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# Streamlines these are the curves 2axy const giving

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Unformatted text preview: 20 T(x, y) = (2x + π) = x + 10 π π and so 20 F(z) = z + 10 π Therefore, on the original region, we have 20 -1 G(z) = sin (z) + 10 π Exercise Set 11 Hand In: (Based on Kreyzsig, p. 811) 1. (a) Find the temperature and complex potential for the following situation: T1 a T2 (b) Now use superposition to do the same for the following: 0º –1 T0 1 0º (C) Finally, repeat for this: 0º 0 0º T0 1 38 (Insulation is at the solid dots.) 12. Fluid & Air Flow (16.4 Kreyszig) We know that electrostatic potentials and temperature are harmonic under suitable conditions. What about fluid flow? Let v denote the velocity field for a fluid flow. The fluid flow in a particular region is called i rrotational if Ô ¿v = 0.† [Recall the interpretation of the curl from calculus]. If v depends on x and y only and has only two coordinates, v = “P(x, y), Q(x, y)‘, then this translates to Py = Qx. On the other hand, a fluid is incompressible (like water and oil) if Ô.v = 0. [Again recall the interpret...
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## This document was uploaded on 03/20/2014 for the course MATH 144 at Hofstra University.

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