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
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=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8dd4d4ad-fe99-4531-a055-62ec1681b086%2F3639aa79-70e0-48bd-8085-9a18fa9d881b%2Fueudnmd_processed.jpeg&w=3840&q=75)
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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