The actual relationship between the three variables is simply D = VT, so that the actual dimensionless equation ( f ( \ pi ) = 0 ) is written:
2.
The equation demonstrating the existence of a product of powers for our problem can be written in an entirely equivalent way : T = \ kappa \ sqrt \ tfrac { m } { k }, for some dimensionless constant ? ( equal to \ sqrt { C } from the original dimensionless equation ).