= Adiabatic nozzle terminal speed
{title2=$u_\infty=c_*\sqrt{(\gamma+1)/(\gamma-1)}$}
For a lossless <polytropic flow> with $\gamma>1$, negligible <gravity> and a sonic throat, the <Bernoulli function> is $u^2/2+c_s^2/(\gamma-1)=(\gamma+1)c_*^2/[2(\gamma-1)]$. On an expanding supersonic branch for which $\rho\to0$, the <specific enthalpy> vanishes and the limiting <velocity> is the displayed value. If area grows as $Cr^2$, <mass conservation> further gives $\rho\sim\dot M/(Cu_\infty r^2)$. A subsonic pressure-confined branch need not have this asymptotic behavior.
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