Past exam of the mathematics course of the University of Cambridge 2005 iii Paper 73 1 iii Solution Created 2026-10-03 Updated 2026-10-14
The density-weighted mean kinematic viscosity isusing . Under the preceding rescaling, letUniqueness of the universal dimensionless solution makes a positive numerical constant independent of . HenceFor Keplerian rotation, . The constant-opacity gas-pressure disk viscosity law is thereforeThe 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.