Dear Sharma,

There are other empirical relations can be used to find out friction factor other than you have mentioned , like ,Haaland equation, in which friction cefficient is expressed in terms of relative roughness and Reynolds number and also Swamy Jain equation , 

With regard your studies, criteria for deciding roughnress of the pipe is to be given imporatance rather than the type of the flow, whether the flow is laminar or turbulant.

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These are only the quick opinions. (1) Many relations are available for the calculation of friction factor; the selection of relation is based on accuracy, precision and simplicity for calculation purpose. Please take note of the term ‘accuracy’ here that essentially means that certain degree of deviation can be expected in the computed value. (2) What matters is how the fluid feels about the pipe surface under given flow scenario rather than what it appears to us.  

Dear Sharma, To answer your question in short, there is no effect of roughness in determining the friction factor in laminar regime. You can still have laminar regimes in rough pipes but as long as Reynolds Number is less than 2100, the relative roughness will have no effect on the friction factor... Instead only f = 16/Re will hold.

Laminar flow is independent of pipe roughness due to the fact that the flow is stratified and covers the roughness. It then behaves like a flow along smooth walls.

The situation is different, if the flow gets turbulent. A very small roughness could be covered completely by the laminar sublayer. This can be possible at Reynolds numbers slightly above the kritical Re-number of 2300 (for pipes). Then the roughness is unimportant.

But the laminar sublayer decreases with increasing Re-number. Therefore at high Re-numbers the laminar sublayer does no longer cover the roughness. In this case pipe roughness becomes important. Friction factor can then be determined by Blasius law or Nikuradse diagram (for pipes) or newer correlations.

For turbulent flow you may use 

For turbulent flow you may use power law or logarithmic law for rough surface.

use power law model for rough surface.

Dear Deewakar.

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Maybe you're in a conceptual confusion that is taking you to some problems.

There are no rough or smooth pipes, which there is SMOOTH TURBULENT FLOW or ROUGH TURBULENT FLOW. Do not forget to TURBULENCE is a characteristic of the flow, not the tube or fluid.

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The wall roughness of a conduit by itself does not define a tube as smooth or rough. Therefore if the Reynolds Number (Newtonian fluids) or Apparent Reynolds Number (non-Newtonian fluids) define a flow as laminar, roughness is not taken in question.

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If you look the book: Handbook of Hydrulic Resistence, IDELCHIK, you will see that even in Corrudated pipes, below a certain Reynolds number the macro-roughness are not considered. Even suggest that you read the second chapter of this book. Even in the third edition, item 14, page 77 is clearly written to answer your question:

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“14. The first regime, called the laminar regime, involves small values of the Reynolds number (up to Re≈2000) and is characterized by  being independent of roughness….”

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Just a little note to everyone, after working Helmut ECKELMANN, "The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow" the notation "laminar sublayer" was abandoned and the correct use is "viscous sublayer". It is only a question of notation, but the phenomenon in viscous sublayer there is strong turbulence relating to local mean velocity, see the conclusion (v) the work Ekelmann:

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"v) Highly intermittent instantaneous values of the Reynolds stress in the vicinity of the wall, with peaks of more than 30 times the mean vaIue, were observed.....".

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I.e., laminar is a word reserved for non-turbulent flow, on viscous sublayer turbulence is present!

@Deewakar, The curious trend on Research Gate seems to continue in the answers to this question also. Some ‘limited’ answers are voted up and some decent answers are voted down.

Some teachers elide over conceptual answers to this question, perhaps because it is too simple for words; or more likely, because they do not know.

Rogerio is right that turbulence is a characteristic of the flow, not the tube or fluid. However, in a given situation, using pipe roughness is convenient as an engineering approach. Similarly, using the classical, familiar term ‘laminar sublayer’ is no crime as everybody understands that it implies ‘viscous sublayer’.

Others have given advice on what formula to use. My intention is not to add to the list but to assist you to get a more fundamental understanding of flow phenomena; it will help you to reason out on your own. Therefore I try giving you a qualitative answer here.

Roughnesses act like miniature bluff bodies and cause local separation and disturbance in the flow. These disturbances are effectively suppressed by the high velocity gradients (and shear) between the stratified layers in laminar flow. This is why we see that all lines for different ε/D collapse to a single line in laminar flow.

Ms. Schröder has given a valuable hint in these words: ‘A very small roughness could be covered completely by the laminar sublayer….. At high Re-numbers the laminar sublayer does no longer cover the roughness’.

With such suppression absent in turbulent flow (except for turbulence of small scale), the disturbances escape into the main fluid. The energy absorbed by the turbulence elements (I advisedly avoid using the term eddies as it means different things to different people) is felt as shear which is transmitted towards the wall as higher friction, the factor corresponding to which interests you here.

Thanks to von Karman, we know that turbulence is a near-wall phenomenon. So it is the roughness size (which determines the scale of the turbulence) rather than the mean velocity (on which you define Re) that affects the friction factor.

What is ‘small’ roughness in pipes of ordinary size can be considerable in mini- and microchannels. That is why the transition Reynolds number in these passages is well below the traditional value of 2100.

Thank you all for kind explanation.

@ Vijay

I have one query to your reply.

As per your explanation (kindly correct if I am wrong in interpreting ) when the Re is low (case of laminar flow) the roughness elements are not significant just like in case of bluff bodies placed in free stream where  there is no flow separation and flow moves along the bluff body,

With increase in Reynolds number, the roughness elements can be exposed or covered by laminar sub-layer, the thickness of laminar sub-layer being inversely proportional to Re.

Towards the end you have mentioned that in micro / -mini channels, the small relative roughness may also be quite significant. Why is it so? Though intuitively it makes sense as the roughness elements which may not be hold significant dimensions at macro-pipes may do so in micro/mini channels. However as you mentioned (and was mentioned by @ Rogerio) that its the Re which will decide whether pipe is rough or not (and hence roughness is significant or not) what is happening at such scale to make even small roughness predominant? 

Dear Vijay Raghavan.

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When you give an answer to a question posed in a general manner, the answer must also be generic and closer to its formulation. This may seem a response from a teacher and not an engineer, but as work on two tasks for almost 40 years, I know that is not maintained the scientific rigor in the presentation of concepts, since incomplete formulations induce the recipient to reply to maintain mistaken views for special situations.

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Language itself and notation used by the questioner, shows that it is concerned with current problems in engineering.

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I think there is more than one engineer response than proposing to whom questinou reading a basic and essential text for any head loss study as the "Handbook of Hydraulic Resistance" of IDELCHIK, which is easily accessible to anyone both in its editions in English, as the oldest in French and Russian.

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Using your quote on nanotubes in your answer, it is clear for this special case of the conduit called viscous sub-layer by laminar sub-layer leads to a characteristic error of the flow behavior in these singular structures. The concept of "slip length", still in development becomes completely anachronic if it were not possible to consider that in areas closer to the wall has a region in turbulent flow, effects of molecular orientation of the fluid particles, or other influencing directly turbulence have to be considered.

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The physical model (and mental) assuming the presence of a laminar sub-layer induces the impression of a flow ordered in layers that would bypass the gently involved in any industrial pipe roughness, leaving no room for interpretation of the effects of fluid-structure interaction important in nanotechnology.

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In summary, to a simple question we also need simple answers, but with enough conceptual rigor, as simplifications or mental models that do not correspond to reality induce future errors.

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Thanks Rogerio. It seems to me that you are agreeing with my response which, IMHO, addresses both the fundamental and engineering aspects.

I have been researching mini- and microchannels and can speak with a degree of certainty about them. I did not touch upon nanochannels in my response at all as I am not qualified in the same way to talk confidently about them. All I know is that there are a whole lot of theories to explain the empirical observations and each protagonist is a fan of his own theory. When the dust settles and the controversy ends, we will know for sure what is what. Till then, I shall keep mum on nanochannels and nanofluids :)

@ Vijay

I am waiting for response reg micro/-mini channels. If you may kindly respond to that,

Thanks

@Deewakar

The effect of wall roughness in micochannels is discussed controversy.

Experiments in channels of rectangular aspect ratio show that:

"The pressure drop correlations, in both the laminar and the turbulent

regime, agree reasonably well with the theoretical and

empirical correlations found for macroscopic channels."

You can find this statement and the experiments on laminar, transition and turbulent, incompressible flow in following article:

Wolf Wibel & Peter Ehrhard (2009) Experiments on the Laminar/Turbulent Transition of Liquid Flows in

Rectangular Microchannels, Heat Transfer Engineering, 30:1-2, 70-77, DOI: 10.1080/01457630802293449

I attach the article as pfd.

Please go through the article I put together to address this very question:

https://www.htri.net/uploads/docs/HTA-1__Effect_of_roughness_Friction_factor.pdf