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I was solving some questions when I came across this:

what is the velocity of liquid molecules in contact with the walls of the tube? and the answer was given that it can have any velocity and then no further explanation. I tried to search from different sources but could not find any reason. My doubt is that by any velocity does it mean it can have zero velocity too? and even maximum velocity?

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  • $\begingroup$ en.wikipedia.org/wiki/Law_of_the_wall? $\endgroup$ – CuriousOne Jan 6 '16 at 1:49
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    $\begingroup$ Wait, velocity of the molecules or velocity of the fluid? Because the ensemble velocity is decidedly different from the molecular velocity. $\endgroup$ – tpg2114 Jan 6 '16 at 1:54
  • $\begingroup$ velocity of the "molecules" of the fluid. $\endgroup$ – Alex Prior Jan 6 '16 at 1:57
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    $\begingroup$ In what context did this question arise? In statistical mechanics, the molecules can take virtually any velocity possible but with a particular probability distribution. It would be easier to give an answer if we knew the context and how to frame it. $\endgroup$ – tpg2114 Jan 6 '16 at 2:05
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    $\begingroup$ @Floris Molecular slip can occur at solid surfaces in microscale flows and so it is possible that the velocity of some/many molecules are nonzero at the wall itself. The normal velocity component is always zero because it won't penetrate the wall, but it is possible for molecules to slide (while the ensemble shows zero velocity). It's possible the question really was referring to molecular speed and not velocity, but it's all rather unclear at the moment. $\endgroup$ – tpg2114 Jan 6 '16 at 2:17
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In laminar flow, fluid moves in defined layers. The boundary layer closest to the wall moves with least magnitude of velocity. The direction of its velocity is the direction of flow through the tube.

In turbulent flow, molecules become disorganized and can move in eddy currents that swirl in any direction, including against each other, regardless of distance from the wall. The velocity of molecules in turbulent flow is not constrained by distance from the wall, although the link I cited says that "a general specific feature of the near-wall turbulent flows is the presence, on the wall, of a thin viscous sublayer, wherein molecular viscosity forces are dominant and the velocity distribution is linear."

Perhaps the answer you cite was trying to illustrate that neither direction nor magnitude of velocity of any one molecule in turbulent flow at the wall is predictable.

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