# A Potential corner flows

1. Nov 5, 2016

### joshmccraney

Hi PF!

Attached is a very small piece of my professor's notes. I would write it out here but you need the picture. Referencing that, $z$ and $\zeta$ are complex variables, the real components listed on the axes, where the vertical axis should have the imaginary $i$ next to it. What I don't understand is how he arrives at the red box. From what I can understand, looking at the second $z$ and $\zeta$ definitions and substituting one in for the other through the variable $r$ we have $$z = \zeta e^{-i \pi+i\theta_0}$$ but from here I don't see how to arrive at the boxed in piece. Any help would be awesome!

I should say I searched everywhere online but no one showed the derivation.

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2. Nov 11, 2016

### Greg Bernhardt

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Nov 11, 2016

### FactChecker

For the natural number n>0, zn is a 1-1 conformal mapping from the area above the angle, Θ0 = π/n, on the left to the upper half plane on the right. That will give you a way of mapping the straight horizontal lines on the right upper half plane to the flow lines of an incompressable, irrotational flow on the left within the angle area.