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What is forming the amount of chamber pressure which is produced in a rocket engine and why would you like to have an higher chamber pressure?

I was calculating the SpaceX Raptor engine for myself, just to know how to get the equations done correct. I struggled a little bit with the chamber pressure because the amount I calculated was far too low. I thought about it and came to the conclusion that you have to decrease the throat area in order to get a higher chamber pressure - which leads to an higher exit velocity. I'm not sure if I'm right, that's why I'm asking.

EDIT: First I tried to calculate the chamber pressure by the formula:

where k = 1.16; M = 3.55 and p = 0.1019 MPa. Because I thought the exit velocity in Mach is given by:

3200m/s is the exit velocity which I found on wikipedia for the rated Isp. According to the Internet the sonic velocity in this area should be around 900m/s. When calculated the chamber pressure according to the equation is about 15.97MPa which is equal to ~160bar.

This leads me to the assumption, that the exit velocity has to be higher than 3200m/s. For my understanding that can only accure if the throat area is much smaller.

I found this equation which confirm my thoughts:

Higher chamber pressure leads to higher exit velocity, which also leads to higher thrust. Maybe i answered the question myself. If so, it would be good to know if I'm right with my calculations/assumptions.

Thank you.

Steve
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  • As a wise person said "Searching this site for "calculate chamber pressure" returns 33 posts, it's likely you can find some helpful information here already, then revise your question and ask for help applying it to your current scenario. Welcome to Stack Exchange! " – Organic Marble Jan 27 '21 at 14:48
  • Thank you for welcoming me. I got all of my equations from here. Except from NASA. I have already looked through all of the posts which were related to chamber pressure and unfortunately found nothing about the factors influencing it. I also found a post of yours mentioning the choked flow - that´s why i was thinking that an smaller throat area would have an impact on it. But I still dont know if this is true and how I can calculate it. – Steve Jan 27 '21 at 19:55
  • Chamber pressure can be difficult to calculate, usually because of the temperature. If you edit your question to show details of the calculations you have done already, someone may be able to help. – Organic Marble Jan 27 '21 at 20:14
  • I gave my best. – Steve Jan 27 '21 at 22:29
  • Nice edit, looks great! – Organic Marble Jan 27 '21 at 22:40
  • Thank you, i appreciate it! – Steve Jan 27 '21 at 23:06
  • I've been looking at your numbers and have a couple of questions: is "p" = exit plane pressure and if so, why is it 1 atm? No real booster engine has an exit plane pressure that high... (I know making it smaller hurts Pc even more) – Organic Marble Jan 27 '21 at 23:31
  • https://space.stackexchange.com/a/41989/39046 In this post p is refered as environmental pressure. That´s why I was using 0.1019MPa - Environmental pressure at sea level. How would you calculate this to get it done right? – Steve Jan 28 '21 at 00:06
  • Do you know the area ratio of the nozzle? – Organic Marble Jan 28 '21 at 00:24
  • This guy gives the exit pressure as 0.6 bar so maybe you are not far off! https://exrocketman.blogspot.com/2019/09/reverse-engineered-raptor-engine.html – Organic Marble Jan 28 '21 at 01:14
  • It should be 40:1 if I'm right. BTW: Cool link, didnt found that one – Steve Jan 28 '21 at 11:23

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