5 quantities, 3 rows, 2 left over

The dimension matrix for the drag on a sphere: one column per quantity, one row per base dimension, and every entry an exponent. Buckingham's theorem is a statement about this matrix and nothing else — the number of independent dimensionless groups is the number of columns minus the rank, computed here by elimination. Nothing about fluids enters until somebody decides which columns to write down.

1 essay calls pi-groups. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

It is also the blast radius. Changing pi-groups changes every figure listed here at once, and on this site it may change what they assert as well as what they show — which is what has to be rebuilt and looked at before the change is believed.