Non-dimensionalization of a Partial Differential Equation

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Hello all, I am interested in replacing the variables of a Partial Differential Equation (PDE) for their non-dimensional counterparts and then group together the dimensionless numbers. I think I would only need to be able to replace the variables and also the derivative operators (as in a change of variables $\hat{x}=x/L$), grouping the dimensionless numbers can be done by hand.

It is a similar procedure to what is being done here: (en.wikipedia.org/wiki/Non-dimensionalization_and_scaling_of_the_Navier%E2%80%93Stokes_equations) . I was wondering if this can be done with SAGE.