Potential Flow and Method of Images with @3blue1brown

Grant Sanderson of 3Blue1Brown asked me to teach him some Fluid Dynamics during his visit to Oxford last year (Feb 2020) - here's what we got up to...

We look at potential flow for a 2D incompressible, irrotational, inviscid fluid, beginning with the flow fields for the most common situations such as uniform flow, stagnation point flow and a line source. We then derive the potentials for each of these flows and use the method of images to construct the velocity field for a source next to a wall, a source next to a corner and finally for an infinite channel.

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[alexwolffe]

Maths, fluid dynamics, Tom and Grant. Simply amazing.

[danielkron]

Ah, yes, two sexiest mathematicians in one video

[franteryda]

Just in time for my fluid dynamics exam! Haven't seen the video yet but man, this collab is epic

[Nick]

im taking a break from learning maths with a maths Video, weird isn´t it ^^

[ManojKumar-cjoj]

I was looking for a video on method of images of electrostatics but ended up watching this amazing fluid video ❤️

[MrWhiteVzla]

I didn't know Tom had his own channel! I just saw the drag equation video on the Numberphile channel and the recommended video was this one. Thank you algorithm!

[luckywssbi]

Greatest math video ever created. I am in awe at how amazing this journey how perfect the format is.

[googleit]

The method of images is so amazing that it deserves a background music of its own: "Mirror on the wall, here we are again...."

[amaarquadri]

Definitely one of the coolest ideas in fluids! One of my favorites is if you have a source at (1, 0) and 2 walls leaving from the origin at slopes of +30 degrees and -30 degrees, then you can replace it with 6 sources at the 6 roots of unity (hexagonal symmetry).

[jmdr]

Could not asked for a better new year gift. I am working with these for past 2 years and it still amazes me how beautiful the math is.

[thunderza]

The thing that strikes me - is the simplicity with which it all has to be approached. If nothing else this shows how to make maths accessible; or that even some of the best minds in math, still when introduced to a new topic, take it from the most basic forms and build on that. Sublime!

[brad]

I think that’s so cool how they differentiate the sum to to get it into a harmonic series for that converges and then they just integrate it back once it’s neat and tidy for the potential they need.

[nickwisely]

"It's like you're looking at the mirror and then you give him a high five. Of course, it will stop there"
That's a very good analogy for a method of images.

[gandalftolkien]

Maybe you guys haven't seen it or it has been a while, but I would check out Feynman's Lectures on Physics. In volume 2 there is a neat section on the method of images for electrostatic potentials!

[benwinstanleymusic]

Thank you Tom and Grant! Just in time for my Fluids exam

[prdoyle]

Wow, amazing. That's one of those concepts you never forget once you've seen it.

[sebastianmorales]

Next: Laminar flows with Dustin, the epic fluid collab, and it doesnt get any better than that

[luorisluo]

i am doing a fluid mechanics master degree and this really brainstorming, thanks so much for sharing.

[ShaunJW]

Both of you are assisting me with my physics maths degree, final year student ❤️

[mudkip_btw]

Never seen the source in a channel before. Thanks Tom great video!