Dimensional Analysis with non-dimensional initial parameter

In summary, the speaker discusses non-dimensionalizing equations for a non-Newtonian fluid model and the inclusion of a non-dimensional parameter, n, in the constitutive equation. They mention using Buckingham's Pi theory to consider all relevant independent parameters and how to handle the situation when a non-dimensional parameter does not appear anywhere. The speaker then shares how they solved the problem and the realization that a dependent parameter includes the non-dimensional parameter. This means it does not have to be taken into account for other quantities.
  • #1
Zoli
20
0
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
 
Physics news on Phys.org
  • #2
I managed to solve it.
 
  • #3
How did you solve it? I have to admit I was stumped and hoped for an answer.
 
  • #4
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.
 
  • #5
That makes sense.
 

1. What is dimensional analysis and why is it important in scientific research?

Dimensional analysis is a mathematical technique used to analyze and understand relationships between different physical quantities. It is important in scientific research because it allows for the simplification of complex systems by reducing the number of variables and identifying key parameters that affect the behavior of a system.

2. What is a non-dimensional initial parameter and how is it different from a dimensional initial parameter?

A non-dimensional initial parameter is a quantity that has been scaled or normalized by a characteristic value of the system. This is different from a dimensional initial parameter, which is a quantity that has not been scaled and has units associated with it. Non-dimensional initial parameters allow for easier comparison between different systems and can reveal underlying relationships and trends.

3. How is dimensional analysis used in the development of mathematical models?

Dimensional analysis is used in the development of mathematical models by identifying key parameters and relationships between them. By reducing a system to its non-dimensional parameters, mathematical models can be developed that accurately describe the behavior of the system and can be applied to different scenarios and scales.

4. Can dimensional analysis be applied to any system or process?

Yes, dimensional analysis can be applied to almost any system or process, as long as there are measurable physical quantities involved. It is a universal technique that has been used in a wide range of fields, including physics, engineering, and biology.

5. How does dimensional analysis help in the process of experimentation and data analysis?

Dimensional analysis can help in the process of experimentation and data analysis by providing a framework for organizing and interpreting data. By identifying non-dimensional parameters, scientists can focus on the most important variables and understand how they affect the behavior of a system. This can also help in designing more efficient experiments and making predictions based on data analysis.

Similar threads

Buckingham-Pi for "algorithmic" non-dimensionalization
    • Other Physics Topics
Replies
2
Views
1K
Dimensional Analysis: Solving Confusing Steps
    • Introductory Physics Homework Help
Replies
4
Views
818
A The Blessings of Dimensionality and Hilbert's 6th Problem
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
How does dimensional analysis account for additive variables in equations?
    • Other Physics Topics
Replies
1
Views
1K
I How to Express Non-regular Prior Distributions by Mathematical Formula
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
339
Dimensional analysis-how one variable scales w/ another
    • Calculus and Beyond Homework Help
Replies
1
Views
754
Consequences of Choosing Incorrect Variables in BuckinghamPi
    • Other Physics Topics
Replies
1
Views
854
Mathematical Biology and Modelling
    • General Math
Replies
1
Views
1K
Dimensional analysis: Energy Transfer
    • Introductory Physics Homework Help
Replies
7
Views
1K
Non-dimensionalization of the energy balance
    • Materials and Chemical Engineering
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top