1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Potential corner flows

  1. Nov 5, 2016 #1


    User Avatar
    Gold Member

    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.

    Attached Files:

  2. jcsd
  3. Nov 11, 2016 #2
    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.
  4. Nov 11, 2016 #3


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Potential corner flows Date
I Potential near the center of a charged hollow sphere Thursday at 12:11 PM
I When Electric Field is 0 is potential also 0? Feb 18, 2018
I Voltage in terms of a battery Jan 31, 2018
I Electric Potential vs Electric Potential Energy Jan 28, 2018