y x = r cos 0 V = Or y = r sine r = √x² + y² χ Flow in "solid body rotation" acts like a solid spinning around an axis. The streamlines are circular, the velocity is purely tangential, and the velocity magnitude is V = r, where is the angular velocity (positive counter-clockwise) and r is the radius. (a) Express the velocity vector V as a function of x and y. (b) Calculate the curl of the velocity vector V × V, indicating clearly the direction of the resulting vector.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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y
x = r cos 0
V = Or
y = r sine
r = √x² + y²
χ
Flow in "solid body rotation" acts like a solid spinning around an axis. The streamlines are circular,
the velocity is purely tangential, and the velocity magnitude is V = r, where is the angular
velocity (positive counter-clockwise) and r is the radius.
(a) Express the velocity vector V as a function of x and y.
(b) Calculate the curl of the velocity vector V × V, indicating clearly the direction of the resulting
vector.
Transcribed Image Text:y x = r cos 0 V = Or y = r sine r = √x² + y² χ Flow in "solid body rotation" acts like a solid spinning around an axis. The streamlines are circular, the velocity is purely tangential, and the velocity magnitude is V = r, where is the angular velocity (positive counter-clockwise) and r is the radius. (a) Express the velocity vector V as a function of x and y. (b) Calculate the curl of the velocity vector V × V, indicating clearly the direction of the resulting vector.
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