Dimensional Analysis with non-dimensional initial parameter

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Discussion Overview

The discussion revolves around the process of non-dimensionalizing equations related to a non-Newtonian fluid model, specifically focusing on the inclusion of a non-dimensional parameter, n, in the context of Buckingham's Pi theorem. The scope includes theoretical considerations of fluid dynamics and dimensional analysis.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant, Zoli, raises a question about how to include a non-dimensional parameter (n) in the non-dimensionalization process, noting that it does not appear in the equations.
  • Another participant indicates they have found a solution but does not initially share the details.
  • A subsequent reply seeks clarification on the solution, expressing confusion and a desire for an explanation.
  • A later reply suggests that the consistency index (K) incorporates the non-dimensional parameter n, implying that it may not need to be treated like other dimensional quantities in the analysis.
  • One participant expresses agreement with the reasoning presented regarding the treatment of the non-dimensional parameter.

Areas of Agreement / Disagreement

The discussion shows some agreement on the idea that the consistency index includes the non-dimensional parameter, but the initial question about how to handle n in the non-dimensionalization process remains partially unresolved, as not all participants have shared their insights.

Contextual Notes

The discussion does not fully explore the implications of excluding the non-dimensional parameter from the analysis, nor does it clarify the specific steps taken in the proposed solution.

Zoli
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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
 
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I managed to solve it.
 
How did you solve it? I have to admit I was stumped and hoped for an answer.
 
DaleSpam said:
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.
 

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