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

foo9008 · May 21, 2016

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)

Worked example text on head loss in turbulent pipe flow, listing dimensions of D, v, rho, delta p, mu, l and eta, and a dimensional group D^a v^b rho^c delta p^d with a circled exponent d and resulting relations 0 = c + d and 0 = -b - 2d.

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

Worked example from a dimensional analysis page: the equation 1 = (kg m^-3)^a (m s^-1)^b (m)^c (kg m s^-2) written in terms of SI units, with the final factor circled in red.

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...

foo9008 · May 21, 2016

foo9008 · May 21, 2016

anyone can reply ?

foo9008 · May 22, 2016

which is correct ?

foo9008 · May 31, 2016

foo9008 · May 31, 2016

is it necessary to put exponent of d ? ??

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

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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