(15 points) Consider the Delta II booster engine whose parameters are given in Table 4.2 of the notes. Take the exhaust to be an ideal gas with specific heat ratio y = 1.2. (a) Using trial-and-error solution of eq. (4.18) in the notes, find the Mach number at the nozzle exit to an accuracy of 0.01. (Note that (4.18) has two solutions; you want the supersonic one, i.e., the one with M > 1.) (b) What is the exhaust pressure at the throat and at the nozzle exit? (c) At what altitude is the nozzle optimally expanded? (It is easy to find standard atmo- sphere data on the web.) (d) What would the engine's sea-level thrust be if the nozzle were truncated at the throat? (Hint: Note that the mass flow rate and the characteristic velocity c* are not affected by the truncation, so you can find c* from the measured sea level thrust and the ideal- gas thrust coefficient CF.) Delta II booster Delta II 2nd stage RCS attitude control Fuel RP1 50% N2H4, 50% UDMH MMH Oxidizer LOX N204 N204 De 21" 11.7" 1.09" Dt 16.2" 7.5" 0.43" De 45.8" 60" 3.02" 8 65 50 T, sea level T, vacuum 164,700 lb 207,000 lb 9850 lb 18 lb m 290 kg/s 14 kg/s 28 g/s Po 39.2 atm Isp, sea level Isp, vacuum 257 s 294 s 320 s 290 s Table 4.2: Parameters for several production biprop engines. A A* +1 (4.18) || = 1 2 - [ (1+222)], M