Flow Mapping Theorem and Obstacles

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fr33d0m
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Hi All

I have one final question that's related to flow problems with obstacles.

Any help would be greatly appreciated as I am finding fluid flows extremely difficult.

q2cb.JPG



"Examinations are formidable even to the best prepared, for
the greatest fool may ask more than the wisest man can answer".
Charles Caleb Colton, 1825
 
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Hi All

Think I've cracked part (i) and (ii). However, I'm stuch on part (iii). I think I need to use the Inverse Function Rule somehow to get the function stated but when I do, it doesn't give the answer. Can someone please help? The inverse function rule states that f (z)'=1/1-1/(f(z))^2.

Dont know if it will help but for part (ii) I got z+(4/z)-(16/z^3)...

Please please help...
 
There is something missing! You say "let [itex]J_{2i} be the function with [itex]\alpha= 2i[/itex]". I presume that somewhere earlier they defined another function [itex]J_{\alpha}[/itex] but you don't include that information.[/itex]
 
The function you specift is given by the following formula:


Jalpha=w+(alpha)^2/w.

Hence j2i=3+4/3 and j2i = 3-4/3. Substituting this into the standard equation of an ellipse for a^2 and b^2 and rearranging gives the required formula. Does this help?