1. (Recitation problem) An 8.5 m³ vacuum tank is to be used to create a flow at an exit Mach number of ME = 2.0 (refer to the figure below). A plug is put into the nozzle and the tank is evacuated until it contains 0.45 kg of air at a temperature of 296 K. When the plug is removed, air flows from the atmosphere into the tank through the converging- diverging nozzle. The throat area is A+ = 6.5 cm². atmosphere Patm 101 kPa (abs) Tatm = 296 K throat AT = 6.5 cm² exit = = volume 8.5 m³ initial mass 0.45 kg initial temp = 296 K a) Determine the design exit diameter. b) Determine the initial pressure in the tank. c) Determine the initial mass flow rate through the nozzle. d) Determine the exit pressure, PE, immediately after the flow begins. e) Determine the tank pressure at which a normal shock wave will stand in the nozzle exit plane. f) Determine the exit Mach number when the shock is in the nozzle at a point where the cross-sectional area is 20% greater than the throat area. g) Determine the time t until the flow in the nozzle first becomes entirely subsonic. Assume that the air in the tank is maintained at a constant value, equal to its initial temperature