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

In summary, the conversation discusses the topic of dimensional analysis and the use of pi groups to simplify equations. According to the first link, when forming a pi group, an exponent is needed for the non-repeating variable, while the second link states that no exponent is necessary. The question arises about which approach is correct and if an exponent is needed for the non-repeating variable.
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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)
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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
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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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  • #2
Bump
 
  • #3
anyone can reply ?
 
  • #4
which is correct ?
 
  • #5
bump
 
  • #6
is it necessary to put exponent of d ? ??
 

What is the Buckingham pi theorem?

The Buckingham pi theorem, also known as the pi theorem or the theorem of dimensional homogeneity, is a mathematical theorem used in dimensional analysis to determine the functional relationships between a set of variables in a physical system.

Who is the theorem named after?

The theorem is named after British physicist Edgar Buckingham, who first published it in 1914.

What is the purpose of the Buckingham pi theorem?

The theorem is used to reduce the number of variables in a physical problem by finding the dimensionless combinations of variables, known as pi terms, that govern the behavior of the system. This simplifies the analysis and allows for the prediction of the system's behavior without performing lengthy and complicated calculations.

What is the significance of the pi terms in the Buckingham pi theorem?

The pi terms are dimensionless numbers that represent the ratios of the physical quantities involved in the problem. They have a physical meaning and can be used to determine the relationship between the variables in the system.

What are some applications of the Buckingham pi theorem?

The Buckingham pi theorem has many applications in various fields, including physics, engineering, and chemistry. It is used to analyze physical systems, design experiments, and develop mathematical models. It is also used in the development of new theories and in the study of complex systems.

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