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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A vortex that rotates at constant angular velocity w about the z-axis has velocity vector field v = w(-yi + xj).
(a) Sketch, on a separate sheet of paper, the vector field with w = 1 and the vector field with w = -1. Then determine the speed ||ü|| of the vortex as a function
of the distance from its center, r.
speed =
(b) Compute div v and curl i.
div v =
curl v =
(c) Compute the circulation of v counterclockwise about the circle of radius R in the xy-plane, centered at the origin.
circulation =
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