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Understanding Reynolds Number

  1. Apr 27, 2009 #1
    Hey guys,

    I'm looking for a little help understanding Reynold's Number. I know that its the ratio of the inertial forces versus the viscous forces. With that being said, everywhere I look, the Reynold's Number is calculated for flow in a pipe or duct or across some sort of surface. Why can't the Reynold's Number be calculated for a random point? For example, if i was interested in the Reynold's Number of air after exiting an A/C duct how could one apply any of the general equations to that? The general equations all use some sort of characteristic length or diameter to make the calculations.
    I assume air (since it is viscous) will have some effect on flow that is introduced into is (such as air exiting a duct), so I would assume there has to be a way to calculate the Reynold's Number for air (knowing the viscosity of the air and the velocity) that is not in any duct or tube or moving across any surface.

    Any help understanding this would be appreciated.

  2. jcsd
  3. Apr 27, 2009 #2
    Reynolds number isnt anything 'real' per se. Its just a non dimensional method of characterising the flow over something, as such it requires a characterisitc length.

    Things that dont have simple geomoetry can be defined by many Re numbers depending on where you take the critial length.

    Where you are going wrong is you are thinking that Re is a property of the fluid, which it isnt. Its a property of the flow.
  4. Apr 27, 2009 #3
    I do realize that Reynold's Number is not a property of the fluid.. but is dependant on the fluids properties.
    My confusion comes with determining the Reynold's number in an open environment such as a room or other open space where there are no defined boundaries where the flow exists.

    So if I were to measure the velocity of the flow out of an A/C duct at a distance of 1 meter from the exit of the duct, would I consider 1 meter to be the characteristic length?

    Thanks for helping.
  5. Apr 27, 2009 #4
    Yep I suppose you could, but the real question is why would you want to? What is intersting about the flow in free air after a duct?
  6. Apr 27, 2009 #5
    "Yep I suppose you could, but the real question is why would you want to? What is intersting about the flow in free air after a duct?"

    Well there is nothing interesting in particular. That was just an example I came up with to explain my question. It had just occured to me that there must be a way to measure flow in free air, but I couldn't seem to find anyplace that touched upon such an occurence.
  7. Apr 28, 2009 #6


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    To answer your question, it's quite simple really. You know the velocity, that can be measured. You also know the viscosity. That only leaves the characteristic length.

    Make it whatever you want. It can be the length of the room, the height of the room; your height, the height of the door, diameter of your car's wheels. It can really be whatever you want. The reason for this causes some (ok, maybe just me) a lot of confusion when reading literature. Different people use different characteristic lengths for various non-dimensional parameters.

    In short, when considering a Reynolds number, it is imperative that the characteristic distance is specified along with it.
  8. Apr 28, 2009 #7


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    Far away from a surface, there is very little shear, and consequently very little gradient in velocity or in pressure differential.

    At (in contact with) a surface, the velocity of the fluid parallel to the surface is taken as 0. This is because the atoms/molecules are in contact (interacting) with the surface. As one moves away from the surface, the velocity increases to the 'free stream' velocity, so there is a gradient, and that is related to the viscosity of the fluid.
  9. May 1, 2009 #8
    When there is risk of ambiguity, absolutely.
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