Perform nondimensionalization with derivatives [closed]

I'm trying to perform nondimensionalization to the following symbolic equations:

eqDn = Subscript[\[Mu], d] * (1/r) * D[r * D[Subscript[u, d][r], r], r] == Subscript[P, d]eqUn = Subscript[\[Mu], u] * (1/r) * D[r * D[Subscript[u, u][r], r], r] == Subscript[P, u]

Using the following substitutions:

subs = {  r -> R * OverHat[r], (* Dimensionless radial distance *)  Subscript[u, d][r] -> Subscript[U,0] * OverHat[Subscript[u, d]][OverHat[r]], (* Dimensionless velocity *)  Subscript[u, u][r] -> Subscript[U,0] * OverHat[Subscript[u, u]][OverHat[r]],   Subscript[P, d] -> Subscript[P,0] * OverHat[Subscript[P, d]],   Subscript[P, u] ->Subscript[P,0] * OverHat[Subscript[P, u]], (* Reference pressure *)  Subscript[\[Mu], d] -> M * Subscript[\[Mu], u] (* Viscosity ratio M *)};

However when I try:

eqDn2 = Simplify[eqDn /. subs]eqUn2 = Simplify[eqUn /. subs]

Mathematica doesn't use the chain rule when presenting the derivatives.Is there a proper way to perform nondimensionalization and keep track of the units when taking derivatives in this case?