Return to Problem 9.19, where the average Mach number across the two-dimensional flow in a duct was calculated, and where θ for the upper wall was 30◦. Assuming quasi-one-dimensional flow, calculate the Mach number at the location AB in the duct.

Data from Problem 9.19:

Repeat Problem 9.18, except with θ = 30◦. Again, we will use these results to compare with a quasi-one-dimensional calculation in Problem 10.16. The reason for repeating this calculation is to examine the effect of the much more highly two-dimensional flow generated in this case by a much larger expansion angle.

Data from Problem 9.18:

Consider a two-dimensional duct with a straight horizontal lower wall, and a straight upper wall inclined upward through the angle θ = 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-Mayer 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.