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Dimensional alalysis to show functional dependence

  1. Oct 11, 2009 #1
    1. The problem statement, all variables and given/known data
    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. Relevant 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.
     
  2. jcsd
  3. Oct 11, 2009 #2
    I tried to make it all pretty with the LaTeX, but it didn't work :(
     
  4. Oct 11, 2009 #3
    Misread question. I thought the u had an exponent of 1, but it had an exponent of L.
     
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