Super Easy Reynolds Number Question

In summary, Reynolds number is a dimensionless number used to characterize the flow of a fluid. It is calculated by dividing the inertia forces by the viscous forces, represented by the equation \frac{ L V}{\nu}. The value of L, the characteristic length, can vary depending on the problem being studied. For example, for flow inside pipes, the characteristic length is the inner diameter of the pipe, while for a flat plate, it is the length of the plate. Other common characteristic lengths include the boundary layer thickness, momentum thickness, roughness height, and Blasius similarity variable. Ultimately, the choice of characteristic length depends on the application and what makes the most sense for the problem at hand. Reynolds number has no direction and
  • #1
member 428835
hey pf!

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

thanks!
 
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  • #2
It depends on the flow situation. For flow inside pipes, the RN is based on the ID of the pipe.
 
  • #3
For Reynolds number, the value of [itex]L[/itex] 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 [itex]x[/itex]-location on the plate. For an airfoil you often see a similar phenomenon, only using [itex]c[/itex], the chord length (chord Reynolds number). Another common few that you will see is [itex]\delta[/itex], the boundary layer thickness, [itex]\theta[/itex], and the momentum thickness, [itex]k[/itex], some roughness height. One that I use a lot in my line of work is [itex]\delta_r = \sqrt{\nu x/U_{\infty}}[/itex], which is related to the Blasius similarity variable ([itex]\eta = y/\delta_r[/itex]). You will also, as mentioned before, see pipe diameter and sphere diameter and all sorts of other numbers. It just depends on the application.
 
  • #4
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.
 
  • #5
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
 
  • #6
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.
 

1. What is the Reynolds number?

The Reynolds number is a dimensionless number used in fluid mechanics to characterize the ratio of inertial forces to viscous forces within a fluid flow. It is named after Osborne Reynolds, a British physicist who first described it.

2. How is the Reynolds number calculated?

The Reynolds number is calculated by multiplying the fluid density by the fluid velocity, by a characteristic length of the system, and dividing the result by the fluid viscosity.

3. What does the Reynolds number tell us about a fluid flow?

The Reynolds number can tell us whether a fluid flow is laminar or turbulent. A low Reynolds number indicates a laminar flow, where the fluid particles move in parallel layers with little mixing. A high Reynolds number indicates a turbulent flow, where the fluid particles move in a chaotic manner with high mixing.

4. What is the significance of the Reynolds number in practical applications?

The Reynolds number is important in determining the behavior of fluid flow in various applications, such as in pipes, pumps, and aircraft design. It helps engineers and scientists predict how the fluid will behave and make informed decisions when designing systems.

5. Is there a critical value of Reynolds number for transitioning from laminar to turbulent flow?

Yes, there is a critical value known as the Reynolds number for transition. This value varies depending on the specific system, but it is generally accepted that a Reynolds number above 4000 indicates a turbulent flow.

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