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Problem 13.31

# Problem 13.31 - Problem 13.31[Difficulty 3 Given...

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Problem 13.31 [Difficulty: 3] Given: Temperature and pressure in a tank; nozzle with specific area Find: Mass flow rate of gas; maximum possible flow rate Solution: The given or available data is: R = 296.8 J/kg.K k = 1.4 T 0 = 450 K p 0 = 150 kPa A t = 30 cm 2 A t = 0.003 m 2 p b = 100 kPa Equations and Computations: Assuming that the nozzle exit pressure is the back pressure: p e = 100 kPa Then the nozzle exit Mach number is: M e = 0.7837 This nozzle is not choked. The exit temperature is: T e = 400.78 K From T e and Eq. 12.18 (12.18) c e = 408.08 m/s Then V e = 319.80 m/s From the ideal gas equation of state, we can calculate the density: e = 0.8407 kg/m 3 Therefore the mass flow rate is: m = 0.807 kg/s When the room pressure can be lowered, we can choke the nozzle.

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