Pressure and Nozzle Length

Theory and Concepts
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How does ambient pressure impact the optimal length of a rocket nozzle?

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

PK Bot’s answer:
The ambient pressure (p_\infty) has a significant impact on the optimal length and design of a rocket nozzle.

When the ambient pressure is lower, the nozzle can be designed to expand the exhaust gases more effectively, allowing for higher thrust. In this case, the nozzle can be longer, as it can achieve a perfectly expanded flow without encountering oblique shocks downstream.

Conversely, if the ambient pressure is higher, the nozzle may need to be shorter to avoid overexpansion, which can lead to oblique shocks and reduced thrust efficiency.

The optimal design is perfectly expanded, i.e., p_e=p_\infty. So p_\infty tells us what p_e needs to be, which in turn tells us what M_e needs to be, which in turn tells us what A_e needs to be. So the ambient pressure sets the design expansion ratio (i.e., A_e/A^*)

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 (RELEVANT)
  2. Chapter 1.1: Rocket Nozzles Part 1 (RELEVANT)
  3. Chapter 1.8: Models (RELEVANT)
  4. Chapter 1 How Stuff Works: How to design a de Laval nozzle (RELEVANT)
  5. Chapter 1.7: Limitations (MARGINALLY RELEVANT)
  6. Chapter 1.5: Isentropic quasi-1D flow relations (MARGINALLY RELEVANT)
  7. Chapter 1.3: Acoustics and Compressible Flow (MARGINALLY RELEVANT)
  8. Chapter 1 Engineering Models: Quasi-1D Compressible Flow (MARGINALLY RELEVANT)
  9. Chapter 5.4: Euler Equation: Streamwise Direction i.e. Bernoulli Equation Part 1 (MARGINALLY RELEVANT)
  10. Chapter 1 How Stuff Works: How pneumatic soil excavators work (MARGINALLY RELEVANT)

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