JoshTheEngineer | Curl of the Gradient of a Scalar Field is Zero @JoshTheEngineer | Uploaded October 2016 | Updated October 2024, 3 hours ago.
In this video I go through the quick proof describing why the curl of the gradient of a scalar field is zero. This particular identity of sorts will play an important role in my future videos on potential flow.
In this video I go through the quick proof describing why the curl of the gradient of a scalar field is zero. This particular identity of sorts will play an important role in my future videos on potential flow.
![Explained: Static Discharge Wicks [Airplanes]](https://i.ytimg.com/vi/B8K_JeZQNNk/hqdefault.jpg "Explained: Static Discharge Wicks [Airplanes]
Explained: Static Discharge Wicks [Airplanes]")
![Streamline Geometric Integral SPM [Mx(pj) and My(pj)]](https://i.ytimg.com/vi/BnPZjGCatcg/hqdefault.jpg "Streamline Geometric Integral SPM [Mx(pj) and My(pj)]
We went through the derivations of the normal velocity geometric integral (Iij) and the tangential geometric integral (Jij). The Iij term is used in the expression to solve for the source panel strengths. The Jij term is used in the expression to solve for the velocity of the flow on each panel. In order to compute the flowfield around the airfoil (off the airfoil), we need to know the X and Y components of the velocity at arbitrary grid points (similar to a CFD solution).
In this video, we go through the derivation of the X and Y velocity geometric integrals (Mx(ij) and My(ij)). These will allow us to compute the flowfield pressure coefficients and the streamlines around the airfoil. Much of this derivation is exactly the same as the Iij derivation, so I will refer you to that video for those details.
RELEVANT VIDEOS
► Panel Methods Playlist
https://www.youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
https://www.youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
https://www.youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
https://www.youtube.com/watch?v=cLdv1UfX1g8
► Normal Velocity Geometric Integral [I(ij)]
https://www.youtube.com/watch?v=76vPudNET6U
► Tangential Velocity Geometric Integral [J(ij)]
https://www.youtube.com/watch?v=JRHnOsueic8
NOTES
- Ill add notes here if I need to.
ERRORS
- If you see an error in the video, please let me know and I will include it here.
REFERENCES
Note: the links are Amazon affiliate links. If you do happen to want to buy the book and use the link below, it helps me out a little.
► Fundamentals of Aerodynamics, Anderson
https://amzn.to/3emVuXU
► Foundations of Aerodynamics, Kuethe and Chow
https://amzn.to/2yMg1Vi
► Theory of Wing Sections, Abbott and Doenhoff
https://amzn.to/2wvZyUt")
![Explained: Load CSV Data [MATLAB]](https://i.ytimg.com/vi/CMaxsZoQuE0/hqdefault.jpg "Explained: Load CSV Data [MATLAB]
This video explains how to load CSV files into MATLAB using textscan.")
![Explained: Linear Interpolation [Math]](https://i.ytimg.com/vi/Cvc-XalN_kk/hqdefault.jpg "Explained: Linear Interpolation [Math]
In this video, I explain how to obtain the equation for linear interpolation between two points. I then go through a simple example.
Linear interpolation can be useful when you need data at points where data does not exist. This happens a lot when looking at tabulated data. Here are some examples of tabulated data where linear interpolation can come in handy:
- Steam/vapor tables in thermodynamics
- Property tables in heat transfer
- Normal shock tables and isentropic relations tables in gas dynamics
In the video linked to below, I show you how to program this equation into a graphing calculator (TI-83), so you can use it on exams or whenever you need a quick estimate.
https://goo.gl/ntTuKl")
![Explained: Airfoil Chord [Airplanes]](https://i.ytimg.com/vi/Eh5W61iswSY/hqdefault.jpg "Explained: Airfoil Chord [Airplanes]
The airfoil chord is a vital part of understanding the angle of attack of an airfoil, as well as other aerodynamic parameters in aircraft design. The definition of the chord line is straightforward, while the definition for the leading edge (LE)/trailing edge (TE) are a little more ambiguous.
Second of All Comment
The first of all comment (that I made in the video) was that the angle of attack actually changes based off of where you define the leading edge to be. The comment I forget to say in the video is that the chord length also changes based on the LE location. For the minimum x value LE, the chord line is longer than the minimum radius of curvature LE.")
