How To: Calculate Circulation

In this video, we will compute the circulation around an ellipse for an arbitrary vector field using MATLAB and Python. First we will look at the equation for circulation, and then transform it into a useful form for its calculation using a discrete vector field. Finally, we will run some code that computes the circulation for an arbitrary vector field in both MATLAB and Python.
The purpose of this code is to be able to compute the circulation, and thus the lift per unit span, of an airfoil in my future vortex panel method video/code. I will also be using it in my potential flow elementary solutions videos.
===== ERRORS =====
► The angle definitions in the MATLAB code shown in the video are incorrect. The Python version was always correct, but I was using an old version of the MATLAB code in the video by accident. The code available on my website has been updated as of 08/19/19, and both Python and MATLAB functions are correct now.
► The error is that you do in fact need a duplicate angle in order to finish the line integral around the ellipse. Without the duplicate angle, it leaves the integrated ellipse open. Including the duplicate angle ensures that the entire ellipse is integrated over (i.e. a closed curve).
===== RELEVANT LINKS =====
MATLAB and Python code from my website
► www.joshtheengi...
GitHub: Panel Methods
► github.com/jte...
===== NOTES =====
► I'm using the circulation defined in Anderson's "Fundamentals of Aerodynamics".
► You can use any other shape you want for the closed curve, but the ellipse is useful for my purposes.

[@user-yd2jl4bx2h]

Had an aerodynamics hw question asking me to do exactly this... I was stuck on it for hours. Thank you!

[@naveenwatertunnel]

thanks for this video!! awesome!!! here my some more ideas, we can do this discrete data integration using sum(udx+vdy), capture the variables along the circle and just do the summation!!

[@etiennelebihan4296]

Nice video ! In the function code, does the integration work similarly with the trapezoid rule if we define a rectangle instead of an ellipse ?

[@JoshTheEngineer]

Thanks! Yea it should still work the same way. I just use an ellipse because that's what I was using for my airfoil circulation calculations. As long as you have a closed curve, you can compute the circulation this way.

[@LearnEngineering678]

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[@chrispi608]

Wow nice! Thank you very much! You got a new subscriber ;)

[@JoshTheEngineer]

Thank you!

[@eirenemeliala3155]

Great video. Can a circulation have a negative sign or always positive?

[@JoshTheEngineer]

Thanks! Circulation can be negative, positive, or zero.

[@sudhasharma52]

Sir can you please tell me how the circulation of conservative force is zero please do reply i really need your help

[@vishnu.prasad.official]

Conservative vector fields are irrotational i.e curl(vector field) = 0. Since circulation is defined as the surface integral of the curl of the vector field over a closed curve ( stokes theorem) circulation is zero.

[@sudhasharma52]

@@vishnu.prasad.official thanku so much for helping me

[@Dani-ox6yw]

great

[@JoshTheEngineer]

Thanks!