What is the pressure of CO2 at the nozzle exit of a rocket?

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SUMMARY

The pressure of carbon dioxide (CO2) at the nozzle exit of a rocket can be determined using the ideal gas law and principles of fluid dynamics. Given the initial mass of the rocket at 30,000 kg and an acceleration of 3g, with four nozzles each having a diameter of 20 cm, the exhaust velocity is 2.0 km/s at a temperature of 600°C. The mass flow rate of the exhaust can be calculated using the area of the nozzles and the exhaust velocity, leading to the determination of the exhaust density and subsequently the pressure at the nozzle exit.

PREREQUISITES
  • Understanding of the ideal gas law
  • Basic principles of fluid dynamics
  • Knowledge of rocket propulsion mechanics
  • Familiarity with thermodynamics, specifically gas properties
NEXT STEPS
  • Calculate the mass flow rate of exhaust using the nozzle area and exhaust velocity
  • Apply the ideal gas law to find the pressure of CO2 at the nozzle exit
  • Study the effects of temperature on gas density and pressure
  • Explore advanced rocket propulsion concepts and performance metrics
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Aerospace engineers, physics students, and anyone involved in rocket design and propulsion analysis will benefit from this discussion.

Spiewgels
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Homework Statement


Initial mass of the rocket is M = 30 x 10^3 kg, while its initial acceleration a = 3g. The rocket has four nozzles of diameter D = 20 cm each. Burning fuel leaves the nozzle with velocity v = 2.0 km/s having temperature T = 600◦C. Assuming fuel is burned completely and the exhaust gas is carbon dioxide CO2, determine its pressure P at the nozzle exit. Neglect air resistance.


Homework Equations


What is the best way to approach this problem? Most of the time I can get the problem started because I know what I'm dealing with in terms of what chapter the topic came from. I'm thinking I'm going to have to do something with the ideal gas law but I was told the problem would not have to worry about degree of freedom. I just need a booster so I can begin to work something out. (Thanks again to the last guys who helped me)


The Attempt at a Solution


Unfortunately, this is one of the few times I had nothing to start with. All I figured out thus far is that I will need to know that CO2 is 44g/mol.
 
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You know the acceleration of the rocket and you know the speed of the exhaust. From this you should be able to compute the mass of exhaust leaving the rocket per second. Since you know the speed of the exhaust and the area through which it passes, this should let you compute the density of the exhaust. Then you are basically where you can start applying what you've figured out so far.
 
ok, i'll get started on it right away...won't get home off the bus for 2 hours so if you happen to be up check out some of the pending work
 

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