Navier-Stokes Equations - Numberphile

Tom Crawford (sporting a Navier-Stokes tattoo) talks about the famed equations - subject of a $1m Millennium Prize.
More links & stuff in full description below ↓↓↓

NUMBERPHILE

Videos by Brady Haran
Animation and edit by Pete McPartlan
Freesound credits: rfhache, nicstage, ashfox, inspectorj
Animation of right angle flow: Keaton Burns, Dedalus

[DocteurZeuhl]

I spent my PhD working on Navier-Stokes, but instead of tattooing the damn formulas on myself, I celebrated the end of my PhD by writing them on a piece of cardboard and setting fire to it while drinking vodka.


EDIT: This is my most liked comment of all time. The world is a silly place <3

[numberphile]

More with Tom Crawford on this topic is coming soon.

[collintmay]

That image of ketchup at 9:30 is actually a special case of the Navier-Stokes equations. Ketchup is a shear-thinning fluid, meaning that, in simple terms, it's a special type of non-Newtonian fluid that becomes less viscous as it is disturbed, then returns to some baseline thickness when you stop disturbing it. There is a modified form of the N-S equations which can handle fluids that get thicker or thinner as they are handled, but it is not covered in this video. Food for thought!

[HavasiP]

I'm jealous of this guy. Not of his intelligence (maybe a little) but of his passion and enthusiasm. I would like to know what that feels like.

[adamgray]

Physicists and engineers: "Why can't you just be normal?"
Mathematicians: *Screaming*

[jmcbresilfr]

10:34 "We kinda find ways to cheat."
Math in physics described in one sentence.

[tulasdanslecubitus]

So after his beef with Eminem, Machine Gun Kelly found a career in fluid mechanics.

[Rotem_S]

"describes any fluid on earth" *uses the incompressible formulation*

[ondermetu]

What a flow like narration, full of enthusiasm and fluent as much as nature taking its course

[marcodesanti]

Navier-Stokes - Invokes Tears

Anagrams are too real sometimes...

[Maniclout]

Who else thought his rho's look like integrals?

[Garbaz]

Funnily enough, Nabla isn't a Greek letter. It's a made up symbol named after the Greek word for a harp.
Sorry, had to be that guy :/

[catherinebrower]

"Further our understanding of Nevier-Stokes equations"
translation
"Plz halp" - science

[billyjames]

Omg this is my tutor at Oxford 😆 he’s amazing btw

[acerovalderas]

This mathematician is excellent. Extremely clear and joyful. I would like to see more videos of him.

[TheRealGuywithoutaMustache]

0:02
When you want to cheat on your test but used permanent Sharpie instead.

0:53 "Something that changes shape to match its container." So… a cat?

[hansb]

You know you're dealing with serious science when you have to ask which way round to read the equation.

[gabrielsetyohandoko]

I am preparing for my undergrad thesis defense 1 hour from now... This video really helps me to understand the governing equation i use on my research. Thanks Numberphile!!!

[kdawg]

Chemical engineer here, so I spent plenty of personal time with the Navier-Stokes equations in Transport Phenomena my junior year. I know mathematicians love pure answers, but using these equations is all about making simplifications and assumptions and setting the right conditions to reduce them to something usable. And doing that requires making extremely smart choices. Probably the most memorable thing from that class for me was going through a famous reduction of the equations, removing insignificant terms and making various assumptions, until the equations could actually be solved analytically. This was first figured out way before computers. The elegance with which these brilliant engineers reduced these equations to a solvable form was, in my opinion, legitimately beautiful. It's similar to how the Schrodinger Equation can be solved exactly for hydrogen. These people had incredible minds.

I would actually watch a dozen or more videos of different simplifications for the N-S equations depending on the context. It requires great ingenuity and can go off in all different directions. That's probably a little equation-y for Numberphile, which is fine, but if some other channel wants to do that, I'm all for it.