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Post by telemeter on Mar 31, 2020 9:54:00 GMT
I am having difficulty showing the required limits for Im(z) in this question. As is explained in the attached note I can only show that Im(z) should be between +/- pi/2 and not pi which the question asserts. I cannot find my error, so any help would be greatly appreciated. The note is here drive.google.com/file/d/1_EC9nd8EeL9aMgiUamdA65CQMph8n6bn/view?usp=sharingWhen I graph my efforts using GeoGebra, I get a good dipole flow (red) and equipotential (grey) pattern in the channel and the flow 'reflects' off the boundaries at +/- pi/2. I do not know what the flow should look like but this reflection appeals to my intuition. The diagram is here drive.google.com/file/d/1k0hrhrlpRA-GUtB9fhxqmV_sqpv-Vgh2/view?usp=sharingAll comments appreciated telemeter |
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Post by Admin on Mar 31, 2020 14:05:27 GMT
telemeter
I have done this exercise but I just haven't published it yet because it needs some finishing touches. I will see if I can see where your problem lies. My graphics look very different to yours.
All I would say without studying it is "Don't forget that arctan is a multifunction".
Vasco
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Post by telemeter on Mar 31, 2020 17:29:56 GMT
Thanks, Vasco
I have pondered the multifunction but as the arctan is the whole of my y component all adding pi does is repeat the pattern further up the imaginary axis. I think I must have gone wrong in my derivation of y...somewhere. I'll keep ruminating.
telemeter
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Post by Admin on Mar 31, 2020 17:59:12 GMT
telemeter
I'm not sure how your maths is related to your graphic, but to get the streamlines you need to plot the level curves of $\Psi$. That is the curves represented by $\Psi=k$ for various values of $k$.
Vasco
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Post by telemeter on Apr 1, 2020 9:47:50 GMT
Vasco You are correct in that I need contributions from other branches of tan to complete the picture. I'll work on that now...as well as an alternative approach. Meanwhile, I have found a glitch in my use of the graphics software, more careful handling reveals this rather pretty picture drive.google.com/file/d/1M_uFmgcx5FNuH2e8ZF4AXE25C8RfzXmw/view?usp=sharingtelemeter |
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Post by telemeter on Apr 1, 2020 12:02:12 GMT
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Post by telemeter on Apr 1, 2020 13:00:36 GMT
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