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Old   March 25, 2017, 11:10
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Hello Everyone!

Perhaps its a very trivial question, but can someone please point out on what does the little "i" and "j" mean when they are associated as a subscript to x and u in the following slide? Also I am a bit confused on why there is no mention of the other variables such as v, w and y and z.
I really appreciate your help.
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Old   March 25, 2017, 16:49
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The i and j belong to vector notation being used, there are many good sources that will explain this better than me so I will let you look them up, any book on vector calculus will do, I used one by P.C.Mattews, it gave a good introduction to vector calculus.

You could probably find a PDF of that book online but I'm not encouraging that !

The other variables have been omitted for clarity, the equations for the y and z axis will be identical to the ones shown for x but with the components changed to suit!

Hope that helps!

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Old   March 26, 2017, 02:41
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It's tensor subscript notation.

u is the entire velocity vector (i.e. u = [u_x,u_y,u_z], not one of its directional components. Same thing with x. This way u_i refers to the individual components and x_i refers to the individual components. The v,w,y,z are not omitted per se, it's just that u and x mean something else. If you want you can replace u and x by another symbol like U and X if you want to make the distinction so that U = [Ux,Uy,Uz] and X = [x,y,z]

u_i means to loop over i or take all its permutations. Pay attention to two different symbols, if they have the same subscript or not (i & i or i & j).
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