Usually in all discussions and arguments of scaling or solving problems using dimensional analysis, the dimensionless constant is indeterminate but it is usually assumed that it is of order 1.
What does "of order 1" mean? 0.1-10?
Is there any way, qualitative or quantitative, to see why the dimensionless constant is of order 1?
Are there exceptions to that? I mean cases where the dimensionless constant is very far from 1? Could you give some examples? Can such exceptions be figured out from dimensional analysis alone?