The Limitations of the Shock Wave

When the upstream Mach number becomes very large, the downstream Mach number (see equation (5.22)) is limited by

$${M_y}^2 = { 1 + \cancelto{\sim 0}{2 \over (k -1) {M_x}^{2}} \over {2k \over k -1} - \cancelto{\sim 0}{1 \over {M_x}^{2}} } \qquad = {k -1 \over 2k}$$ (5.38)

This result is shown in Figure (5.3). The limits of the pressure ratio can be obtained by looking at equation (5.16) and by utilizing the limit that was obtained in equation (5.38).