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Problem 1: Space-Shuttle Main Engine is designed with the given criteria Design altitude 60,000 feet (18,300 m), where atmospheric pressure is, Patm=7171.64 Pa- 1.04010 psi. At this altitude the exhaust jet is fully expanded. Nozzle exit Mach number - 5.05 (calculated) Throat area 93 square inches (600 cm²) Nozzle exit area 50.265 square feet (4.6698 m²) Chamber total pressure - 2,747 pounds per square inch (18,940 kPa) at 100% power Assuming you can use the 2-D shock/expansion theory: Calculate the static pressure at the nozzle exit plane and the flow-turning angleright after the flow exits the nozzle at: sea level, where Patm 101325 Pa 14.696 psi b) 100,000 feet, where Patm 1090. 16 Pa - 0.158 psi Problem 2: We are designing a wind tunnel to achieve a Mach-4 flow with flow static temperature, T-10°C, flow static pressure, P-1 atm (101325 Pascal). Tunnel test section is to be 1m². In order to achieve this temperature in the test section, a constant diameter pipe equipped with a heater is used to increase the total temperature between the storage tank and the plenum chamber. We are assuming that the tunnel is already started, thus ignoring the total pressure change that would occur if there was a normal shock present in the test section. Use T-1.4, R-287 J. (kg K), C-1004.5 J. (kg K) a) calculate the total temperature and the total pressure required to achieve, T-10°C (static temperature), P-1 atm (static pressure), at M-4 in the test section using isentropic relations. b) calculate the total mass flow rate passing through the test section. c) calculate the heat-transfer rate required if the pipe heater entrance flow velocity is, V-50 m/s, at a temperature, T-25°C. Hint: Pipe exit total temperature is same as the one calculated in part a). d) calculate the pipe exit Mach number e) calculate the total pressure ratio required between the exit and the entrance to the pipe. Then calculate the storage tank total pressure required. Hint: The pipe exit total pressure is same as the total pressure calculated in part a). tost sedtion C-D nozze starage tark hearler pipe chamber Problem 3: A 10 m long shock tube prior to the breaking of the diaphragm has Helium on one side (5m long) at P4-100 atm and Methane on the other side at Pr-1 atm. Both gases are at 25C. a) calculate the shock-wave speed, W. Hint need to calculate the P:/P: first. b) calculate the speed behind the initial shock, Up c) calculate the reflected shock-wave speed, Wil Helium, 100 alm 25C Methane (Ch4), 1 atm, 25C Helium molecular weight-4 1.66 Cp- -5.188 kJ (kg K) Methane molecular weight 16 7 1.32 Cp- 2.226 kJ (kg K)

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