Glad you like the explanations! Ultimately, I try and have these videos go at conversation speed, not writing speed (less lecture-style). You could try and watch them at a slower playback speed, or potentially have the PDF of the notes open on the side?

I try to!

The pressure will be the stagnation pressure at the point where the fluid stops, which is typically the highest pressure point in the flow (you have traded all the bulk kinetic energy of the fluid for internal energy).

haha I'm glad you enjoyed it

​@@prof.vanburen yes 100% .whlle studying the working of Cd nozzle i came across a doubt. at second critical pressure when normal shock is at the end of the Cd nozzle the exit pressure which is the downstream pressure of the normal shock and at third critical pressure at which the normal shock has completely gone away form the CD nozzle so between second and third critical pressure there is a sudden huge drop in exit pressure (is my understanding right Prof?)

hi sir, in rayleigh flow,during addiion of heat why should the static temperature drops to increase the velocity in high subsonic speed (above M = 0.845) till Mach 1 ? and how does cooling of supersonic flow results in increse of velocity sir??

i can understand the process by looking at the enthalpy specific volume graph, but i cant understand the fundamentals sir

No problem!

I'm glad you got it!

I'm glad it helped!

No problem! Happy it helped

Excellent question! Generally, the pressure data is pointwise and discretized along the surface, so fitting a function to it that you can then integrate is prone to errors. Certainly not impossible, and it has been done a bunch in the past. A particular favorite of mine is an experiment by GI Taylor, famed fluid mechanician, who flew an aircraft and simultaneously took pictures of a manometer in the cockpit that represented the pressure distribution over the wing in flight back in the early 1900s.

Best of luck in your studies!

No problem! When Gamma(z) is arbitrary, the way to find it is a guess and check method (see around 19:28 in the video). You would start with guessing a Gamma distribution, then through a series of steps you can solve for the lift distribution which gives you a new Gamma. Plug this Gamma back into the beginning, and do that iteratively until Gamma converges. The video might be more clear!

@@prof.vanburen thanks a lot for the reply.

Aw thanks!

Glad you liked it!

I'd love to! I am sure I will eventually have to teach another class for uni, at that point more videos would be needed. Do you have any recommended courses?

No problem!

Thanks!!

This is a good place to start I hope!

I'm glad they helped!

Thanks for the feedback!

Thanks! I would start to explore projects you can DIY with open-source tools like XFoil (a vortex panel method solver), Simscale (a full CFD solver), and design tools like OpenVSP from NASA. This will get you designing and testing the flow over various objects you find interesting,

I think this is a good place to start if you have the math and physics background already, though maybe I would do Fluid Mechanics then Aerodynamics. There are a ton of online resources to learn, specifically NASA has a few learning modules that are open to everyone and very approachable.

I think so too!

Most welcome!

Aw thanks!

I'm not sure what you mean. Are you referring to the vortex initiated at the start of the flow---as in when the airfoil first accelerates?

@@prof.vanburen yes, exactly that

Do you mean generally how a foil might turn the flow downwards, producing the circulation that is the footprint of lift? Or how in reality the no-slip boundary leads to a boundary layer full of rotational flow?

@@prof.vanburen the latter. I think this validates the Kutta condition

Thank you for watching!

You're welcome, good luck in your studies!

Ah thank you so much!

My pleasure! I looked through the video again because I wanted to be sure, I am not sure where Cp (which is sometimes pressure coefficient) pops up, but I suspect you mean Cl instead, as in the lift coefficient? If so, I should say first that Cl does not *perfectly* stay the same at different scales. Other concepts like turbulence and Reynolds number come into play here. However, for the most part, it is sufficiently equal across a wide range of different scales. This is because take into account all the variables that impact lift when we scale the problem. A bigger airfoil would produce bigger force at the same air speed, but lift coefficient takes that into account by scaling with the area. Does this help at all? Otherwise, I think the text by Anderson might be helpful here. Otherwise, my video in fluid mechanics on non-dimensional numbers more completely goes over these concepts in a way that is not restricted to aerodynamics.

Thank you!

Hey hi , I'm also doing aerospace engineering ( first year) and the college starts July 10 . I'm more passionate to learn about space shuttles , and i want to self learn . Is you can suggest me on how to self learn ? Thanks a lot ❤

I am glad they helped!

@TITAN_2608 Rocket science! I am not sure of any good references in this specific area---it's not really my area of expertise. I know NASA has a ton of good online resources, that's probably where I would start.

@@prof.vanburen thanks a lot

Thanks for clarifying!

Thanks for clarifying!

Thank you, I really appreciate you going through the videos so closely and catching my (many) goofs!

Thanks, but we will have to agree to disagree on this one. While I think the folks at NASA can be brilliant, I have seen the explanation you are referring to you and I don't find their rebuttal of the idea complete. And I think that's okay, because this is a very hard problem that doesn't get a simple answer! If flow passes by curvature---like one wall with a hill or the leading edge of an airfoil---it needs to react. If things are slow, the fluid just entirely (up to effectively infinitely away from the surface) moves up and over the curve and it is happy. This does not lead to the Venturi effect which is generally used to explain contracting enclosed systems. However, if it is moving rapidly by this curvature, shifting upwards takes time, and the flow might not have that time to react due to compressibility. So, if it can't get out of the way in time (and conservation of mass needs to be obeyed otherwise the world explodes) the flow can can do things like increase in density or speed up in this 2D approximation. Why is speeding up not an option for mass conservation? Would this not be a "virtual" contraction, where the "top wall" of the Venturi is really just reaction time? I know NASA in that reference discusses the flat plate as evidence, but the flat plate also leads to flow fields with curved streamlines that behave like more curved surfaces. Also, it talks about the bottom-side of the airfoil but there curvature is not nearly as rapid. Furthermore, the speed up explanation in this video is specifically attributed to traditional airfoil shapes and is only a smaller part of the big picture. It is this effect in combination with the others that lead to the supreme lift of airfoils. I am not sure my explanation is any more convincing, but I also don't see where in the aeronautics series from NASA that they explain the acceleration of flow around the curvature at the top of the airfoil, which certainly happens. It seems that course online just leads to "Euler equations are complicated". Yes they are. I have seen other explanations that include consideration of angular velocity and centrifugal things, but they didn't resonate with me (or perhaps I just didn't understand them well enough). Anyway, thanks for getting me to think about it more deeply!

Haha I have a mathematically talented grad student who also won't let me live this down. You're very correct here...but it certainly looks like a chain rule 🤔

My pleasure!

My pleasure!