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Consider the velocity field given by u = y/(x2 + y2) and v = −x/(x2 + y2).          Calculate the vorticity.

Consider the velocity field given by u = y/(x2 + y2) and v = −x/(x2 + y2).          Calculate the vorticity.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Consider the velocity field given by u = y/(x2 + y2) and v = −x/(x2 + y2).          Calculate the vorticity.

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4) Consider the steady two-dimensional flows with velocity fields Y x² + y² and U = x x² + y² U= V = X Y x² + y² x² + y² a) What are their vorticity and divergence away from (x, y) = (0,0)? V b) What is their circulation around any circle about the origin? c) How much fluid volume is flowing into or out of any circle around the origin per unit time in each of them? d) Compute and plot the streamlines for both flows.
Transcribed Image Text:4) Consider the steady two-dimensional flows with velocity fields Y x² + y² and U = x x² + y² U= V = X Y x² + y² x² + y² a) What are their vorticity and divergence away from (x, y) = (0,0)? V b) What is their circulation around any circle about the origin? c) How much fluid volume is flowing into or out of any circle around the origin per unit time in each of them? d) Compute and plot the streamlines for both flows.
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