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Old Jan 11th 2017, 12:18 AM   #1
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A very basic doubt about boundary layers

Please refer the figure(click on the link):
"Introduction" of chapter "Laminar Boundary Layers" from the book "Viscous Fluid Flows" by F M White.

The author shows how for high reynolds number we have thin boundary layers, but the explaination just does not convince me. I tried to understand it on several occasions but I just can't, and I can't seem to ignore it too. So, it is not letting me move forward in the chapter.

The result is based on the fact that if boundary layers are to be thin, the diffusion time(time required for viscous effects to spread across streamlines) should be much shorter than the residence time(time a particle spends over a flat plate)

I think it should be opposite. Because for a given amount of time, if diffusion time is very short, the effects of viscosity would reach much farther away from wall while the particle is still around plate(as residence time is longer, and it will take longer time to cross the plate). So by the time even a particle far away from the wall will cover the plate length, it would feel the viscous effects(I am using simple idea that less time required means more distance covered). But with this logic, I get low reynolds number for thinner boundary layers.

What am I missing here?


Last edited by pk25; Jan 11th 2017 at 06:33 AM.
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Old Jan 13th 2017, 04:51 PM   #2
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I think the text is poorly and misleadingly worded.

Diffusion is usually thought of as the movement of fluid molecules from a region of high concentration to a region of low concentration.
However I think it is reasonably obvious that the rate of diffusion will depend on the fluids viscosity.
A highly viscous fluid will diffuse more slowly than a low viscosity fluid.
Thus the diffusion time can be used to give a measure of how rapidly the flow can change from the speed U to zero,
and thus how thick the boundary layer will be.
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