to Mach number under the condition of constant speed of sound, but this is noted to be equivalent to stating that Reynolds number is proportional to velocity.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between Mach number and Reynolds number, with no consensus reached on whether they can be directly correlated. The discussion remains unresolved regarding the implications of viscosity in high-speed flows.

Contextual Notes

Participants highlight the complexity of the relationship between Mach number and Reynolds number, noting that assumptions about fluid properties and flow conditions may affect interpretations. The discussion also reflects uncertainty regarding the significance of mathematical relationships presented.

charlies1902
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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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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.
 
Also, what if you have high speed flow of a very viscous fluid?
 
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?
 
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
 
Kinematic viscosity is really more of a mathematical tool than anything else.
 
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?
 
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?
$$Re=\frac{\rho v D}{\mu}=\frac{\rho c D}{\mu}\frac{v}{c}=Ma\frac{\rho c D}{\mu}$$
 
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.
 

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