The density-weighted mean kinematic viscosity is
using . Under the preceding rescaling, let
Uniqueness of the universal dimensionless solution makes a positive numerical constant independent of . Hence
For Keplerian rotation, . The constant-opacity gas-pressure disk viscosity law is therefore
The particular scaling convention changes the representation of but not this physical law. Its nontrivial powers come from balancing viscous heating, diffusive cooling and vertical support together, rather than assuming a fixed temperature or thickness.