# Is Reynold's number really matter?

1. Oct 7, 2008

### Donny

Can I neglect it when talking about drag force or making a wind tunnel test? Why is it so important?

2. Oct 7, 2008

### Troels

Reynolds number is not something you can "neglect", that is a complete misconception.

Reynolds number arises when the Navier-Stokes flow equation is brought to dimensionless form and it is, roughly speaking a measure of inertial effect compared to viscous effects.

Reynolds number tells you what kind of flow you are dealing with, and thus, which *other* things you might neglect: If Re << 1 you have what is known as a viscous or laminar flow, and the convective terms in the NSeq may be dropped - nice thing!. If on the other hand you have Re >> 1 you have a inertial or convective flow, and things get a whole lot more nasty.

Reynolds number is quite important in calculation of drag, as the drag force in laminar flow scales as $$\sim v^{\phantom}$$ while in inertial flow it scales as $$\sim v^2$$ and only Reynolds number can give you an idea of which to use in you particular case

Last edited: Oct 7, 2008
3. Oct 7, 2008

### Donny

Interesting facts, I never know about that before.

You said that drag calculation was affected by Reynold's number, but how to get the right Reynold's number value when we are talking about wind tunnel and there is an object in it.

Is it true that different size of an object, temperature and speed condition in wind tunnel will give different Re?

4. Oct 7, 2008

### rcgldr

It's basically air speed times wing chord distance:

http://en.wikipedia.org/wiki/Reynolds_number

A lot of small, slow speed, wind tunnel smoke stream tests can give a false, overly laminar, impression of air flow across a wing, because the Reynolds number is too small.

5. Oct 7, 2008

### Andy Resnick

The Reynolds number can be defined several ways, one way is Re = $\frac{2\rho Q}{\pi \mu L}$ where $$\rho$$ is the fluid density (which can depend on temperature), $$\mu$$ the viscosity (which also depends on temperature), Q the volumetric flux of fluid (which will depend on velocity) and L a length scale.

The Reynolds number, like any dimensionless group, is used for several types of analysis. First, one can compare different geometries and fluid characteristics in a rational manner. Second, the relative importance of one phenomena with respect to another (viscosity vs. inertia, velocity vs. diffusivity, surface tension vs. gravity, etc...) can be related rationally and this gives insight as to what is the most important characteristic governing a system.

As an extreme example, ship designers can use flow chambers containing liquid helium as the fluid- the viscosity is near zero, so incredibly large Reynolds numbers can be simulated, corresponding to large ocean-going vessels. This allows the use of small-scale models that physically fit in the lab.

6. Oct 7, 2008

### FredGarvin

Last edited: Oct 7, 2008
7. Oct 8, 2008

### Donny

When working on a prototype or a small model can I assume in all condition the Reynold's number are the same? For example, same speed, same temperature, etc will result the same Re.

8. Oct 9, 2008

### Andy Resnick

Defintely not. Look at the definition of the Reynolds number I wrote above- if the size of the object changes, the velocity must also change, holding the other parameters constant.

The Reynolds number is a *combination* of parameters.

9. Oct 9, 2008

### Donny

oke thank you for your explanation.

And also whoever replied to this thread. I'll figure it now. ;)