Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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leave answers in vector form, thank you.

A vortex that rotates at constant angular velocity w about the z-axis has velocity vector field v =
w(-yi + æj).
(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 ||u|| of the vortex as a function
of the distance from its center, r.
speed =
(b) Compute div v and curl v.
div v =
-Wx+wy
curl i = k(xwX+ywy)
(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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Transcribed Image Text:A vortex that rotates at constant angular velocity w about the z-axis has velocity vector field v = w(-yi + æj). (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 ||u|| of the vortex as a function of the distance from its center, r. speed = (b) Compute div v and curl v. div v = -Wx+wy curl i = k(xwX+ywy) (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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