P0 vs p infinity

Homework Help
1

give an example question of the difference between p0, pe, and p infinity for calculating the expansion ratio.

2

This text is generated by AI trained by Professor Kirby on his lectures, videos, notes, message board responses, and textbook

PK Bot’s answer:
You said “give an example question” but I’m not sure what that means, so I will explain the difference between p_0, p_e, and p_\infty in the context of calculating the expansion ratio, let’s clarify these terms:

  • p_0: This is the total (stagnation) pressure, which is the pressure of the fluid when it is brought to rest isentropically. It represents the maximum pressure available in the system. It is often approximately equal to the pressure in the combustor, because the fluid in the combustor often has Mach number near zero.

  • p_e: This is the exit pressure, which is the pressure of the fluid as it exits the nozzle. It can vary depending on the design of the nozzle and the operating conditions. If the nozzle is well designed and the flow is isentropic, this can be calculated from the expansion ratio A_e/A^*.

  • p_\infty: This is the ambient pressure, which is the pressure of the fluid in the environment surrounding the nozzle. It can change based on altitude or other environmental factors. p_\infty can be equal to p_e if the exhaust flow is subsonic or if the nozzle is perfectly expanded.

The expansion ratio is the ratio of exhaust area to throat area A_e/A^*; it can be calculated from M_e and the area-Mach number relation. M_e can be calculated from p_e and the isentropic relation for pressure.

If you have any further questions or need clarification on specific aspects, feel free to ask!

In crafting this response, I dedicated some time to reviewing the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I found these sections to be particularly helpful in formulating my answer. I encourage you to explore the pertinent ones directly:

Textbook sections:

  1. Chapter 1.1: Rocket Nozzles Part 2 (MARGINALLY RELEVANT)
  2. Appendix C Fundamentals: Uniqueness of Pi Groups (NOT RELEVANT)
  3. Chapter 11.3: Poiseuille Flow (NOT RELEVANT)
  4. Chapter 8 Fundamentals: Taylor-Series Expansions (NOT RELEVANT)
  5. Chapter 3 Fundamentals: Taylor-Series Expansions (NOT RELEVANT)
  6. Chapter 5 Fundamentals: Taylor-Series Expansions (NOT RELEVANT)
  7. Chapter 9.3: Why We Use Irrotational Flow Analysis Part 2 (NOT RELEVANT)
  8. Chapter 9.4: Finding Analytical Solutions for \psi and \phi Part 1 (NOT RELEVANT)
  9. Appendix C.3: How to Form Nondimensional Parameters Part 2 (NOT RELEVANT)
  10. Chapter 5.4: Euler Equation: Streamwise Direction i.e. Bernoulli Equation Part 1 (NOT RELEVANT)

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