Why Are There Only 3 Pi Groups in Dimensional Analysis?

[foo9008]

Homework Statement

Is the question wrong ?

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 ?

 

[foo9008]

How to do this question?

 

[haruspex]

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.