Converging-Diverging Nozzle Pressure Delineations

In my converging-diverging (CD) nozzle video (link below), we saw that there were seven different flow conditions in a nozzle. If know what exit-to-reservoir pressure ratio our engine is operating at (see notes below), then we can define what condition our nozzle is operating at based on three pre-computed 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 exit-to-reservoir pressure ratio that our engine is operating at. For instance, if we are analyzing the Space Shuttle Main Engine (RS-25) 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 - Converging-Diverging Nozzle Pressure Delineations
www.joshtheengi...
→ Solving the Area-Mach Number Relation
www.joshtheengi...
→ CD Nozzle MATLAB Code - GitHub
github.com/jte...
→ Compressible Flow Relations Code - GitHub
github.com/jte...
===== RELEVANT VIDEOS =====
→ Explained: Converging Diverging Nozzle
goo.gl/7MBSck
→ Area-Mach Number Relation [CPG]
goo.gl/t8QE9T
→ Normal Shock Relations
goo.gl/Bvv2jj
→ Stagnation Relations
goo.gl/yrT9D4
===== REFERENCES =====
► Modern Compressible Flow, Anderson
► Gas Dynamics, Volume 1, Zucrow and Hoffman
► Elements of Gasdynamics, Liepmann and Roshko

[@riseofzen]

This has been incredibly helpful, thanks a lot! My lectures mentioned the different pressure ratios that results in the different flow conditions but never went over how to calculate them

[@danielwalker5682]

Yours are some of the very best engineering education videos going. The way you handle the various cases is so clear. Every now and then, I get called upon to cover for a colleague and teach this material. I normally love equations, but I have always found these compressible flow eqns a pig. I teach the classes these days to solve problems using tables (which incidentally I churn out with Matlab and which I will happily share with anyone who's a use for them). Tables and interpolation is the way I was taught in the 1980s, using Howatson, Lund and Todd's Engineering Tables & Data (with gamma=1.4, of course!) and a text book by Massey. The (simple) codes I've written employ interpolation on a table rather than iterative root finding. I am definitely going to refer our students to your videos on this subject. Thank you.

[@JoshTheEngineer]

Thanks for the kind comment! I'll admit that in undergrad, some of the derivations were a little tedious, but it's really nice to be able to see exactly where the equations come from, and it helps when trying to solve unfamiliar problems. I'm a big fan of showing all the different methods you can use to solve a problem (like my normal shock example problem video), which also helps people understand the limitations for certain methods (like when tables are only good for gamma = 1.4). Thanks again for watching!

[@danielwalker5682]

@@JoshTheEngineer Praise well deserved. Absolutely great channel. Totally agree. Of course, unless you've at least seen a derivation, you're not every really going to properly grasp a theory or be able to apply it to the full. Unfortunately these days, at least in some of our engineering schools, "derivation" is becoming a dirty word. (It's good the way you separate out the derivations from the use.) Many (tho' not all) just want to know how to get the answer, by-passing the "first let's understand the principles" step. Keep up the great work.

[@MichaelMeUp]

GOd Bless you, you just saved me from getting destroyed at in fluids final

[@JoshTheEngineer]

Glad I could help!

[@junuhunuproductions]

7:42 I guess when rockets liftoff, the Normal Shock is not inside the nozzle, but the state is over-expanded, but as it goes into space, it becomes under-expanded(whilst passing the point where the efficiency is the greatest)

[@JoshTheEngineer]

Yep, you got it.

[@erodriguez1137]

Great videos! Hope you add more soon.

[@JoshTheEngineer]

Thanks! I'm working on it!

[@pofunee]

03:55 NINE-NINE!!!

[@qwertyuiop9060]

AMAZE

[@JoshTheEngineer]

Thanks!

[@shemafonso3206]

Nicely explained I hv a doubt, Say I'm designing a cd nozzles where the inlet pressure (combustion zone) is 5 bar (and of course velocity will not be zero thr). So can i take that 5 bar as stagnation pressure or do i need to find stagnation pressure?

[@manelsouguir8126]

M exit is not equal to M1 because we have normal sock at the exit. Can you tell me please which relation have you used to calculate M exit ? I think we cannot use the normal sock relation P2/P1 ( as you have said at 6.51 , because it is function of M1 isentropic), we cannot also use the isentropic relation of pressure because we have a sock . I guess we must use the relation A/A* .

[@NitziPitzi1]

Hey Josh! How did you know that the normal shock is at the exit in the first place?

[@Hunter93-21]

Why are the turbine nozzles made divergent after the throat?

[@abdullahal-asmari5847]

One thing I dont get is how people relate the stagnation pressure before the shock to the static pressure AFTER the shock? the flow over a normal shock is adiabatic but the stagnation pressure after the shock is lower than the stagnation pressure before the shock so how do people find the pressure after the shock by using the stagnation pressure before the shock? it makes no sense and its driving me crazy.

[@penes2488]

i think you can still use the relations P2/P1 and P1/P0 (P0 being stagnation pressure before the shock), because P1/P0 doesn't depend on the shock and P2/P1 doesn't depend on P0

[@dipanjandey1603]

Great vedio.. Me= f(area ratio, gamma), can you tell me the exact function?

[@JoshTheEngineer]

Thanks! I have a video (kzbin.info/www/bejne/eoPNiJd6rbuniK8) and blog post (www.joshtheengineer.com/2016/11/16/solving-the-area-mach-number-relation/) about the area-Mach number relation if you want more details.

[@MsDehane]

first i want to tell you that you are amazing also i want ask you if you can make video where you explain the characteristic method for design a CD nozzle think you very much Sir

[@JoshTheEngineer]

Thank you! I'm going to make a Method of Characteristics video for rocket nozzle design very soon. I just have a few other videos I need to finish first.

[@manelsouguir8126]

Can you tell me please when Pe = Pb ?

[@paulboughosn6174]

if you found an answer, let me know hahahaha.. I'm confused too

[@himoukooora6669]

red couler in tabble its bad plz change your couller annd you are great prof

[@JoshTheEngineer]

I've moved away from using the red marker since like you said, it's hard to see. Thanks for the suggestion.

[@beachboardfan9544]

...need yourself a bigger whiteboard, and a patreon account.

[@JoshTheEngineer]

I've thought about switching to a bigger whiteboard, but I think there would just be too much going on at one time. I think the best way to watch my videos is to follow along on a piece of paper. But I agree, sometimes it gets a little cramped. I post so irregularly that I wouldn't feel right having a Patreon account at the moment. Plus, I have videos pertaining to a variety of different topics, so not every video is interesting to everyone subscribed. Right now, the skippable ads are a good medium that I hope don't annoy too many people!

[@guilhermechaves5957]

could you explain briefly why airplanes consumes less fuel at high altitudes? I did not find any video that talks about this subject. Sorry if there is any typing error, I had to use google translator to convert portuguese into english.

[@beachboardfan9544]

Google translator did good! 👍

[@beachboardfan9544]

Wooo first!