In my convergingdiverging (CD) nozzle video (link below), we saw that there were seven different flow conditions in a nozzle. If know what exittoreservoir pressure ratio our engine is operating at (see notes below), then we can define what condition our nozzle is operating at based on three precomputed pressure ratios:

1) Choked Isentropic Subsonic
2) Normal Shock at Nozzle Exit
3) Choked Isentropic Supersonic

In this video, we will compute the pressure ratios needed to obtain the three states listed above for a given nozzle area ratio (Ae/At).

===== NOTES =====
→ In this video, we can say that At = A* for each case because the flow is choked, and we do have sonic flow at the throat.

→ We generally know the exittoreservoir pressure ratio that our engine is operating at. For instance, if we are analyzing the Space Shuttle Main Engine (RS25) on the launchpad, then we know the exit pressure is approximately 101.325 kPa. We also know from the engine's specifications that the reservoir (or chamber) pressure is approximately 20.64 MPa. Dividing the two appropriately gives the pressure ratio we are looking for.

===== RELEVANT LINKS=====
→ Blog Post ConvergingDiverging Nozzle Pressure Delineations
http://www.joshtheengineer.com/2017/1...

→ Solving the AreaMach Number Relation
http://www.joshtheengineer.com/2016/1...

→ CD Nozzle MATLAB Code GitHub
https://github.com/jte0419/Converging...

→ Compressible Flow Relations Code GitHub
https://github.com/jte0419/Compressib...

===== RELEVANT VIDEOS =====
→ Explained: Converging Diverging Nozzle
https://goo.gl/7MBSck

→ AreaMach Number Relation [CPG]
https://goo.gl/t8QE9T

→ Normal Shock Relations
https://goo.gl/Bvv2jj

→ Stagnation Relations
https://goo.gl/yrT9D4

===== REFERENCES =====
► Modern Compressible Flow, Anderson
► Gas Dynamics, Volume 1, Zucrow and Hoffman
► Elements of Gasdynamics, Liepmann and Roshko