Shock speed in a symmetric cloud collision ($S=(\gamma -1)V/2$)

Two identical cold clouds approach at speeds $\pm V$ in their center-of-momentum frame. Reflection symmetry makes the uniformly compressed gas stationary. A shock moving outward at $S$ sees upstream speed $V+S$ and downstream speed $S$; their ratio equals the strong adiabatic compression $(\gamma +1)/(\gamma -1)$. Solving gives the displayed speed. For a monatomic gas $S=V/3$. Finite-cloud breakout ends the steady upstream supply and requires a subsequent boundary-release calculation.