Looking at the Moody chart I think to myself, the friction factor doesn't decrease much at all with Reynolds number after a certain point. I wonder if laminar flow is more efficient in a sense, and what sense would that be?

Moody diagram

I understand that in laminar flow you have clear lines that the fluid doesn't cross, whereas that wouldn't be true in turbulent flow. We could imagine a pipe with a divider placed in the middle to keep the fluid from mixing in eddies, but that would just create more friction with the divider. There are thinkable cases, however, where you could introduce a divider that moves along with the fluid, in particular, the Taylor-Couette flow...


This setup describes basically one cylinder rotating within another cylinder with a fluid in-between them.

Concentric rotating cylinders

Let's say that you kept the fluid the same, and the distance between the inner cylinder and outer cylinder the same. In that system, let's say you insert a divider at a radius in the middle of the annular area, and this divider was mostly buoyant in the fluid, so it's not experiencing friction on the edges, and it also is free to rotate with the fluid.

Would doing so actually reduce the frictional torque on the rotating inner cylinder? If you could introduce an infinite number of infinitely thin dividers is there a theoretical limit to how much you could reduce the retarding torque? Would that just make it laminar, or laminar-ish?

  • $\begingroup$ What do you mean by a 'divider'? It is not really clear to me from the question. $\endgroup$
    – Bernhard
    Feb 28, 2013 at 11:42
  • $\begingroup$ @Bernhard I mean a sheet, although it shouldn't matter what it's made of. Imagine a sheet of tin foil fashioned into a cylinder of a diameter half way between the inner cylinder and the outer cylinder. Then you drop it in. Anything that will prevent fluid from crossing and hold its shape should do. $\endgroup$ Feb 28, 2013 at 12:15
  • $\begingroup$ Interesting idea. It would certainly seem that you could potentially reduce the frictional torque that way. Are there Moody diagrams for Taylor-Couette or just Couette flow? $\endgroup$ Dec 2, 2013 at 22:18
  • $\begingroup$ Laminar flow tends to produce less shear stress at boundaries and is more efficient in that regard. However, turbulence tends to stabilize boundary layers by transferring momentum into them and can therefore be useful at preventing boundary layer separation thus resulting in reduced form drag. There are plenty of examples where one or the other is desirable. In the case of pipe flow, laminar is definitely the winner. $\endgroup$ Dec 2, 2013 at 22:26
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    $\begingroup$ You're on solid ground in terms of the idea that elements running in the streamwise direction can interfere with turbulence. The work that I've seen is mostly related grooves etc. on surfaces. I don't know of anything on introducing free floating elements (maybe two-phase flow?). This is some of the early work: arc.aiaa.org/doi/abs/10.2514/3.60126 $\endgroup$ Sep 4, 2014 at 18:27

1 Answer 1


YES. It can "Laminarize" the flow. And this will reduce the friction too.

If I think adding infinite number of infinitely thin dividers, we are then actually reinforcing the fluid like concrete is reinforced with steel. In praxis we are actually just changing the viscosity of the fluid, which -obviously- makes it less turbulent. Study hydraulic fluids/oils; Their main character is the constant visocosity over a wide range. Possibly low, that there is least viscous losses, but enough high that there is no foaming tendency.

It should be noted that the Laminar flow conditions can be hold up to Re > 150 000, and there actually isn't any upper limit for Laminar flow. (ie.. Ven Te Chow, Open Channel Hydraulics)

I think that if you can Increase viscosity, and decrease surface tension, you can reach this kind of flow state really easily. There is a good old video about the issue here; https://www.youtube.com/watch?v=1_oyqLOqwnI&list=PL0EC6527BE871ABA3&index=12 They say there the same; over Re> 100 000 laminar flow is possible. (~8 min 25 s)

I actually claim that there is no Causality between velocity and Turbulence. It's just a correlation. And thus Reynolds number is actually quite meaningless. More info about this idea is provided here; https://www.youtube.com/playlist?list=PLgUc9kJnDMMExJivT2dWh9dAjdYYUgOFE


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