Question

k = 1.4, R = 287 J/kgK and Cp = 1004 J/kgK. Air at a stagnation pressure of 1000 kPa and stagnation temperature of 700 K enters (via a Laval nozzle with an exit to throat area ratio of 1.38 preceding the duct) a constant area duct with heat addition of 800 kJ/kg. (a) Show that if the flow is choked in this system, the flow must be thermally choked because the Mach number (M) at the throat of the nozzle must be less than 1. What range of back pressures will choke the system as described? (b) (5 pts. extra credit) Calculate the Mach number (M) at the throat of the nozzle for choked flow. 

          k = 1.4, R = 287 J/kgK and Cp = 1004 J/kgK. Air at a stagnation pressure of 1000 kPa and stagnation temperature of 700 K enters (via a Laval nozzle with an exit to throat area ratio of 1.38 preceding the duct) a constant area duct with heat addition of 800 kJ/kg.

    (a) Show that if the flow is choked in this system, the flow must be thermally choked because the Mach number (M) at the throat of the nozzle must be less than 1. What range of back pressures will choke the system as described?

    (b) (5 pts. extra credit) Calculate the Mach number (M) at the throat of the nozzle for choked flow.
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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k = 1.4, R = 287 J/kgK and Cp = 1004 J/kgK. Air at a stagnation pressure of 1000 kPa and stagnation temperature of 700 K enters (via a Laval nozzle with an exit to throat area ratio of 1.38 preceding the duct) a constant area duct with heat addition of 800 kJ/kg. (a) Show that if the flow is choked in this system, the flow must be thermally choked because the Mach number (M) at the throat of the nozzle must be less than 1. What range of back pressures will choke the system as described? (b) (5 pts. extra credit) Calculate the Mach number (M) at the throat of the nozzle for choked flow.
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Transcript

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00:01 In this question, the nozzle is designed and assuming the flow is adiabetic and the exit mac number is 2 .8.
00:10 So the stagnation pressure and temperature is to make a pascal.
00:16 This is the stagnation pressure and the temperature stagnation temperature that is 150 degrees celsius.
00:24 So let's read the question.
00:27 The mass flow rate is 5 kg per seconds and the adiabetic index is 1 .40.
00:36 Taken so this is assuming the ideal gas so we are calculating the exit pressure temperature and area and throat area so exit pressure exit temperature thought area these quantity we are calculating so the throat area we can call critical area mass flow rate this is b0 speed of sound that is k divided by rt0 so this is k plus 1 divided by 2 this is k minus 1 now you can put all the values so critical area that is equal to 5 kg per seconds, 10 power 6.
01:20 This is 1 .4.
01:23 This is 287.
01:24 This is 423 .15...
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