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Unformatted text preview: vy = -2xy
(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
-0.5 0 1 2 3 4 -1
-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):
=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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