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# Reynolds Number for Moving Wire

## Reynolds Number for Moving Wire

(OP)
I am wondering how you calculate the Reynolds Number, Re, for wire moving in a fluid. What characteristic dimension do you use; and what criteria do you use to determine a turbulent state?

My approach would be to use

Re = vD/viscosity(k)
v = velocity of wire
D = diameter of wire
viscosity(k) = kinematic viscosity
And to use the criteria for flow over a flat plate. Does anyone have any experience with this?

Thank You

Don
dleffingwell@snet.net

### RE: Reynolds Number for Moving Wire

I have not dealt with this particular issue, but if I understand your scenario correctly, one wire of cross section D moves through a fluid.  To model this mathmatically, you'd have to "pretend" that the fluid is moving over the wire.  Hence, your analysis seems correct.  The difficulty in using the flat plate model is that the wire does probably not allow enough surface to model the transition from laminar to turbulent flow before becoming turbulent due to collisions with the flow coming from the opposite side.  The aeronautical engineers have a different method to calculate the flow, with a cylinder as their model (circular cross section).  It is a rather involved process, and frankly I don't remember how to calculate it.  However, I'm sure there are materials out there to figure it out.

### RE: Reynolds Number for Moving Wire

(OP)
Thanks for your input. In this case the wire is moving with a velocity vector concurrent with the axial centerline of the wire. (Parallel to the length of the wire). After reviewing several books on convection heat transfer, and some other input from other forums, I concluded that the model for a flat plate was the right approach, with "L", the length of the wire being the characteristic dimension and Re, the Reynolds Number should be of the magnitude of 5 x 10^5 as a criteria for turbulent flow. Because I have not studied or used this type of analysis for 25 years, I was hoping that someone on the Internet having the experience could enlighten me. Out of 6 posts on differently located forums, and a dozen or so e-mails, yours is only the third response. One said I was right; the other gave the approach above. (Mike Lindeburg at  http://www.ppi2pass.com).

There are many references on the Internet for hot-wire anemometers, in which the flow is perpendicular to a cylinder. One site actually gives expressions for varying the flow from 90 degrees to almost parallel.

Donald Leffingwell
dleffingwell@snet.net

This site gives relationships for varying yaw angles

http://www2.eng.cam.ac.uk/~hph/current-research/hph/hot-wire/hot-wire.html

This site is titled: "Free and Forced Convection from a Heated Cylinder".  It uses experimental data and theory to demonstrate the concepts.

http://www.me.wustl.edu/ME/labs/thermal/me372b3.htm

Both are very good.

### RE: Reynolds Number for Moving Wire

For the situation you are giving, it is required to consider that the wire is stationary with fluid is moving 0ver on it. The criteria for determining Reynolds number is also absolutely perfect but it is necessary to consider if the fluid is moving through pipe or any other shaped component.Then accordingly the characteristic dimension will change.

### RE: Reynolds Number for Moving Wire

Your approach for calculating the Reynolds number is correct, but the critical value is going to be much smaller than for a flat plate, depending on how you define turbulence...  If you are looking at when you begin to get vortex shedding, the critical Re is around 35.  There is also a critical point where the boundary layer becomes turbulent and the drag coefficient suddenly drops.  For a cylinder, your value of 5e5 is correct.

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