The renormalization factor that converts the solar wind tube area into an effective de Laval nozzle area is exactly Chapman's hydrostatic density profile, by construction rather than by dynamics.
Schrijver,Solar and Stellar Magnetic Activity, Cambridge Univ
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On the Role of Chapman's Hydrostatic Solar Wind Mechanism in Parker's Hydrodynamic Solar Wind Model
The renormalization factor that converts the solar wind tube area into an effective de Laval nozzle area is exactly Chapman's hydrostatic density profile, by construction rather than by dynamics.