Then z add a circulation at the origin with some

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Unformatted text preview: l function F(z), which will be singular at these points. Examples c lnz. The lines of flow are obtained by setting the 2π imaginary part = 0, giving arg(z) = const, suggesting a source or sink at the origin. To (A) Point Source T ake F(z) = 2 Note that we should get the same flux regardless of the shape or size or the surrounding surface, as long as that surface encloses only the given singular point. The reason for this is that the discrepancy between the integrals over two difference surfaces is itself a surface integral over a region where the divergence is zero, and so the difference is zero by the divergence theorem. 46 determine which, we need to compute the outward flux in 2 dimensions. First, we get the resulting vector field: c cz c“x, y‘ v = F'(z) = = 2= 2 2 2πz– 2π|z| 2π(x + y ) Which is a radially outward flow of magnitude c/(2πr). We now compute its strength: Thinking of a 3-dimensional cylinder as out surrounding volume, we are reduced to computing the limit of Ûc...
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