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I have encounter this notion: "Dimensionless Thickness". Does anyone have any idea how to interpret this? One can find such a term here.

My interpretation is that the name comes from the fact that the thickness alone doesn't mean too much, but it means a lot if it is related to a reference number (e.g. $ratio = t/t_{reference}$, where t is the dimensionless thickness).

If this is true, can anyone provide me with an example of such a term in the fluid-dynamics, mechanics or thermodynamics field?

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    $\begingroup$ it means simply that the dimension has been divided by some reference length. Any intro to fluid dynamics text will have a whole chapter devoted to dimensional analysis. $\endgroup$ – agentp Nov 14 '16 at 2:26
  • $\begingroup$ A lot of times I remember seeing this in undergrad fluid mechanics was in terms of a pipe length L, which was some number of multiples of the pipe diameter. This was a thumb rule to determine if flow was fully developed. $\endgroup$ – Chuck Nov 15 '16 at 20:34
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    $\begingroup$ As for examples: the standards for normative elements - say, nut/bolt threads often use these. Given base parameters like bolt diameter, a lot of other parameters are defined for a whole family of threads, by providing ratio to the base parameter. That way a whole family of sizes can be defined through a very small set of basic parameters - all the rest is derived from these through the ratios. $\endgroup$ – SF. Nov 18 '16 at 12:22
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What matters is not the dimensional value of the thickness but rather the ratio with a reference thickness like you stated.

Examples I can think of are when dealing with turbulence: $U^+$ and $y^+$ which are the non-dimensional velocity and distance from the wall, respectively, when discussing the Law of the Wall in Turbulence.

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