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A. Starting with the flow past a circular cylinder in the z-plane, use the inverse Joukowski transformation to derive the flow past an ellipse. The answer is in our notes.

A. Starting with the flow past a circular cylinder in the z-plane, use the inverse Joukowski transformation to derive the flow past an ellipse. The answer is in our notes.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A. Starting with the flow past a circular cylinder in the z-plane, use the inverse Joukowski transformation to derive the flow past an ellipse. The answer is in our notes. B. With c = a in the Joulowski transformation, the ellipse becomes a flat plate. To examine this flow, we used a trick to write it in terms of z (rather than Z): Ue ia -Ueia a? /z2–iT/27z Uz – iv, = 1-a2 / 22 Show that the singularity in the flow at z = +a disappears if the circulation is I= -4rUa sina, and show that the flow at that point is Ux = U cos a, V% = 0.
Transcribed Image Text:A. Starting with the flow past a circular cylinder in the z-plane, use the inverse Joukowski transformation to derive the flow past an ellipse. The answer is in our notes. B. With c = a in the Joulowski transformation, the ellipse becomes a flat plate. To examine this flow, we used a trick to write it in terms of z (rather than Z): Ue ia -Ueia a? /z2–iT/27z Uz – iv, = 1-a2 / 22 Show that the singularity in the flow at z = +a disappears if the circulation is I= -4rUa sina, and show that the flow at that point is Ux = U cos a, V% = 0.
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