# Dimensional alalysis to show functional dependence

#### General_Sax

1. Homework Statement
Use the method of dimensional analysis to show that the functional dependence in equation (1) can be derived from an observational expression: [TEX]lambda = k*mu*f^m*T^n[/TEX].

2. Homework Equations
[TEX]lambda=k\sqrt {{\frac {T}{\mu}}}{f}^{-1}[/TEX] (1)
[TEX]lambda = k*mu*f^m*T^n[/TEX]
[TEX]\mu={\frac {{\it kg}}{m}}[/TEX]
[TEX]T={\frac {{\it kg}\,m}{{s}^{2}}}[/TEX]

3. The Attempt at a Solution

First I solve for n.

[TEX]m={\frac {{m}^{n}}{m}}[/TEX]
n = 2

Now I solve for m.

[TEX]0=0={1/s}^{m}{s}^{-2\,n}[/TEX]
m = -4

so now I have:

[TEX]\lambda={\frac {ku{T}^{2}}{{f}^{-4}}}[/TEX]

I don't understand what the question means by "show that the functional dependence in equation (1). . ."

In equation (1) we were told that [TEX]\lambda[/TEX] and T were variables. Well in equation I've derived [TEX]\lambda[/TEX] and T could very well be variables, but I don't think I understand the question. But, if the question is asking me to equate the two expressions and prove an "identity", then I can't do that. Any help welcomed and appreciated.

When I try to "work" the units out they don't work out at all.

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#### General_Sax

I tried to make it all pretty with the LaTeX, but it didn't work :(

#### General_Sax

Misread question. I thought the u had an exponent of 1, but it had an exponent of L.

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