Can anybody identify the equation on this t-shirt? It’s hilarious.
I tried searching the SDMB and had no luck, so I hope this isn’t a redundant thread.
I don’t know what it means, but I want that shirt!
Looks like the Conservation of Energy Equation in Fluid Dynamics expressed in integral form (with a few identities thrown in to make it look nicely complex).
Go to this page and scroll about halfway down:
http://www.physics.udel.edu/wwwusers/jim/Fluid%20Dynamics/Fluid%20Dynamics2.htm
I got my sister a shirt like this, but with Maxwell’s Equations in place of that one.
Actually, I believe it’s the Navier-Stokes star gas equation
My favorite Maxwell Equation T-shirt read:
Wouldn’t be surprising, since that’s a fluid dynamics problem, deriving from the same assumptions. When I google “Navier stokes” it’s still generally given in differential form.
This is what I get for not having much fluid dynamics and no astrophysics.
I have often pondered the question of what the result of such lacunae might be. Now I know. 
The fact that there are people on this Board who know these things amazes and pleases me. The closest I ever got to Advanced Fluid Dynamics was a keg of Old Peculier at a Beerfest one year. 
Bah, grimpixie, everyone knows that God works with B, not H. H is just a convenient fiction, to pretend that media are uniform and that the fields inside of them are somehow special. But God knows better, and deals directly with the charged particles and the vacuum between.
For that matter, God also knows about the inherent Lorentz invariance of fields in spacetime, and thus would use the Faraday tensor, and He also knows about that one magnetic monopole sitting somewhere and enforcing the quantization of charge. But it’s only the curl parts of the equation that matter, for light, anyway. 
Heh, when I Googled for “Navier-Stokes star gas equation,” I get a single hit: a Yahoo store site selling the shirt. In this case, it’s black on a white t-shirt.
p.s. How is “Navier” properly pronounced.
Those aren’t even the biggest problems. Even He (and, what’s worse, Chronos) forgot about boundary conditions.
Its an integral for a fluid control volume problem. Basically, it is if you stood in a river and watched a glob of fluid go by and you wanted to know the net force on that glob. To do that problem you define an imaginary boundry that encloses the fluid
The first integral term is the compression of the fluid in question. I forget exactly what beta is defined as, but it relates to the Volume/Surface Area. Doing that integral returns the net force on a control volume due to expansion/compression of the fluid.
The second integral is calculating the net force on a moving, rotating reference frame in a fixed reference frame. Its basically a bunch of math stuff, which the derivation of I don’t want to go into. As a tid bit, the 2wV[sub]xyz[/sub] term is what is commonly known as the coriolis effect.
The third integral is a surface integral that comes from the bernoulli equation applied accross the control surface. I am not sure, but it appears that this part of the equation is wrong. Instead of V[sub]xyz[/sub], I believe it should be V[sub]xyz[/sub][sup]2[/sup]/2.
The last term is an integral that accounts for the change in momentum (remember that change in momentum/change in time equals force) of the fluid inside the control volume.
This is basically the most scary and unweildy equation you could think of for a Mechanical Engineer. The individual portions of the equation aren’t that complicated. MEs use them all the time, and probably everyone could understand them eventually. To use an analogy, its not too hard to pat your head, rub your stomach, hop on one foot, or do a hoola-hoop. On the other hand, doing all 4 things at the same time are tough to do.
I would say that 99.9999% of MEs see this in school once, and never use it again. Of those, the really smart ones solve the problem quickly becuase they are just that good. The smart ones, but not super brilliant ones, look at this and say “Fuck this!”, put something down and go for partial credit. The middle of the pack ones work their ass off for a few days and come up with the right answer. Then the bottom of the barrel engineers work their ass off for days and still don’t get it.
This would make a hell of a shirt all by itself…
I alwys used to pronounce it “Nav-e-air” until my advisor pointed out that actually its pronounced “Nave-e-ar”, so I’d go with “Nave-e-ar”.
I’ve always heard it as Nah (as in Nahhh, I don’t want to)-Vee(the letter ‘v’)-Eh(like the Canadians, eh?). He was French, so that pronunciation makes sense.
Well quite. And that’s a better approximation of how I used to pronounce it. Until I was told it was wrong. 
I emailed the t-shirt site to the local college astronomy professor and he confirmed that it’s the Navier-Stokes star gas equation. I’m assuming that fluid problems in 3-space are all more-or-less analogous, so I’m therefore assuming that the answer is neither contrary nor contradictory to treis’s explanation, which was very helpful, BTW. Thanks!!
He also said it’s something like “Na-vie-err.” It sounds wrong, given the man was French, but who am I to judge?
p.s. This bit of punctuation ambiguity amused me:
“Bottom-of-the-barrel engineers” vs “bottom of the barrel engineers” made me chuckle, because being the worst of the “barrel engineers” gives me visions of Monty Python.
You don’t want to get anywhere near the bottom of a barrel engineer, I can assure you!
BTW, I just got back from my son’s math bowl competition. I wish I’d seen this before and we’d got these shirts for all of the kids (second grade). That might have freaked out the competition.