Is Exponential Needed for Non-Repeating Variable in Buckingham Pi Theorem?

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Homework Help Overview

The discussion revolves around the application of the Buckingham Pi Theorem in dimensional analysis, specifically focusing on the treatment of non-repeating variables and the necessity of exponents in forming Pi groups.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to compare two different sources regarding the treatment of non-repeating variables in the context of the theorem. They question whether an exponent is necessary for the non-repeating variable, delta P, while referencing specific examples from the sources.

Discussion Status

The discussion appears to be ongoing, with participants seeking clarification on the correct approach to the exponent for the non-repeating variable. There is a lack of consensus, as multiple interpretations are being explored, and participants are actively prompting for responses.

Contextual Notes

Participants note that the question is distinct from previous threads, indicating a specific focus on the nuances of the theorem's application. There is an emphasis on the need for clarity regarding the treatment of variables in dimensional analysis.

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Homework Statement


https://projects.exeter.ac.uk/fluidflow/Courses/FluidDynamics3211-2/DimensionalAnalysis/dimensionalLecturese4.htmlaccording to this link , when we form the pi group , we need to put an exponent for the non-repeating variable ,( in this case , delta P is non-repeating variable , D , v and rho are repeating variable)
FXVC7K7.png
http://www.efm.leeds.ac.uk/CIVE/CIVE1400/Section5/dimensional_analysis.htm (refer to 7 )however , in this case , we do not have to put exponent on the non-repeating variable , the author just putF = (MLT^-2 ) instead of (MLT^-2)^d
k9bJMDc.png


Homework Equations

The Attempt at a Solution


Which is correct ? the first or second one ? is exponential needed for non-repeating variable ?
P/s : this is not same as the question i posted in another thread...
 
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anyone can reply ?
 
which is correct ?
 
bump
 
is it necessary to put exponent of d ? ??
 

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