As far as I understand that you want to predict a flow in a microchannel (whether it is a turbulent or laminar). First, A flow in a microchannel is always a laminar flow so the Reynolds number is well within the limits(you can validate it by plugging in all the values of rho, mu, L and u).

Since I am unable to understand what and how are you plotting a Re and f (what is f?). I would suggest using Particle Image Velocimetry (PIV) to measure the flow of microbeads inside your channel.

Yes, it is indeed a very fundamental concept. 

You can define 'f' the same way for the entire range of flow from laminar to turbulent.

Reynolds' classical experiment consisted of injecting a streak of dye and visualizing it.

In turbulent flow, the dye mixes across the channel in short order while in laminar flow, the streak persists for a long distance.

Visualizing flow in a transparent microchannel may be impractical. PIV is even more so. 

It certainly is possible to have turbulent flow in microchannel, but in applications, the pressure drop will be so high as not to be economical.

I suggest you look up the graphs of f vs Re in the old classic 'Compact Heat Exchangers' by Kays and London. It will tell you all that you want to know. 

If possible plot vvelocity profile across the pipe.If you can not plot velocity profile try to detect pipe vibration as turbulent flows induced vibration in pipe

Hi all,

Thanks for your kind replies. I would like to seek some further clarification. When we say at micro scale there is deviation or transition to turbulent flow at some lower Reynolds number, my concern is how do we say that. 

Recently I came across a text in F M White text book for literature which said that if Pressure drop is directly proportional to Average velocity then flow is laminar. However when it is a quadratic fit or some other fit like V^(0.75) we say it us turbulent.

Any comments on this approach.

This question has already been answered in my earlier post. It is difficult to reproduce figures or formulae here, hence I suggested you to see the book by Kays and London.

DelataP is indeed represented by f and a distinct change of slope in f vs Re, with or without transtion, occurs in the plot. It applies to microchannels also. This is by far the easiest and most accurate method compared to the other suggestions here.

Now please go look for that book. 

I would say they can be specified from the velocity oscillation.

Measure the velocity of the liquid at the end of the pipe, and then:

1. Calculate the Reynoldsnumber Re : velocity* length/ viscosity.

2. If Re< 1 check Hagen-Poiseuille law by measuring the throughput  mass/sec.

Literature: Landau/Lifshitz "Hydrodynamics".

Wilfried's answer has the following problem.

In the first place you do not know the transition Reynolds number. It decreases as passage dimension decreases. If you do not know transition Re, you cannot find if the flow is laminar or turbulent by calculating the Re no.

If you do know what is the transition Re, you already have the answer you want and do not need Wilfried's or anyone else's answer.

What I had suggested works, irrespective of whether the channel is of normal dimensions or a minichannel or a microchannel. If you cannot find the book, I will photocopy a page from the book (if there are no violations of copyright) and attach in my next post.

THe discussion here is not leading anywhere , it is a meer waste of time

I agree with Mohamad Afifi in respect of a majority of the answers. I did not want to upload my own publication that gives completely adequate answers to Deewakar Sharma's question, considering the copyright issues with the publisher.That is why I suggested Kays and London's book.

I suggest that Sharma look up my paper (Afifi too, if he is interested) R. Tiruselvam, Vijay R. Raghavan, Double tube heat exchanger with novel enhancement: part I—flow development length and adiabatic friction factor, Heat Mass Transfer (2012) 48:641–651. In particular, see Figs 9 through 13.

If Sharma is unable to get a copy of the paper, he might make a request through RG and

I can send him the authors version privately through RG.

That is a positive answer

Dear All,

May be I misunderstood the question, but the difference between the turbulent and laminar flows, in general, is very easy to distinguish... Just look at them.

I am doing DNS of turbulent flows and I am checking my numerical resultls against experimental ones... I am doing DNS of plane channel and boundary layer flows and I know if I take, for example, Re=750 for Couette flow, which corresponds approximately to Re_tau = 51, then I know that I will get turbulent flow...

I am sorry if I am completely out of the discussion. But from the title of the question, this came to my mind :)

george

Dear all, 

Thanks for kind response and answers.Couldn't check this for long.

@Vijay I have download the research article and will go through it and get back in case there are any queries further.

Thanks

Sure Deewakar, you are most welcome.

Reynolds no. is the ratio of viscous force to inertial force.

Re= density*velocity*characteristic length/kinematic viscosity

Re

From experimental data for a pipe assuming fully developed flow, if Reynolds number is less than 2000, the flow is taken to be compulsorily laminar, transition occurs between 2000-4000 and turbulent occurs compulsorily at greater than 4000. Reynold conducted an experiment with valve fitted to a pipe and introducing dye in water. As the valve is opened gradually, he observed the laminar flow converting to turbulent and also turbulent flow converting to laminar when he slowly closed the valve. Upon all the considerations, it is now taken granted that for flow through pipe less than 2300 is laminar flow and greater than 2300 is turbulent.

Laminar flows and turbulent flows.

Laminar flow occurs when the fluid flows in infinitesimal parallel layers with no disruption between them. In laminar flows, fluid layers slide in parallel, with no eddies, swirls or currents normal to the flow itself. This type of flow is also referred to as streamline flow because it is characterized by non-crossing streamlines.

In turbulent flow vortices, eddies and wakes make the flow unpredictable. Turbulent flow happens in general at high flow rates and with larger pipes.

The flow is

• laminar when Re < 2300
• transient when 2300 < Re < 4000
• turbulent when 4000 < Re

I think the Re ranges which are presented are for the cases that have been studied before. When you want to know if your flow (maybe a new unknown case) is laminar or turbulent, the Turbulence Intensity is an appropriate criterion. This is just my opinion! Correct it please, if you think that is wrong!