# Relationship between Mach number and Reynolds number

1. Nov 27, 2015

### charlies1902

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?

2. Nov 27, 2015

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. Nov 27, 2015

### Staff: Mentor

Also, what if you have high speed flow of a very viscous fluid?

4. Nov 29, 2015

### charlies1902

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. Nov 29, 2015

### Staff: Mentor

When we talk about how viscous a fluid is, we are taking about its dynamic viscosity.

Chet

6. Nov 29, 2015

Kinematic viscosity is really more of a mathematical tool than anything else.

7. Nov 29, 2015

### charlies1902

I'd like to know this as well.

If we're talking about hypersonic flow, what does mean in regards to viscous effects?

8. Nov 29, 2015

### Staff: Mentor

$$Re=\frac{\rho v D}{\mu}=\frac{\rho c D}{\mu}\frac{v}{c}=Ma\frac{\rho c D}{\mu}$$

9. Nov 29, 2015

### charlies1902

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. Nov 29, 2015

### Staff: Mentor

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. Nov 29, 2015

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.