Why Are There Only 3 Pi Groups in Dimensional Analysis?

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SUMMARY

The discussion centers on the dimensional analysis of physical quantities, specifically addressing the number of Pi groups derived from the Buckingham Pi theorem. The original poster asserts that there should be four Pi groups based on their calculation of dimensions, but the consensus is that only three Pi groups exist due to the relationship between the six quantities and the three fundamental dimensions: mass (M), length (L), and time (T). The correct interpretation is that with six variables and three dimensions, the formula yields three dimensionless groups.

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Homework Statement



Is the question wrong ?
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Homework Equations

The Attempt at a Solution


I found that the number of dimension = 6 , primary dimensionof velocity is L / T , which is 2 , number of repeating variable = 2 , so , there are 6-2 = 4 pi group , why the question only gt 3 pi group ?
 
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How to do this question?
 
foo9008 said:
y is L / T , which is 2 , number of repeating variable = 2 , so , there are 6-2 = 4 pi group , why the question only gt 3 pi group
Not sure where you get that formula from. As I understand it, you have 6 quantities that, between them, involve 3 dimensions (MLT), so the equation can be written relating 6-3=3 dimensionless expressions.
 
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