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Similarity solution indices

  • Thread starter Yalldoor
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Homework Statement



A question asks me to show the Navier-Stokes equation reduces to [tex]u_{t} - Vu_{y} = {\nu}u_{yy}[/tex] which I have done no bother. Then it asks to find an appropriate solution for u(y,t).


Homework Equations





The Attempt at a Solution



I'm seeking a similarity solution for it, and have set [tex]u(y,t) = f(\eta)[/tex] where [tex]\eta = yt^{n}[/tex]. Making the substitution, I get:

[tex]n(\eta)t^{-1}f'(\eta) - Vt^{n}f'(\eta) = {\nu}t^{2n}f''(\eta)[/tex]

This is where the problem is, in chooing a value of n to satisfy the power of t, can I divide throughout by [tex]t^{n}[/tex] thus removing it from the second term and then proceed to set n = -1/2, or do I have to take into account the fact it's technically [tex]t^{0}[/tex] in the second term?
 

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