= Ballistic marginal-escape stellar wind
{title2=$v(r)=\sqrt{2GM/r}$}
A steady outward radial flow with negligible pressure force conserves $v^2/2-GM/r$. If its speed at a reference radius equals the mechanical <escape velocity>, this constant is zero and $v\propto r^{-1/2}$. <Conservation of mass> gives $\rho\propto r^{-3/2}$. An adiabatically evolving <ideal gas> carried along that leading flow has $p\propto r^{-3\gamma/2}$ and $T\propto r^{-3(\gamma-1)/2}$.
Finite <specific enthalpy> changes the dynamical problem: the full conserved <Bernoulli equation> is $v^2/2+h-GM/r=B$. At the same boundary mechanical escape speed, $B=h_e$ rather than zero. A warm wind therefore needs its enthalpy and equation of state specified before the explicit ballistic velocity can be replaced by a consistent pressure-driven solution.
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