Planar blast-wave energy scaling
= Planar blast-wave energy scaling
{title2=$Z\propto t^{2/3}$}
For a planar adiabatic explosion with energy per unit area $E$ in a uniform medium of <mass density> $\rho_0$, the conserved energy has form $E=I\rho_0Z\dot Z^2$, with a finite positive integral $I$ of the <similarity profiles>. Hence $Z=C(E/\rho_0)^{1/3}t^{2/3}$. If $E$ is shared by two fronts, its fraction assigned to either side is absorbed into $C$.