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 ingCOSOSolutionCA)Show fow is potential FindAs we Enowdrdr î + rdoô + rsino dy Y so 9 =cos o? +sine ô%3DNow findCurl arsinoyrocurl a =resinoi.e.cOso sino1- rê co -0) + rsinoy - sine - (- sino)%3DHencecurl a =0Sofrow 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), whereM is a constant.a) Show that the velocity is of the potential kind.b) Find the velocity potential and the equations of thestreamlines.

In orthogonal curvilinear co-ordinates i.e. when u, v, w are expressed in terms of rectangular…

Answered: At a point in an incompressible fluid…

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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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.

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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