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PS1_solution - AAE 334 PS-1 SOLUTIONS Note In general the...

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AAE 334 PS-1 SOLUTIONS Note: In general, the final values of flow variables are presented with 5 significant digits .The numbers used in the calculations are of 7 significant digits. PROBLEM 1a For an adiabatic flow, the total enthalpy is a constant. Note that ( ) [ ( ) ] The speed of sound and the Mach number . [ ( ) ] [ ( ) ] [ ( ) ] PROBLEM 1b From Appendix B, for hg = 0 m, we have
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At the reservoir, Hence at the nozzle exit, assuming isentropic expansion we have ( ) ( ) We have the standard isentropic relation ( ) ( ) Pe=101325 Pa => Using the ideal gas equation for reservoir conditions we have ( ) At the nozzle exit, ( ) Also
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PROBLEM 1c We have the conversion ( ) ( ( ) ) Therefore the exit temperature in Kelvin can be determined to be The stagnation temperature or the reservoir temperature is then given by ( ) ( ) We have the standard isentropic relation ( ) ( ) Pe=101325 Pa => Using the ideal gas equation for reservoir conditions we have ( ) At the nozzle exit, ( ) Also
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PROBLEM 1d For Helium ̂ ( ) The density of Helium is same as that of air for conditions described in problem 1c; the ideal gas equation results in the required value for the temperature at the exit.
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