Dimensional Analysis with non-dimensional initial parameter

[Zoli]

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.

Thanks,
Zoli

 

[Zoli]

I managed to solve it.

 

[Dale]

How did you solve it? I have to admit I was stumped and hoped for an answer.

 

[Zoli]

How did you solve it? I have to admit I was stumped and hoped for an answer.

I realized 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.

 

[Dale]

That makes sense.