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A high-altitude passenger airplane is cruising at an altitude (=) of approximately 40,000 ft. Determine the ratio of the pressure at the flight altitude (pz) and the pressure at standard sea-level (p:), meaning: papi, in the following different methods. For each case, you must start from the governing equation (hydrostatic equation: dp =-ped= ) and derive appropriate equation first, and then determine the ratio for each case. For simplification, assume that the gravity is being constant (standard sea-level value). (a) What is papi, if air is assumed to be incompressible gas (density is constant, standard sea-level value: p = A = p )? (b) What is papi, if air is assumed to be isothermal gas (temperature is constant, standard sea-level value: T, =T, =T)? (c) What is papi, using the U.S. standard atmosphere model (temperature is a variable from sea-level to 36,000 f altitude and then stays constant from 36,000 ft to 66,000 ft)? The lapse rate (from sea-level to 36,000 fl) is given as: / =0.00357 "R/f. Do not use U.S. standard atmospheric data from the table. Use the equation you derived (gradient region from sea-level to 36,000 ft and then isothermal layer from 36,000 ft to 66,000 ft), assuming that the gravity is constant