1. consider the flow of air through a convergent-divergent nozzle with a throat cross-section at = 0.4m2 and an exit-to-throat area ratio of 1.616. assuming that the reservoir conditions are p0 = 5.5 · 105p a and t0 = 550◦c, determine the exit mach number me and the mass flow ˙m through the nozzle when the pressure outside the reservoir pa attains the following values:
(a) pa = 5.0 · 105p a.
(b) pa = 2.2 · 105p a.
(c) pa = 0.4 · 105p a.
(d) draw the pattern of shocks and expansion waves at the nozzle exit for the last case.
2. in low-speed incompressible flow, the peak pressure coefficient (at the minimum pressure point) is cp = −0.48. estimate the critical mach number for the given airfoil, using the prandtl-glauet rule.

Your starship, the aimless wanderer, lands on the mysterious planet mongo. as chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 14.0 m/s returns to the ground in 5.70 s ; the circumference of mongo at the equator is 2.20×10^5 km ; and there is no appreciable atmosphere on mongo. (a) the starship commander, captain confusion, asks for the following information: what is the mass of mongo? (b) if the aimless wanderer goes into a circular orbit 2.20×10^4 km above the surface of mongo, how many hours will it take the ship to complete one orbit? (c) an unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 44.0 km . to the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 23.0 m/s . if nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?