Is the ratio of maximum to average velocity in a pipe flow the same for both the laminar as well as the turbulent models?
I tried solving a pipe flow problem using a CFD software but I got different values of the ratio for the two cases ie. Laminar and turbulent using k-epsilon model. Can anyone throw some light on this?
The (average!) velocity profile in a turbulent flow is more flattened than the parabolic profile in a laminar flow. Hence, the ratio is not the same; the maximum is higher in the laminar case.
The (average!) velocity profile in a turbulent flow is more flattened than the parabolic profile in a laminar flow. Hence, the ratio is not the same; the maximum is higher in the laminar case.
Laminar flow is strictly different from turbulent flow, hence the ratio of their mean velocity cannot be thesame. The ratio can be approximately same if the flow considered is fully developed
In laminar regime you have a quadratic solution on the velocity profile, that is a well known ratio of 3/2 between the maximum of the parabola and its area. Conversely, the mean velocity profile does not follow such 3/2 law as you can see from the theoretical law of the wall.
Turbulent velocity profile is different from laminar velocity profile. Hence, the ratio of maximum to average velocity in a pipe is not the same for both flows. For turbulent flow, the ratio is related to Reynolds number. Whereas, the average velocity in fully developed laminar pipe flow is one half of the maximum velocity. Please see the following file.
Thank you , friends, for your useful replies. Now it is much clearer to me although I am yet to discover an explicit relation for the ratio of maximum to average velocities. The pdf attached by Dr. Hossna Darabi is quite detailed and useful and as told by Cees Haringa, the velocity profile is much flatter. I think I might be able to find an explicit relation in some handbook.
For turbulent flow, maximum velocity is approximately 1.1 times average velocity. Whereas, the average velocity in fully developed laminar pipe flow is one half of the maximum velocity
The ratio of maximum to average velocity in a pipe flow for
laminar flow is 2
Turbulent flow 1.1 to 1.15
Mohsen, I appreciate your recommendation, but I would personally recommend the answers by Filippo and Sreekala, who took the effort to provide a more quantitative answer ;)
The velo ratio max/average under turbulent conditions depends on the Reynolds number. There is the Superpipe in Princeton and the Cottbus Large Pipe (CoLa) where the problem is studied, and there are enormous papers trying to understand the measurements, it's not trivial and very old unsolved problem as already mentioned by Feynman years ago in his "Six pieces ...". We could fly to the moon but a common water tube we cannot understand. A challenge for thinkers and maybe the solution can be found based on the attached paper. We are working about it ...
The ratio of maximum to average velocity in a pipe flow for laminar flow is is different of turbulent flow.
Due to the fact that the form of velocity distribution at the entrance of the pipe is different from other regions, Until the flow is fully developed.
Where it becomes a uniform velocity distribution.
Thank you Dr. Ziegfeld for the reference on the CoLa facility. I was not aware of it, and it can be very helpful for my research.
I'm not too sure what you are trying to achieve. The above responses have answered your question - the max./average velocity depends on your mass flow velocity, hence your Reynolds number. At low values the velocity profile is almost parabolic and at high values it is almost flat.
However if you need this information to more precisely define pressure drop in a line then there are several correlations available based on observations over various pipeline lengths. The liquid ones are quite accurate if one accepts that they are applicable over a defined length range. Many of the early ones are based on water whose properties (viscosity, density, etc.) are not the same as those for hydrocarbons. One observation is that pipelines follow the contours of the land so measured values of pressure drop contain a head variation component.
If you are looking at gas flow range then there are many empirical expressions available, all applicable to a limited range. There is much information on this correlated by the various trade associations, especially that for natural gas.
If you are looking at mixed flow (gas/liquid or even boiling) then you have a lot of reading to do. Much has been said but their is no universal formula (yet).
If you need this data to predict heat transfer parameters then you are looking into turbulent flow to increase heat transfer rates. Laminar flow may be associated with low pressure drop but also with low heat transfer. You need mass movement to get the heat from the wall to the central core. If the flow velocity is low, then mechanical augmentation is sometimes used, though this is not popular in fouling service.
I hope that this response is not too long.
Thank you all for your answers. I have got the answer from your responses.
Just as suggestion, consider the velocity profile u+(y+) obtained from DNS at several Re_tau numers. You can compute the integral of u+ along y+ to get the area and take the value of u+ max at y+=Re_tau. Do that for some Re_tau values and compute the ratio.
As complements to previous replies, I think the additions below can be useful specially for quantitative estimations.
The velocity profile for laminar flow is the well-known parabolic form
u(r)/umax=2(1-r^2/R^2)
The resulting average velocity is one half of the maximum velocity
uav/umax=0.5
For turbulent pipe flow among the numerous empirical velocity profiles, the simplest and the best known is the power-law velocity profile expressed as
u(r)/umax=(1-r/R)^1/n
where R is the pipe radius and n is a parameter (exponent) which depends of the Reynolds number i.e. n=n(Re).
An empirical approximation of this dependence can be expressed as
n(Re)=c·ln(Re)
where c=0.62 for Re≤2·Re^5 and c=0.65 for Re>2·Re^5
Based on this approach on obtained the following relationship between the average velocity and maximum velocity for turbulent flow
uav/umax=2n^2/(n+1)(2n+1)
It is to mention that
-the value n=7 is applicable to a wide range of pipe flows and is the one commonly used resulting uav/umax=0,817
-the empirical power law cannot be used to calculate the wall shear stress!!
The original question asked for the relationship of the peak to average velocity in pipe flow in laminar versus turbulent flow regimes, to which many have replied saying that the velocity profile changes with Reynolds Number. However many empirical relationships exist with pipe flow problems hence my question on application of this knowledge.
For example, to predict the pressure drop in gas pipelines there are several expressions which all give different results for a fixed set of conditions but but each give a reasonable approximations to reality over a unique limited (different) range. These expressions include:
(i) General flow equation
(ii) Weymouth
(iii) AGA
(iv) Colebrook-White
(v) Panhandle A
(vi) Panhandle B
(vii) IGT plus many more.
If you wish to operate on a smaller scale, you could add heat transfer and changes in phase and really complicate matters.
The ratio of maximum to average velocity is higher for laminar since the profile of velocity for turbulent flow is more flat compared with laminar.
The ratio is not the same; the maximum is higher in the laminar case.
The laminar and turbulent flows should have different average velocities because they use different models, and they also have different velocity profiles within the pipe.
You will need to check your Reynolds number to know which case is the "real" case. The computer will apply the equations you tell it to (laminar or turbulent), but it's our job to know which equation to apply for the situation.
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