4. In a table of vector differential operators, look up the expressions for V x V in a cylindrical coordinate system. (a) Compute the vorticity for the flow in a round tube where the velocity profile is = vo [1-(³] V₂ = Vo (b) Compute the vorticity for an ideal vortex where the velocity is Ve= r where constant. 2πг (c) Compute the vorticity in the vortex flow given by Ve= r 2лг 1- exp ( r² 4vt (d) Sketch all the velocity and vorticity profiles.
4. In a table of vector differential operators, look up the expressions for V x V in a cylindrical coordinate system. (a) Compute the vorticity for the flow in a round tube where the velocity profile is = vo [1-(³] V₂ = Vo (b) Compute the vorticity for an ideal vortex where the velocity is Ve= r where constant. 2πг (c) Compute the vorticity in the vortex flow given by Ve= r 2лг 1- exp ( r² 4vt (d) Sketch all the velocity and vorticity profiles.
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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![4. In a table of vector differential operators, look up the expressions for V x V in a cylindrical coordinate
system.
(a) Compute the vorticity for the flow in a round tube where the velocity profile is
= vo [1-(³]
V₂ = Vo
(b) Compute the vorticity for an ideal vortex where the velocity is
Ve=
r
where constant.
2πг
(c) Compute the vorticity in the vortex flow given by
Ve=
r
2лг
1- exp
(
r²
4vt
(d) Sketch all the velocity and vorticity profiles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2af3f565-c9d4-43d4-b32b-cec980ab9b87%2F07702028-c3df-4849-b564-2bc3b6730afe%2Fh52whef_processed.png&w=3840&q=75)
Transcribed Image Text:4. In a table of vector differential operators, look up the expressions for V x V in a cylindrical coordinate
system.
(a) Compute the vorticity for the flow in a round tube where the velocity profile is
= vo [1-(³]
V₂ = Vo
(b) Compute the vorticity for an ideal vortex where the velocity is
Ve=
r
where constant.
2πг
(c) Compute the vorticity in the vortex flow given by
Ve=
r
2лг
1- exp
(
r²
4vt
(d) Sketch all the velocity and vorticity profiles.
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