Flow Mapping Theorem and Obstacles

[fr33d0m]

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.

"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

 

[fr33d0m]

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...

 

[HallsofIvy]

There is something missing! You say "let J_{2i} be the function with \alpha= 2i". I presume that somewhere earlier they defined another function J_{\alpha} but you don't include that information.

 

[fr33d0m]

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?