Dimensional Analysis

Suppose we are interested in a quantity that is equal to some constant times A^a B^b C^c , where A,B,C have independent dimensions and \# is dimensionless \text{Quantity} = \# A^a B^b C^c. We can often resort to dimensional analysis to figure out what a,b,c should be. This approach can be particularly powerful when we know that the quantity of interest depends on very few parameters and that there is a unique combination of them that gives us the quantity with the correct dimension. Note that we cannot determine the constant \# , but we would guess–and hope–it would be O(1) .