Streamlines and stream function [Aerodynamics #6]

In this lecture, we discuss methods for visualizing a flow field and develop tools to better diagnose flows. Pathlines, streaklines, and streamlines are all different ways to visualize a flow, yet in a steady flow they're all the same. We mathematically define streamlines in detail, then build a new "stream function" that defines the set of streamlines based upon the velocity field.
Free downloadable notes (PDF with white background) can be found at my website: sites.udel.edu/vanburen/educa...

[@kenankenan6371]

Dear Prof. Van Buren you are a gift from God. Thanks for this invaluable lectures.

[@prof.vanburen]

Aw thanks!!

[@joyia.1]

Now that is not fair, this channel deserve more subscribers.

[@prof.vanburen]

Aw thanks! I am happy with everyone involved, regardless.

[@squpsqup2708]

The best ever I wish most professors to be like you

[@prof.vanburen]

Aw thanks!

[@sricharanbhat4227]

Wonderful sir. Please continue teaching aerodynamics with real life problems

[@prof.vanburen]

I'll try! Thank you.

[@eliocrapun7782]

Dear Prof. Van Buren, I really appreciate the lectures that you made. You are clear, didactic, straight to the point. You made a master work. Congratulations! P.S. What software have you used to criate the presentations? Thank you.

[@prof.vanburen]

Thanks---I'm glad you like them! To make each video, I record my voice using Audacity and the Windows native screen recorder (Xbox Game Bar actually) to record the notes written in OneNote. (The voice and written notes are recorded at different times). I then combine everything and edit together using Adobe Premier Pro.

[@eliocrapun7782]

​@@prof.vanburen Thank you for all that you teach in this course. I used your inductive logical way to explain to non math audience how a wing (they call it foil) under water is able to fly a sailboat. Merci pour votre travail.

[@mannangattyt9957]

Sir lecture is easily understood. Thank you sir.

[@prof.vanburen]

Thank you!!

[@flth1040]

14:40 that is not the chain rule, that is the definition of the total differential😊

[@furkandugeroglu7187]

Professor, I would like to ask a question: in 12:40, we wrote a new function g(x,y)/h(x,y) and made it equal to the difference between the c2-c1. But according to the equation we got from the integral, isn't it has to be equal to g(x,y) - h(x,y) ? Why we made it equal to the g(x,y)/h(x,y)? Waiting for your answer.

[@prof.vanburen]

Nice catch! It should be the new constant c2/c1 = c. Luckily, since we are defining new constants anyway, it has no consequence on the subsequent material.

[@amirpasagic162]

@@prof.vanburen Was wondering the same. In that case constants C2 and C1 used e.g. in 13:35 are not the same as used in ~12:50?

[@Dan-mw4zu]

Hey there! I've just discovered your channel and absolutely love your content, but I'm having a difficult time understand why 'c' remains constant for a streamline with stream function ψ(x,y) = c, and I was wondering if you might be able to shed some light on the matter.
I know that c is just the value of the stream function, but when you expand it all out, c is technically the ratio of two integral constants [c1 and c2] of two equal and nondescript functions [g(x,y) and h(x,y)] that you create by integrating the differential equation [dy/dx - v/u] of a streamline, which is a very abstract mouthful. What about c specifically makes it so that for all x- and y- coordinates in a flow field, it remains constant along what might be a very complex streamline? Wikipedia states that the stream function is constant because 'streamlines are tangent to the flow velocity vector of the flow', but that just seems to be referencing that how streamlines always follow the direction of the field. I'd be really grateful for any insight you could provide.

[@amirpasagic162]

I also had a bit of a hard time understanding that, but it seems to simply be so by definition. All the variable dependent parts are put on one side and form function Psi, while everything on the other side is simply constant and does not depend on variable, hence neither changes thru space or time. We were warned that function is rather built then derived :)

[@amirpasagic162]

​ @Prof. Van Buren I don't fully understand how could we simply replace C with mass flow (per unit length). Is is cause mass flow is supposed to be constant along a single stream line? (or between stream lines, given mass cannot pass them, hence they effectively act as tubes of constant mass flow)

[@prof.vanburen]

Hey Dan! Sorry I am late to this, I saw the comment and intended to sit down and think about it, then 7 months happened.
@Amir hit it right on the head, imo. It is super common for aerodynamicists to search for some physical foundation of stream/potential functions, and in truth they are just built because sometimes they lead to better physical intuition of the flow or, more often than not, lead to a simpler mathematical strategy to solve complicated equations.

[@prof.vanburen]

Yep! I think your thought process is correct, the streamlines act as boundaries so mass flow is conserved between them.