Tangents and normals in determining the kinematic of fluid flow

What arw the significances of tangents and normals in determining the kinematic of fluid flow?

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Originally Posted by al-habsi

what arw the significances of tangents and normals in determining the kinematic of fluid flow?

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There is this cool thing called Google. Maybe you've heard of it. If you make the cut, you may be given access to it;):D.



I am not going to go over the calculus of all this, but here is a basic example of flux of the flow field.

Suppose we have a portion of the surface . Call this portion, say, .

Find this portion of the above surface that lies above the xy-plane and say it is oriented upwards. We can find the flux, , of the flow field across .



R is the projection of the surface, sigma, on the xy-plane. Since it is oriented upwards, we can write:



Using polar coordinates:





When we canceled the radical, that comes from a theorem.



where the + is used if sigma has positive orientation and - if it is negative orientation.

This is a little bit oin the topic, which barely scratches the surface.

Hope it helps a little. Calculus texts will probably touch on the topic in the latter sections under surface integrals, flux, divergence theorem, Stokes' Theorem, etc.

But try googling or finding a book on the topic. Your question is painted with a broad brush.

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There is this cool thing called Google. Maybe you've heard of it. If you make the cut, you may be given access to it.

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Believe me I have try it and thanks for your answer but it not the answer for my question ;)

The kinematics of a flow describes the motion of the fluid without taking
Into account the forces that cause this motion

Normals show direction because they are perpendicular to the tangent at a point.

Here is a link to a power point that may help a little:

http://www.esm.vt.edu/~dtmook/AOE510...Kinematics.pdf

This site is being rather slow this morning, so I am going to log off for a while.