text: In the case of the hyperbolic conservation law (), we have seen that the shock speed can be obtained by simple division. However, for the 1D Euler equations (), () and (), we have the vector state variable  and the jump conditions become
  Equations (), () and () are known as the Rankine–Hugoniot conditions for the Euler equations and are derived by enforcing the conservation laws in integral form over a control volume that includes the shock. For this situation  cannot be obtained by simple division. However, it can be shown by transforming the problem to a moving co-ordinate system
  (setting , ,  to remove ) and some algebraic manipulation (involving the elimination of  from the transformed equation () using the transformed equation ()), that the shock speed is given by
  where  is the speed of sound in the fluid at upstream conditions.