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Unformatted text preview: vy = -2xy 2 22 (x +y ) Warning: This method of plotting is not accurate unless one uses a very small ∆t and plots lots of points. As you move along the curve, you are really changing from one streamline to another. As an example, if we started at (0, 1), the streamline should trace out a quadrant of the circle and then stop at the stagnation point, but instead we get: this with ∆t = .12: 48 2.5 2 1.5 1 0.5 0 -0.5 0 1 2 3 4 -1 -1.5 -2 -2.5 Notice that the line starting at (-5, 0) stops when it hits the cylinder because of the stagnation point there Exercise Set 14 1. Verify the claims in (D): (a) that the stagnation points are where claimed, (b) that they are on the unit circle id K ≤ 4π, and on the imaginary axis otherwise. 2. Set up an Excel spreadsheet to plot a as follows, so that you get around 200 points (allowing you to use a small value of ∆t): ∆t x y ∆x ∆x x0 y0 vx∆t vx∆t =x0 + ∆x =y0 + ∆y (First copy the right-hand cells one level, and then copy everything.)For extra credit, you can set it up to plot several streamlines... 15. The Jouk...
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This document was uploaded on 03/20/2014 for the course MATH 144 at Hofstra University.

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