Page:Threeshockwaves.pdf/8

 Let the shock OB be of a given intensity $$\zeta_{1,2}$$. Then according to the Rankine-Hugoniot equations in the forms (1) and (2) the velocity of the gas in region 1 normal to the shock front OB in units of the velocity of sound in this region is given by equation (3) and accordingly

The velocity of the gas in the region 2 both in magnitude and in direction can therefore be readily determined through the equations (1) and (2). For crossing the shock OC inclined at an angle $$\beta$$ to the direction of OB we can again use the Rankine-Hugoniot equations with

Thus with the foregoing values for $$\sigma_\perp$$ and $$\sigma_\parallel$$ we can deduce the conditions behind OC. In particular we shall arrive in region 3 with a definite direction for the motion of the gas in this region. Moreover

Now the shock OE must be so inclined to the direction of motion OA in region 1 that the pressure behind the shock OE is the same as in region 3. In other words the equation determining the angle