One-dimensional properties of normal shock waves
Consider the flow model shown in Fig. 6.7a in which a plane shock advances from right to left with velocity щ into a region of still gas. Behind the shock the velocity is suddenly increased to some value и in the direction of the wave. It is convenient to superimpose on the system a velocity of tq from left to right to bring the shock stationary relative to the walls of the tube through which gas is flowing undisturbed at tq (Fig. 6.7b). The shock becomes a stationary discontinuity into which gas flows with uniform conditions, p, p, tq, etc., and from which it flows with uniform conditions, рг, pi, мг> etc. It is assumed that the gas is inviscid, and non-heat conducting, so that the flow is adiabatic up to and beyond the discontinuity.
Momentum, in the absence of external and dissipative forces
Pi +Pu =P2 + P2u