In a fluid flow problem there are five natural parameters. These have dimensions in terms of length L, mass M and time T as follows:

To determine how many non-dimensional parameters can be constructed, seek values of p, q, r, s and t so that VprqDrgsmt is dimensionless. Write the equations for p, q, r, s and t in matrix form and show that the resulting 3 × 5 matrix has rank 3. Thus there are two parameters that can be chosen independently.
By choosing these appropriately, show that they correspond to the Reynolds number Re = VρD/μ
and the Froude number Fr = Dg/V².