Potential Flow Part 2: Details and Examples

This video gives more examples of potential flows and how they establish idealized fluid flows. They are found by solving Laplace's equation, which is one of the most important PDEs in all of mathematical physics.

@eigensteve on Twitter

This video was produced at the University of Washington

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0:00 Introduction & Overview
1:05 Contour Integrals
10:22 Example Potential Flow
17:38 Listen Up! Solutions to PDEs Establish Vector Fields

[meysamjafari]

Your teaching approach is amazing! It sets a high standard for other educators to follow.

[curtpiazza]

Wow! I like how you bring the theory to life with the applications! 😊

[lowerbound]

Your lecture is extremely clear and motivating. I really love that you tried to connect different subjects into one. Thanks for the lecture😻

[teddyp]

Love your lectures, and amazing approach, making everything crystal clear:)

[arkyin]

definitely excellent course， i take this course as an outline and fill in the details. Really linked a lot of things i learned before. Thanks!

[motbus]

Dear professor Steve. Thanks once again for the amazing content.
If I may ask/suggest, could you also set some minutes with code demonstration as well? thank you

[yizhu]

Thank you！very informative and inspiring

[Alliban]

The area integral at 3:28 has to be multiplied by the normal vector of the area acc. to my understanding, since curl gives a vector, but the outcome of the integral should be a quantity (or the integral has to be written using components).

[hagopbulbulian]

Prof. Steve :
Thanks for the lectures but I have some unexplained equation at 5 minute of your video lecture
You wrote twe equations
1) on the area ) = on the volume)
2) on the area) = int(divergence (v).differentiation on volume)

Isn't there some thing about those two equations
You used the same theory on both equations and one time it gives rotation the other time divergence?

[ReaperUnreal]

I really appreciate the example here, it helped solidify the idea of what's going on here. I think I'm going to try it for myself with a few extra analytic functions. If I'm being super petty though, drawing check marks from the big part first irked me. Still absolutely loved the video though.

[nickwisely]

Professor Steve, I would like to know more about the proof of how taking the specific derivative potential flow function and stream function could lead the same vector field? Will it stay true in every condition?

Thank you, really love you lecture.

[hameedmusa-basheer]

thank you DR. @24:20 you mentioned your class coding out the field and dropping particles in them for visualization, what app helps to do that? matlab?

[himanshuraj]

you are amazing sir...the example is really good

[kevincardenas]

Thanks a lot for these videos! Are they getting uploaded 1 per week?

[niled.r.]

Hi, thank you for the videos! I would like to ask, if the vector field is a "general solution" for the pde? I don't get yet, when does the idea of specific solution come(when some additional/ boundary conditions are defined)

[rodbhar]

Would be helpful to know what the physical interpretation of Laplace’s equation is.

[martinsanchez-hwfi]

Is it always true that analytic--> harmonic?

[danielvolinski]

23:30 The Laplacian of Ψ(x, y)=sin(π x) sin(π y) is not 0

[shakennotstired]

Thanks! eagerly waiting for the next videos in this series

[luismeron]

Hey man I couldnt understand anything from the moment you got the two sin, can you please explain better