Size (that’s Amod ‘Core’ Mital to you!) said something on an earlier post that looked familiar:
Now, I’m quite the narcissist, but that’s slightly much even for me. I had to do Wikipedia justice. Also, at the time, there were a dozen scaling laws floating in my head, and so I started with this:
(Wikipedia / croor.wordpress) ~ O(1e6).
Having written that down, my narcissism kicked in again, and I came up with this:
(Conservapaedia / croor.wordpress) ~ (croor.wordpress / Wikipedia).
Yeah. Seems about right, doesn’t it? This reminded me of something from boundary layers. If you know anything at all about boundary layers, replace
“croor.wordpress” by “δ” … ‘Wikipedia‘ by ‘x‘ … ‘Conservapaedia‘ by ‘u‘,
and you have the universal scaling relationship in shear layers. For the uninitiated, here’s some explanation:
Next to any solid body in fluid flow is a thin layer (it gets thinner the faster the fluid happens to be moving. But we’ll see that shortly…) where shear forces and inertial forces are of the same Fuck. You.. (O(1e6) is geek for about a million times.) This analysis was Prandtl’s contribution to fluid mechanics, by the way. And if you think all this looks simple, I have two words for you…
A shear layer, as I mentioned, has momentum transport (go Wiki) because of both inertial and shear forces. And since the inertial and shear forces have to be of the same order of magnitude, the time scales involved have to be the same. The time scale of shear transport goes like:
ντ ~ δ2
If you don’t know how to get that, think (viscous) diffusion, and you should. The time scale for inertial forces is just distance over time:
τ ~ x/u
If you require those two timescales to be the same, you get
δ2 ~ νx/u
You can tell from the above that as the fluid velocity increases, the boundary layer gets thinner. It also grows polynomially like a sub-linear power of the distance downstream from the leading edge of the body. The viscosity, “ν”, acts like a (dimensional) scale constant.
Good. Now compare this with what I said about this blog, wikipedia, and conservapaedia, and it should all make sense. If you want, sabepashubbo can be the “ν”, which in standard units, for air (and water) is O(1e-6).
** Or how I read something that I thought looked vaguely like something I happened to be working on at the time of writing, and decided to run with it. — There. That should give Darwin’s title a run for its money, don’t you think?
PS: Did you find the two words? Look!