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There is fluid in between two boundaries $\operatorname{Im} z = a$ and $\operatorname{Im} z = -a$, with a vortex of strength $Q$ at the origin.

I need to find the complex potential using method of images.

Now, when you have this question but with a line source strength $Q$ instead, you end up with an infinite series of sources of strength $Q$ as you attempt to balance each boundary. However, when I balance the vortex with an image vortex above at $2a$ with strength $-Q$ and the same at $-2a$, it seems to me that the system is balanced, as whichever boundary you look at, the centre vortex seems to balance both the images.

Is this correct, and so I get a potential of $$w(z) = -{iQ\over 2\pi}\log(z) + {iQ\over 2\pi}\log(z-2ai) + {iQ\over 2\pi}\log(z+2ai)?$$

I can't really get my head around how vortices intereact with each other, when there is another vortex directly between them.

Thanks for any help!

Dominic Michaelis
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Mt123
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  • You can find some good starting points on how to format mathematics on the site here. This AMS reference is very useful. If you need to format more advanced things, there are many excellent references on LaTeX on the internet, including StackExchange's own TeX.SE site. – Zev Chonoles Feb 22 '13 at 21:46
  • Thank you. Was wondering how people did that. Hope this edited version is better! Thanks. – Mt123 Feb 22 '13 at 21:55

1 Answers1

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prove that the two-dimensional irrotational motion of a liquid bounded by the lines y=0,y=2a due to a source at the point(o,a) is given by the complex velocity potential W=-mlogcosh(z/2a)

samsuddin ahmed
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