# Similarity solution indices

1. Nov 13, 2008

### Yalldoor

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

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

$$n(\eta)t^{-1}f'(\eta) - Vt^{n}f'(\eta) = {\nu}t^{2n}f''(\eta)$$

This is where the problem is, in chooing a value of n to satisfy the power of t, can I divide throughout by $$t^{n}$$ 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 $$t^{0}$$ in the second term?