What determines that the flow of a nozzle is always mach one (M=1) at the throat? When does it meet mach 1 and become choked? Why does it stay choked at the throat even as the combustor pressure still increases?
This text is generated by AI trained by Professor Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
Your question can be answered literally, but your question might also hint at a misunderstanding of what choked flow means.
Are you asking “why does a nozzle remain choked when the combustor pressure goes up?” or are you asking “why does the mass flow rate remain the same when the combustor pressure goes up?”
If you are asking “why does a nozzle remain choked when the combustor pressure goes up?”, the answer is that the flow is choked as long as p_0/p_\infty is big enough for the flow to go sonic at the throat. Basically any combustor in any rocket that is actually running will always generate enough p_0/p_\infty to choke the throat. If you increase p_0, then p_0/p_\infty will be even higher, and if it was choked before, it will definitely still be choked after you raise p_0.
If you are asking “why does the mass flow rate remain the same when the combustor pressure goes up?” – it doesn’t. When we say that a nozzle is choked, we mean the mass flow rate (and everything else in the converging portion of the nozzle) is not a function of what happens in the diverging section or the ambient pressure. So the mass flow rate remains the same when the ambient pressure goes down. It is not correct to say that the mass flow rate remains the same when the combustor pressure goes up. Mass flow rate when the flow is choked is linearly proportional to p_0 (but independent of p_\infty):
\dot{m}= \sqrt{\gamma\left(\frac{2}{\gamma+1}\right)^{\frac{\gamma+1}{\gamma-1}} } A^* \frac{p_0}{\sqrt{RT_0}}
To formulate this response, I reviewed the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked their significance below. If they are marked as relevant, I encourage you to take a look at them:
Textbook sections:
- Chapter 1.5: Isentropic quasi-1D flow relations Part 1 (HIGHLY RELEVANT)
- Chapter 1.5: Isentropic quasi-1D flow relations Part 2 (HIGHLY RELEVANT)
- Chapter 1.1: Rocket Nozzles Part 4 (HIGHLY RELEVANT)
- Chapter 1 Fundamentals: The Area–Mach-number relation is derived by combining conservation of mass … (HIGHLY RELEVANT)
- Chapter 1.1: Rocket Nozzles Part 1 (HIGHLY RELEVANT)
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