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

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The discussion centers on whether an exponent is necessary for non-repeating variables in the Buckingham Pi Theorem, specifically regarding the variable delta P. One source suggests that an exponent should be included for non-repeating variables, while another indicates that it is not required. The confusion arises from differing interpretations of dimensional analysis principles. Participants seek clarification on which approach is correct and whether an exponent for the non-repeating variable is essential. Ultimately, the debate highlights the nuances in applying the Buckingham Pi Theorem to 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)
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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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anyone can reply ?
 
which is correct ?
 
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is it necessary to put exponent of d ? ??
 

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