Super Easy Reynolds Number Question

[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!

 

[SteamKing]

It depends on the flow situation. For flow inside pipes, the RN is based on the ID of the pipe.

 

[boneh3ad]

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.

 

[member 428835]

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.

 

[SteamKing]

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

 

[boneh3ad]

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.