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At a point in an incompressible fluid having spherical polar co-ordinates (r, 0, 4), the velocity components are (2Mr¯3 cos 0, Mr-2 sin 0,0), where M is a constant. a) Show that the velocity is of the potential kind.

At a point in an incompressible fluid having spherical polar co-ordinates (r, 0, 4), the velocity components are (2Mr¯3 cos 0, Mr-2 sin 0,0), where M is a constant. a) Show that the velocity is of the potential kind.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter7: Locus And Concurrence
Section7.2: Concurrence Of Lines
Problem 7E: Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a...
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In the attachments, I have the question and the answer of its part (a) given to us. 

Could you kindly explain why we factor out a term   1/[r^2 * sin(theta)] in the place where we take the curl of velocity?If that's a standard method, how is that derived?

Thank you!

Given : O = M. s ing COSO Solution CA) Show fow is potential Find As we Enow dr dr î + rdoô + rsino dy Y so 9 = cos o? + sine ô %3D Now find Curl a rsinoy ro curl a = resino i.e. cOso sino 1 - rê co -0) + rsinoy - sine - (- sino) %3D Hence curl a =0 So frow id potenfial type of.
Transcribed Image Text:Given : O = M. s ing COSO Solution CA) Show fow is potential Find As we Enow dr dr î + rdoô + rsino dy Y so 9 = cos o? + sine ô %3D Now find Curl a rsinoy ro curl a = resino i.e. cOso sino 1 - rê co -0) + rsinoy - sine - (- sino) %3D Hence curl a =0 So frow id potenfial type of.
At a point in an incompressible fluid having spherical polar co-ordinates (r, 0, 4), the velocity components are (2Mr-3 cos 0, Mr¯2 sin 0,0), where M is a constant. a) Show that the velocity is of the potential kind. b) Find the velocity potential and the equations of the streamlines.
Transcribed Image Text:At a point in an incompressible fluid having spherical polar co-ordinates (r, 0, 4), the velocity components are (2Mr-3 cos 0, Mr¯2 sin 0,0), where M is a constant. a) Show that the velocity is of the potential kind. b) Find the velocity potential and the equations of the streamlines.
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