Super Easy Reynolds Number Question

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Discussion Overview

The discussion revolves around the calculation of the Reynolds number, particularly focusing on the appropriate choice of characteristic length (L) in various flow situations, such as around a plate or within a pipe. The scope includes theoretical considerations and practical applications in fluid dynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that for a plate of length 20 ft, L could be 20, but questions whether this is always the case.
  • Another participant states that the choice of L depends on the flow situation, noting that for flow inside pipes, L is based on the inner diameter (ID) of the pipe.
  • A different participant explains that L is a characteristic length that varies depending on the phenomenon being studied, mentioning various lengths used in different contexts, such as the length of the plate or the chord length for airfoils.
  • One participant expresses confusion about how pipe diameter can be relevant, arguing that forces are primarily perpendicular to the cross-section, questioning the application of Reynolds number in this context.
  • Another participant clarifies that Reynolds number does not have a direction and emphasizes that the choice of characteristic length is based on convenience for scaling equations or results.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate choice of characteristic length for calculating Reynolds number, indicating that there is no consensus on a single approach. The discussion remains unresolved regarding the implications of using different lengths in various flow scenarios.

Contextual Notes

Participants highlight that the choice of characteristic length can depend on the specific application and flow conditions, suggesting that there may be limitations in generalizing the use of L across different scenarios.

member 428835
hey pf!

when it comes to calculating the reynolds number, i realize it is defined as \frac{inertia forces}{viscous forces}=\frac{ L V}{\nu} thus, if we have a plate of length 20 ft. with fluid flowing around it, would L=20? if so, is this always the case? would we always have L=the length of the object?

thanks!
 
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It depends on the flow situation. For flow inside pipes, the RN is based on the ID of the pipe.
 
For Reynolds number, the value of L is just a characteristic length for the problem at hand. What length you choose depends on the phenomenon you are trying to study. For flat plate, you often see the length of the plate for a total length Reynolds number or just use the x-location on the plate. For an airfoil you often see a similar phenomenon, only using c, the chord length (chord Reynolds number). Another common few that you will see is \delta, the boundary layer thickness, \theta, and the momentum thickness, k, some roughness height. One that I use a lot in my line of work is \delta_r = \sqrt{\nu x/U_{\infty}}, which is related to the Blasius similarity variable (\eta = y/\delta_r). You will also, as mentioned before, see pipe diameter and sphere diameter and all sorts of other numbers. It just depends on the application.
 
thanks for the replies! but bonehead, how would pipe diameter work? wouldn't we (mostly) have no forces working parallel to the diameter (or cross section)? i mean, inertial forces take us forward and viscous take us backward, but it seems both of these are perpendicular to the cross section.
 
joshmccraney said:
thanks for the replies! but bonehead, how would pipe diameter work? wouldn't we (mostly) have no forces working parallel to the diameter (or cross section)? i mean, inertial forces take us forward and viscous take us backward, but it seems both of these are perpendicular to the cross section.

This article derives Reynold's Number for pipe flow:

http://en.wikipedia.org/wiki/Reynolds_number#Flow_in_pipe
 
Reynolds number has no direction. It is all about what you wish to use (or what comes naturally) to scale your equations or results. Different problems have different naturally convenient characteristic length scales.
 

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