Uploaded February 2017 | Updated September 2026, 2 weeks ago
In this video I'll go through an example showing why the nozzle on a jet engine needs to open up wider when the afterburner is on. You can tell that an afterburner is on when you see the visible radiation in the afterburner/jet pipe.
I'll be making some more in-depth videos about converging nozzles, converging-diverging nozzles, nozzle flow, choked flow, etc. If you haven't already, subscribe so you can be notified when I post them!
===== NOTES =====
► Quick note regarding flow choking: You can increase the mass flow rate even when the flow is choked by increasing the upstream stagnation pressure. When I said you couldn't increase the mass flow rate anymore, it was for a fixed stagnation pressure, because that's what you usually have coming out of the turbine of the engine. So that plot on the board is valid for a fixed P_0, when we keep decreasing P.
===== REFERENCE VIDEOS =====
→ Turbojet Thrust Equation:
goo.gl/gyaalq
→ Stagnation Relations:
goo.gl/yOSNeL
→ Isentropic Relations:
goo.gl/vxhrLH
→ Speed of Sound:
goo.gl/3qZhII
===== ASSUMPTIONS AND NOTES =====
1) The nozzle is isentropic.
- Adiabatic: no heat is added or removed.
- Reversible: no friction, shocks, etc.
2) The working fluid is air. Of course the actual working fluid will be the mixture of air and combustion products. This assumption avoids extra calculations that can certainly be done, but are unnecessary for the outcome of this example.
3) The air is a calorically perfect gas (specific heats are constant).
4) The engine is fitted with a converging nozzle (not converging-diverging).
5) The direct result of turning the afterburner on results in an increase in the stagnation temperature of the fluid.
6) The flow is steady through the nozzle.
7) The flow is quasi-1D.
8) Mass flow rate and stagnation pressure do not change when the afterburner is turned on.
9) Values used are just characteristic numbers that might be valid for real engines.
10) If you do have a converging-diverging nozzle, then to get supersonic flow (higher exit velocities), you will still need to have choked flow. In order to increase subsonic flow to supersonic flow in a CD nozzle, the nozzle must be choked.
===== THUMBNAIL IMAGE =====
Photo: SAC Ben Stevenson/MOD [OGL nationalarchives.gov.uk/doc/open-government-licence/version/1/)], via Wikimedia Commons
In this video I'll go through an example showing why the nozzle on a jet engine needs to open up wider when the afterburner is on. You can tell that an afterburner is on when you see the visible radiation in the afterburner/jet pipe.
I'll be making some more in-depth videos about converging nozzles, converging-diverging nozzles, nozzle flow, choked flow, etc. If you haven't already, subscribe so you can be notified when I post them!
===== NOTES =====
► Quick note regarding flow choking: You can increase the mass flow rate even when the flow is choked by increasing the upstream stagnation pressure. When I said you couldn't increase the mass flow rate anymore, it was for a fixed stagnation pressure, because that's what you usually have coming out of the turbine of the engine. So that plot on the board is valid for a fixed P_0, when we keep decreasing P.
===== REFERENCE VIDEOS =====
→ Turbojet Thrust Equation:
goo.gl/gyaalq
→ Stagnation Relations:
goo.gl/yOSNeL
→ Isentropic Relations:
goo.gl/vxhrLH
→ Speed of Sound:
goo.gl/3qZhII
===== ASSUMPTIONS AND NOTES =====
1) The nozzle is isentropic.
- Adiabatic: no heat is added or removed.
- Reversible: no friction, shocks, etc.
2) The working fluid is air. Of course the actual working fluid will be the mixture of air and combustion products. This assumption avoids extra calculations that can certainly be done, but are unnecessary for the outcome of this example.
3) The air is a calorically perfect gas (specific heats are constant).
4) The engine is fitted with a converging nozzle (not converging-diverging).
5) The direct result of turning the afterburner on results in an increase in the stagnation temperature of the fluid.
6) The flow is steady through the nozzle.
7) The flow is quasi-1D.
8) Mass flow rate and stagnation pressure do not change when the afterburner is turned on.
9) Values used are just characteristic numbers that might be valid for real engines.
10) If you do have a converging-diverging nozzle, then to get supersonic flow (higher exit velocities), you will still need to have choked flow. In order to increase subsonic flow to supersonic flow in a CD nozzle, the nozzle must be choked.
===== THUMBNAIL IMAGE =====
Photo: SAC Ben Stevenson/MOD [OGL nationalarchives.gov.uk/doc/open-government-licence/version/1/)], via Wikimedia Commons




![Explained: Nozzle Mass Flow Rate
One of the important variables in determining how much thrust a rocket can produce is the mass flow rate. In this video, we will derive an expression for the mass flow rate through a converging or converging diverging nozzle.
NOTES
► This expression only works when the flow is choked. For a converging-diverging (CD) nozzle, the flow should always be choked (although you still need to check). A little more care is needed when using the expression for a converging nozzle, because a lot of converging nozzles operate under conditions where they are not necessarily choked.
RELEVANT VIDEOS
→ Rocketdyne F-1 Mass Flow Rate Example
https://goo.gl/Ezp54H
→ Converging-Diverging Nozzle
https://goo.gl/jrsyoJ
→ Sonic State (Critical, Star)
https://goo.gl/vhjESy
→ Area-Mach Number Relation [CPG]
https://goo.gl/j4FwQX
REFERENCES
► Notes by Matt MacLean
► Modern Compressible Flow, Anderson
► Elements of Gasdynamics, Liepmann and Roshko
► Gas Dynamics, Zucrow and Hoffman
THUMBNAIL IMAGE
By NASA (NASA Human Space Flight Gallery (image link)) [Public domain], via Wikimedia Commons Explained: Nozzle Mass Flow Rate](https://i.ytimg.com/vi/aMTmRCdmvVQ/mqdefault.jpg)
![Explained: Turbojet Thrust Equation
Lets derive the thrust equation for a turbojet engine! In this video Ill show you how to derive the thrust equation for a single-inlet, single-outlet air breathing engine (turbojet is kind of just a buzzword here, because the engine doesnt necessarily need to only be a turbojet).
Yes, this video is heavy on the math, but Im planning on starting a video series called In a Nutshell, which will take some of my math-heavy videos and break them down in to shorter, more easily understandable videos that focus on the big picture. Stay tuned for those.
RELEVANT VIDEOS/LINKS
→ Mass Conservation Derivation
https://goo.gl/Qx7PZ6
→ 1D Mass Conservation
https://goo.gl/hM46LU
→ Momentum Conservation Derivation
https://goo.gl/DuYHcG
→ 1D Momentum Conservation
https://goo.gl/8uo6VM
→ Surface Area Blog Post
https://goo.gl/1s2z2X
→ Turbofan Thrust Equation Derivation
http://www.joshtheengineer.com/2017/04/08/turbofan-thrust-equation/
EXTRA LINKS
► This is the Wikipedia page for Turbojets, and while I dont tend to like Wiki pages for math, take a look at the Net Thrust section.
https://en.wikipedia.org/wiki/Turbojet
ASSUMPTIONS
1) Flow is reversible external to the engine
2) Steady state
3) No viscous forces
4) No heat addition
5) No body forces
6) Velocity only has X-direction component
7) Momentum from fuel flow rate is negligible
THUMBNAIL PICTURE ATTRIBUTION
By Jeff Dahl [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC BY-SA 4.0-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/4.0-3.0-2.5-2.0-1.0)], via Wikimedia Commons
Modified slightly by me Explained: Turbojet Thrust Equation](https://i.ytimg.com/vi/aNyYxVHBSWQ/mqdefault.jpg)

![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 engines 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
http://www.joshtheengineer.com/2017/12/17/converging-diverging-nozzle-pressure-delineations/
→ Solving the Area-Mach Number Relation
http://www.joshtheengineer.com/2016/11/16/solving-the-area-mach-number-relation/
→ CD Nozzle MATLAB Code - GitHub
https://github.com/jte0419/Converging_Diverging_Nozzle
→ Compressible Flow Relations Code - GitHub
https://github.com/jte0419/Compressible_Flow_Relations
RELEVANT VIDEOS
→ Explained: Converging Diverging Nozzle
https://goo.gl/7MBSck
→ Area-Mach 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 Converging-Diverging Nozzle Pressure Delineations](https://i.ytimg.com/vi/b5q022xNgp0/mqdefault.jpg)


