Chapter 9, Problem 9.18P

(The purpose of this problem is to calculate a two-dimensional expanding supersonic flow and compare it with the analogous quasi-one-dimensional flow in Problem 10.15.) Consider a two-dimensional duct with a straight horizontal lower wall, and a straight upper wall inclined upward through the angle $\theta =\text{3}°$. The height of the duct entrance is 0.3 m. A uniform horizontal flow at Mach 2 enters the duct and goes through a Prandtl-Maycr expansion wave centered at the top corner of the entrance. The wave propagates to the bottom wall, where the leading edge (the forward Mach line) of the wave intersects the bottom wall at point A located at distance $x_A$ from the duct entrance. Imagine a line drawn perpendicular to the lower wall at point A, and intersecting the upper wall at point B. The local height of the duct at point A is the length of this line AB. Calculate the average flow Mach number over AB. assuming that M varies linearly along that portion of AB inside the expansion wave.