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Dimensional Analysis with non-dimensional initial parameter

  1. Jan 19, 2014 #1
    I would like non-dimensionalize the equations which describe a non-Newtonian fluid model. In the constitutive equation (power-law model) there is a non-dimensional parameter: n. According to Buckingham's Pi theory, I must take all the relevant independent parameters (variables, constants, etc.) into account to form non-dimensional parameters. Parameter n should also be included, but (since it is non-dimensional) it will not appear anywhere. How can I handle this situation? I am sure that there are other areas in physics where initially known non-dimensional parameters turn up.

  2. jcsd
  3. Jan 20, 2014 #2
    I managed to solve it.
  4. Jan 20, 2014 #3


    Staff: Mentor

    How did you solve it? I have to admit I was stumped and hoped for an answer.
  5. Jan 20, 2014 #4
    I realised that a dependent parameter (the consistency index: K[Pa s^n]) includes this non-dimensional parameter and this is the only one that changes when we consider a power-law fluid instead of a Newtonian fluid. Therefore we do not have to take this non-dimensional parameter into account as for the other quantities.
  6. Jan 20, 2014 #5


    Staff: Mentor

    That makes sense.
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