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A vortex that rotates at constant angular velocity w about the z-axis has velocity vector field = 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 of the vortex as a function of the distance from its center, r. speed = (b) Compute div and curl . div = curl = (c) Compute the circulation of counterclockwise about the circle of radius R in the zy-plane, centered at the origin. circulation =

A vortex that rotates at constant angular velocity w about the z-axis has velocity vector field = 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 of the vortex as a function of the distance from its center, r. speed = (b) Compute div and curl . div = curl = (c) Compute the circulation of counterclockwise about the circle of radius R in the zy-plane, centered at the origin. circulation =

Advanced Engineering Mathematics
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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A vortex that rotates at constant angular velocity w about the z-axis has velocity vector field = 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 of the vortex as a function of the distance from its center, r. speed= (b) Compute div and curl . div - curl = (c) Compute the circulation of counterclockwise about the circle of radius R in the zy-plane, centered at the origin. circulation=
Transcribed Image Text:A vortex that rotates at constant angular velocity w about the z-axis has velocity vector field = 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 of the vortex as a function of the distance from its center, r. speed= (b) Compute div and curl . div - curl = (c) Compute the circulation of counterclockwise about the circle of radius R in the zy-plane, centered at the origin. circulation=
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