Uploaded April 2016 | Updated September 2026, 2 weeks ago
This video goes through a step-by-step derivation of the 1D conservation of momentum equation from the integral form.
Here is a link to my video on the derivation of the momentum conservation equation:
goo.gl/LN5zUk
This video goes through a step-by-step derivation of the 1D conservation of momentum equation from the integral form.
Here is a link to my video on the derivation of the momentum conservation equation:
goo.gl/LN5zUk
![Explained: Converging-Diverging Nozzle
Why do rocket engines look the way they do? In this video, Ill be explaining what a converging-diverging (CD) nozzle is, and how the flow changes as it passes through it.
See the Relevant Videos section below for some more in-depth videos on each of the flow states, including examples!
NOTES
► At 11:28, I say so far, we have subsonic flow throughout the nozzle for all these cases. I meant to say that we have isentropic flow throughout the nozzle for all these cases.
RELEVANT VIDEOS
Pressure Ratio Delineations
https://goo.gl/VQnH1n
Normal Shock in the Nozzle Calculations
https://www.youtube.com/watch?v=b0wvwkKqoVw
Overexpanded Flow Calculations
Coming soon!
Underexpanded Flow Calculations
Coming soon!
Area-Mach Number Relation
https://goo.gl/j4FwQX
Sonic State (Critical, Star)
https://goo.gl/vhjESy
Normal Shock Relations
https://goo.gl/bhw6Ln
Isentropic Relations
https://goo.gl/mkdNHd
Stagnation Relations
https://goo.gl/hBY2AV
RELEVANT BLOG POST
http://www.joshtheengineer.com/2016/11/16/solving-the-area-mach-number-relation/
REFERENCES
► Notes by Matt MacLean
► Modern Compressible Flow, Anderson
Amazon Link: https://goo.gl/9B7F8H
► Elements of Gasdynamics, Liepmann and Roshko
Amazon Link: https://goo.gl/brfScu
► Gas Dynamics, Zucrow and Hoffman
Amazon Link: https://goo.gl/mwLk8L
THUMBNAIL IMAGE
By NASA (NIX #: MSFC-0201422. [1], Alt. URL.) [Public domain], via Wikimedia Commons Explained: Converging-Diverging Nozzle](https://i.ytimg.com/vi/p8e8A3sdVOg/mqdefault.jpg)

![Explained: Normal Shock Relations
In this video we will go through the full derivation of the normal shock relations. We will solve for downstream Mach number (M2), velocity ratio (u2/u1), density ratio (rho2/rho1), pressure ratio (P2/P1), and temperature ratio (T2/T1). We will assume the gas is calorically perfect (i.e. the specific heats are constant), which allows us to solve for all these values as only a function of specific heat ratio (gamma) and the upstream Mach number (M1).
ERRORS
► For the board from 9:09 - 10:33, the terms in brackets on the top line are correct, but the terms in brackets on the next two lines are incorrect (I switched a negative sign with a positive sign). When I bring the expression over to the next board at 10:34, the bracketed term is back to being correct, with a negative sign instead of the positive sign. [Thank you Pratheesh Prabhakar]
► From 21:44 to the end of the video, the second bracketed term in the final T2/T1 equation should be inverted (i.e, I have written it there as rho2/rho1, where it should really be rho1/rho2 as mentioned on the line above). [Thank you Pratheesh Prabhakar and Osama Hamdy]
RELEVANT VIDEOS
→ 1D Mass Eqn
https://goo.gl/0vesye
→ 1D Momentum Eqn
https://goo.gl/FHFUi4
→ 1D Energy Eqn
https://goo.gl/RSXVyc
→ Thermally Perfect Gas
https://goo.gl/maElnm
→ Specific Heats
https://goo.gl/kdf1B7
→ Isentropic Relations
https://goo.gl/Q8Rv9O
REFERENCES
► Notes by Matt MacLean
► Modern Compressible Flow, Anderson
► Elements of Gasdynamics, Liepmann and Roshko
► Gas Dynamics, Zucrow and Hoffman Explained: Normal Shock Relations](https://i.ytimg.com/vi/pR7mWvDWEJY/mqdefault.jpg)

![Explained: Hydrogen Burnoff Igniters [Space Shuttle]
What are the sparks seen beneath the space shuttles main engines just before launch? These sparks come from the hydrogen burnoff system that makes sure there is no excess hydrogen near the engines before ignition.
The sparks from the igniters can be seen in the video below at 1:09.
http://www.youtube.com/watch?v=T7vGqQUhciE Explained: Hydrogen Burnoff Igniters [Space Shuttle]](https://i.ytimg.com/vi/pahefmotTNk/mqdefault.jpg)

![Explained: Thermally Perfect Gas (TPG)
In this video, we will go through the derivation of why, for a thermally perfect gas (TPG), the energy and enthalpy are only a function of temperature, and not of two state variables. We will be using the combined 1st & 2nd law of thermodynamics (video [1] below for derivation).
RELEVANT VIDEOS
[1] : https://goo.gl/soiSr9
REFERENCES
:: Notes by Matt MacLean
:: Modern Compressible Flow, Anderson
:: Elements of Gasdynamics, Liepmann and Roshko
:: Gas Dynamics, Zucrow and Hoffman Explained: Thermally Perfect Gas (TPG)](https://i.ytimg.com/vi/prnGHlfCBrM/mqdefault.jpg)


![Explained: Tire Slip Angle
Lets talk about tire/tyre slip angles! Ill go through two ways of thinking about it. The first is the mathematical description, which will be useful for my later videos on vehicle dynamics. The second is the physical description of what is happening in the tire contact patch when a tire is operating at a finite slip angle.
NOTES
► One thing I forgot to make a note of is that even though the terminology calls it a slip angle, the rubber in the footprint is rarely slipping. In my foot-on-a-treadmill example, you can see that the only time the rubber starts to slip is towards the rear of the print. This is because towards the rear of the print, the normal (vertical) force pushing the rubber onto the road, and the friction coefficient between the road and the rubber, are no longer able to keep the rubber from sliding back to its undeflected position. Its more complicated than this, but thats the general reason.
RELEVANT VIDEOS
→ Tire Axis System
https://goo.gl/W4Y9iR
SEMI-RELEVANT VIDEOS BUT NOT REALLY
→ How to Calculate Top Speed
https://goo.gl/T4UvN4
→ F1 Aerodynamic Drag at Top Speed
https://goo.gl/oyStsp
THUMBNAIL PHOTO CREDIT
By Phil Guest (Flickr: [1]) [CC BY-SA 2.0 (http://creativecommons.org/licenses/by-sa/2.0)], via Wikimedia Commons Explained: Tire Slip Angle](https://i.ytimg.com/vi/rbhkfD1Dxo4/mqdefault.jpg)
