Understanding Reynold's Number & Characteristic Length

[nanunath]

Hello...
Reynold's Number is given by:

where:
is the mean fluid velocity (SI units: m/s)
L is a length of the object that the flow is going through or around (m)
μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/m/s)
ν is the kinematic viscosity (ν = μ / ρ) (m²/s)
is the density of the fluid (kg/m³)
Q is the volumetric flow rate (m³/s)
A is the pipe cross-sectional area (m²)
{Taken from wikipedia:http://en.wikipedia.org/wiki/Reynolds_number" }

What I don't get is "Characteristic Length"...how do I decide it for a particular flow??
Wikipedia says its just conventionally taken..diff people can take diff chacteristic lengths...
Why??How?

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Also...does choice of characteristic length have any connection with the nature of viscous forces...if yes how?
Plz help me on this ... I have bee through few boooks ... but unable to understnd how to decide the "Characteristic length"...I mean why we should take "diameter" only for a tube...why not radius??..and if I take radius[the non-conventional way]...what is the effect...what am I exactly doin?

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Thirdly...
For a shell and tube heat exchanger ...how do I decide the characteristic length...because I had been through a paper on Shell and tube Heat exchangers..in which the Reynold's number[Shell side flow!] is given by:
R_e=[density]*[mean velocity of flow]*[outer diameter of tubes!{not the shell!...why?}]/[mu]

Why is that the tubes outer diameter is considered for the shell side flow??
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In short my main question is : "How to decide the most suitable Characteristic Length"...
Plz help me on Heat exchanget question also...

Lastly:
Any views are most welcome...waiting for your relpies...
Thankssss in advance!

 

[LeonhardEuler]

There is some ambiguity in choosing L, but in any context where the value of Re is used, the symbol should be defined. Since flow in circular pipes is so common, you can assume they always mean the diameter in this context. Obviously, if you used the radius, you would be off by a factor of 2. There is no reason that the diameter is better than the radius, if the radius was the convention, then things like the onset of turbulent flow would just be a factor of two different.

There are definitely situations you could imagine where it is not at all clear what to choose. If there is some formula for such a situation that uses Re, it must define what L is or the formula is not useful.

Still, most of the time you can figure out what L should be to within a factor of 2. Generally, there is some characteristic length for the geometry where the flow occurs. If there is a sphere in a large channel, it is the diameter of the sphere. It there is a narrow duct, where one dimension of the duct (perpendicular to the flow) is much much larger than the other, it is the smaller dimension.

 

[Cyrus]

Characteristic length can be anything you want. It doesn't change the physics of the flow. You need a length when nondimensionalizing. It doesn't matter what characteristic length is used. If you're using performance data from a table, you have to use their convention of characteristic length for the data to be physically meaningful.

 

[nanunath]

Thanks a lot Cyrus & LeonhardEuler!....

Characteristic length can be anything you want. It doesn't change the physics of the flow. You need a length when nondimensionalizing. It doesn't matter what characteristic length is used. If you're using performance data from a table, you have to use their convention of characteristic length for the data to be physically meaningful

Thanks...that definitely answers my "Heat exchanger" question...
In fact that also tells why mostly a certain dimension is used as a characteristic length...

Generally, there is some characteristic length for the geometry where the flow occurs. If there is a sphere in a large channel, it is the diameter of the sphere. It there is a narrow duct, where one dimension of the duct (perpendicular to the flow) is much much larger than the other, it is the smaller dimension

Thanks...
I think I get the point...
but would really be happy if you guide me as to if "Viscous forces" play a role here...

Thanks a lot...

 

[Cyrus]

The role of viscos forces depends on the Reynolds number and the setup.

 

[nanunath]

Hmmm...thanks a lot once again...Cyrus...

I think this is going to be my last question on this:...
Question:
So when we learn from textbooks that the flow is laminar when R_e is less than 2000...similarly the transient and turbulent flow ranges for R_e...
What are the restrictions on using the above stated criteria for identifying a flow as laminar/transient/turbulent...[I think that range is specified for flow through pipe only..with diameter as characteristic length but not so sure...so please correct me]
as if I choose a certain characteristic length the non-conventional way this range for classifying the type of flow ,it won't be necessarily true...Right?..[It may sound dumb..and I'm so sorry for that...:shy:]

Also...
If I'm calculating R_e for some non common,non standard case...like shell side flow through a Shell-and-Tube-Heat-exchanger with a completely new type of baffle...that means...this flow is going to have its own range of R_e for classifying it into 1 of the 3 types of flow...so How do I decide this range for Laminar,transient,laminar flows for my non-standard case?...

 

[Cyrus]

Hmmm...thanks a lot once again...Cyrus...

I think this is going to be my last question on this:...
Question:
So when we learn from textbooks that the flow is laminar when R_e is less than 2000...similarly the transient and turbulent flow ranges for R_e...
What are the restrictions on using the above stated criteria for identifying a flow as laminar/transient/turbulent...[I think that range is specified for flow through pipe only..with diameter as characteristic length but not so sure...so please correct me]

You answered your own question.

as if I choose a certain characteristic length the non-conventional way this range for classifying the type of flow ,it won't be necessarily true...Right?..[It may sound dumb..and I'm so sorry for that...:shy:]

Right.

Also...
If I'm calculating R_e for some non common,non standard case...like shell side flow through a Shell-and-Tube-Heat-exchanger with a completely new type of baffle...that means...this flow is going to have its own range of R_e for classifying it into 1 of the 3 types of flow...so How do I decide this range for Laminar,transient,laminar flows for my non-standard case?...

Experiment or CFD (If this setup has never been done before)

You need to realize that the Re number is really just a nondimensionalization. That is to say, it has existence but not uniqueness. Look at the case of a pipe:

Re < 2000 = \frac{\rho V D}{\mu}

if we use a different characteristic length (holding all else constant), then the flow with this characteristic length will be laminar provided:

Re < 2000 \frac{D_{new}} {D}

 

[nanunath]

Exactly...thats what I had thought of..[thanks to you!]...
So that means...
Laminar/turbulent/transient flow will be decided by observing the flow patterns...
Like...if its through a circular pipe...the velocity distribution will be parabolic in laminar flow ...that would decide the range of the non-conventional R_e calculated for Laminar flow...followed by transient..then turbulent...right??
Which more factors [like velocity above]...would help me in deciding these ranges for R_e?...

 

[Cyrus]

Exactly...thats what I had thought of..[thanks to you!]...
So that means...
Laminar/turbulent/transient flow will be decided by observing the flow patterns...
Like...if its through a circular pipe...the velocity distribution will be parabolic in laminar flow ...that would decide the range of the non-conventional R_e calculated for Laminar flow...followed by transient..then turbulent...right??
Which more factors [like velocity above]...would help me in deciding these ranges for R_e?...

I think you need to go back and reread what I wrote.

 

[nanunath]

Ya...I Re-read it...
I understood that we got to use CFD[/experiment] for that...
But I don't know what CFD exactly does...so could you please tell me very specifically what factors [Which results from CFD...very specifically]...would help me in concluding about the type of flow...followed by range of R_e??

[It may sound that I'm asking repeated questions...but I'm doing so to get rid of the slimmest chance of interpreting your well-thought statements in the wrong way...I think]

I hope that question wasn't dumb enough..if it is..I'm sorry once again!

 

[Cyrus]

I don't think you caught on to what I was saying. If you use a different characteristic length, then transition will occur at a different Reynolds number. The only reason why this transition number is different is because of the difference in chracteristic length that was used. The difference is the ratio I gave above.

CFD and/or experiment is used when you don't already have data to look up. http://en.wikipedia.org/wiki/Computational_fluid_dynamics" solves for the flow. If you care about transition and boundary layers, you have to look at the time histories of the pressure at the walls. If they vary with time the boundary layer is turbulent. If they are constant, the boundary layer is laminar because the flow has low shear stresses.

Which book are you using for fluid dynamics? This should all be in there if your trying to do any kind of fluid analysis.

 

[nanunath]

If you care about transition and boundary layers, you have to look at the time histories of the pressure at the walls. If they vary with time the boundary layer is turbulent. If they are constant, the boundary layer is laminar because the flow has low shear stresses

Thanks..thats what I was seeking for...
I have used some local book for our subject "Fluid Mechanics" Academic course...but this all wasn't mentioned in there...the only thing I remember that was stressed on in that book was R_e expressed in the form of Inertia force/Viscous force...and velocity distribution in laminar flows...and some standard experimental relations for turbulent flow...
whats more surprising is that it never mentioned anything of R_e having no physical significance actually...nothing of the things you about R_e you enlightened upon me ...was mentioned in there...

Anyways..can you please recommend me a good Fluid Dynamics book...I think my book doesn't have all this...probably because the syllabus didnt have it[it was a local book specially compiled for our university syllabus]

If you use a different characteristic length, then transition will occur at a different Reynolds number. The only reason why this transition number is different is because of the difference in chracteristic length that was used. The difference is the ratio I gave above.

I think..I did get that ... u explained that from your very first reply very clearly...Thanksss...

Thanks a lot ...for all your help...

 

[Cyrus]

Thanks..that what I was seeking for...
I have used some local book for our subject "Fluid Mechanics" Academic course...but this all wasn't mentioned in there...the only thing I remember that was stressed on in that book was R_e expressed in the form of Inertia force/Viscous force...and velocity distribution in laminar flows...and some standard experimental relations for turbulent flow...
whats more surprising is that it never mentioned anything of R_e having no physical significance actually...nothing of the things you about R_e you enlightened upon me ...was mentioned in there...

Anyways..can you please recommend me a good Fluid Dynamics book...I think my book doesn't have all this...probably because the syllabus didnt have it[it was a local book specially compiled for our university syllabus]I think..I did get that ... u explained that from your very first reply very clearly...Thanksss...

Thanks a lot ...for all your help...

Get https://www.amazon.com/gp/product/0470067225/?tag=pfamazon01-20 book.

 

[minger]

Just for semantics here, since we're discussing the importance of specifying the characteristic length. Nanunath, when we write Reynolds number, both the capital R and lower case e are regular script. The subscript used then is often used to denote the characteristic length used. For example:
<br /> \begin{equation}<br /> \begin{split}<br /> Re_l &amp;= \frac{Vl}{\nu} \\<br /> Re_D &amp;= \frac{VD}{\nu}<br /> \end{split}<br /> \end{equation}<br />
...just something that was slightly bothering me.

 

[nanunath]

Thanks for correcting me..mginger...
Ok..I think that brings the thread to an end...
Final thanks to Cyrus..for valuble help...