In other words streamlines go under f to streamlines

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Unformatted text preview: n the most nearest the origin, where the width of the flow channels is widest: A typical flow channel [The above potential also gives a model of the flow along any flow channel such as the one above.] also, the flow speeds up as the flow channel gets narrower and narrower. This is how water pistols work. (B)Flow around a cylinder This leads to a description of § again: 40 This region D maps into H via w = z + 1/z, and, on H, § can again be taken to be § = Ay Giving us a complex potential È 1˘ F(z) = AÍz + ˙ Î z˚ iø To see the real and imaginary parts, use polar form: z = re . This gives È iø 1 -iø˘ È È 1˘ 1˘ F(z) = AÍre + e ˙ = AÍr + ˙ cos ø + i AÍr - ˙ sin ø Î ˚ Î ˚ Î r r r˚ So we can now get the potentials and streamlines in polar form: Equipotentials: È ˘ Ír + 1˙ cos ø = const Î r˚ Kind of complicated to draw these piggies - wait until we do things parametrically in the next section. Streamlines: È ˘ Ír - 1˙ sin ø = const Î r˚ Again, these are not standard curves. However, at large distances, 1/r ‡ 0...
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This document was uploaded on 03/20/2014 for the course MATH 144 at Hofstra University.

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