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I just watched “Downsizing”. They have this method of shrinking people down to sizes of around 5 inches.

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Now, suppose you downsize a person of say, 5 feet to 5 inches, which turns out to be about (1/12) times his original height. Then, the Reynolds number for such a person would also be 12 times smaller. This much I understand.

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What I don’t understand and really want to know is, how would such a person “feel” in a medium having a Reynolds number 12 times smaller ?

I believe I understand Reynolds no. to be a helpful mathematical tool in analysing different flow regimes in fluid dynamics. I, however, don’t have a clear understanding of how change in sizes alone affects the perception of the flow around that body ( the “feel”), keeping the density and dynamic viscosity the same.

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    $\begingroup$ I don't know specifics; but they would definitely experience flows a lot differently than a regular sized person. When testing scale models in wind-tunnels for example; you need to actually adjust flow rates to compensate for non-linear scaling effects. $\endgroup$ – JMac Feb 6 '18 at 14:59
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    $\begingroup$ you should read this absolutely fascinating lecture by E. M. Purcell: Life at low Reynolds number, Am. J. Phys. v.45, No.1, Jan 1977. $\endgroup$ – hyportnex Feb 6 '18 at 15:09
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    $\begingroup$ -1 Not clear what you are asking. Questions about perception (the "feel" of something) are subjective, hence outside of physics. Please re-frame your question using physical concepts. $\endgroup$ – sammy gerbil Feb 6 '18 at 15:31
  • $\begingroup$ @sammygerbil what a person feels or perceives depends upon the density and viscosity of the medium he is in. The question was aimed at knowing how this perception can change when only the size is factored in the Reynolds no. keeping the density and viscosity the same. Does the perception of surroundings change, as both the density and viscosity are the same, or does the change in Reynolds no. Become the decisive factor in altering that perception. It’s always fun to know how Downsizing someday in near future might affect those aspects of our lives which we take for granted. $\endgroup$ – RedHelmet Feb 6 '18 at 15:46
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    $\begingroup$ @sammygerbil I think you're being overly pedantic here. It's pretty clear (to me at least) what is meant and I was able to answer it accordingly. Changing the ratios of forces does change the relative impact those forces have a body, and so that body would "feel" something different. No need to go after common-use English for a conceptual, entry-level question. $\endgroup$ – tpg2114 Feb 6 '18 at 17:39
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Think of the Reynolds number as the ratio of inertial forces ($u L$) to viscous forces ($\nu$). Using that process, shrinking the length by 12 is equivalent to multiplying the viscosity by 12. Does that help you figure out what it would feel like?

The other thing to bear in mind is that the height is 1/12, so the Reynolds number for things like flying head/feet first is scaled by 1/12. But, what about the diameter of the body? Or maybe the square root of the surface area? These things may have changed by other factors, which would change how things "feel" relative to the motions that those sizes factor into.

All in all, an entertaining thought exercise.

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  • $\begingroup$ This is exactly what I wanted to know. As you mentioned that sizing down the length 12 times is equivalent to factoring the viscosity 12 times. But is that equivalence only mathematical (like in keeping the Re no. the same) or is that really how it works? I mean, how do I logically convince myself that a downsized person would necessarily feel like existing in a medium that’s 12 times more viscous, or 12 times less dense equivalently ? Also, if he sees the equivalent density 12 times lesser, would it be that much difficult to breathe because of low oxygen around ? Is that how all this works ? $\endgroup$ – RedHelmet Feb 6 '18 at 15:06
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    $\begingroup$ @RedHelmet That is, basically, how all scale testing in wind/water tunnels works. We assume if we hold the non-dimensional numbers constant, then the flows are equivalent. There's other numbers that come into play, like Mach number or Prandtl number of Knudsen number, etc.. But, if we keep the numbers constant that apply to our physics of interest, then yes -- it is equivalent. Something like breathing isn't a Reynolds-number controlled effect, so that probably wouldn't scale with Reynolds number. But what the wind on your face feels like is, so that would scale. $\endgroup$ – tpg2114 Feb 6 '18 at 15:10
  • $\begingroup$ For breathing, maybe capillary action is important (getting oxygen out of the airs and into the cells in the lungs) and so something like the Capillary number or Bond number would need to also be held fixed in addition to Reynolds number. Or maybe there's other parameters that are important, I don't know too much about biological processes at small scales. $\endgroup$ – tpg2114 Feb 6 '18 at 15:12
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    $\begingroup$ @tpg2114 I think when we start considering the oxygen like that, things will fall apart quickly. For example, how do these people scale. Does all the matter shrink, leading to 12x smaller cells and atomic structure? Then wouldn't they have to basically only interact with shrunken objects? Or are they just re-made as smaller versions of themselves? How would they do that while keeping cellular features in-tact? Basically, I think asking what the fluid-flow experience is like at 1/12th scale is fine; but trying to make biological processes make sense basically has to be "magic". $\endgroup$ – JMac Feb 6 '18 at 15:43
  • $\begingroup$ @JMac Totally agree. I was just trying to drive home the larger point, using breathing as an example, that not everything scales with Reynolds number and there's a wide range of other numbers that exist to provide scaling for the physics of interest. Ideally, one could choose the working fluid so everything scaled identically and 1-to-1 scale tests could be made. $\endgroup$ – tpg2114 Feb 6 '18 at 15:51

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