1. The problem statement, all variables and given/known data In buckingham pi theorem, you have p=n-k dimensionless groups (π1, π2,...) where n=number of total variables and k=number of total units among the variables For example, lets say we want to relate: ρ~m/L3 (density) μ~m/L*t (viscosity) v~L/t (velocity) d~L (distance) Da~L2/t (diffusivity) k~L/t (mass transfer coefficient) In this case, n=6, k=3 (m, L, t) so we have 3 non dimensional groups. In the solution to this problem, 3 common variables are chosen, Da, ρ, d, such that: π1=Daaρbdck π2=Dadρedfv π3=Dagρhdiμ So in this case, Da, ρ and d are chosen as the common variables among all groups. I am wondering why these three variables were chosen specifically. Can a different combination of variables be chosen to achieve the correct answer? Also, were three variables chosen because there are three units?