Uploaded September 2017 | Updated September 2026, 2 weeks ago
How can we use U-substitution to solve this integral? In this video, I'll walk you through the solution steps.
===== NOTE =====
- I made this video because I need the result of this integral in my aligning torque video (link below).
- If you want to see an application of this integral, see my video on circular centroids (link below).
===== RELATED VIDEOS =====
: : Aligning Torque
goo.gl/pMfq1s
: : Centroid of a Circular Segment
goo.gl/URd9Pj
: : Integral: Trig-Substitution
goo.gl/hNVVfz
: : Aligning Torque Simulation
goo.gl/NwVJjb
How can we use U-substitution to solve this integral? In this video, I'll walk you through the solution steps.
===== NOTE =====
- I made this video because I need the result of this integral in my aligning torque video (link below).
- If you want to see an application of this integral, see my video on circular centroids (link below).
===== RELATED VIDEOS =====
: : Aligning Torque
goo.gl/pMfq1s
: : Centroid of a Circular Segment
goo.gl/URd9Pj
: : Integral: Trig-Substitution
goo.gl/hNVVfz
: : Aligning Torque Simulation
goo.gl/NwVJjb
![Explained: GUI Exit Button [MATLAB]](https://i.ytimg.com/vi/9Tli0Fiw7r4/mqdefault.jpg "Explained: GUI Exit Button [MATLAB]
Create an exit push button for your MATLAB GUI using this code. When the exit button is pressed, the command window will be cleared, the variables that you specify will be removed from the workspace, and the figure (GUI window) will be deleted.
Explained: Make a GUI [MATLAB]
https://www.youtube.com/watch?v=42xLYuMIexg
Do download the .m and .fig files from this video, visit this page on my website.
http://www.joshtheengineer.com/2015/01/05/explained-matlab-gui-exit-button/")
![Explained: Bring Data To Front In Chart [Excel]](https://i.ytimg.com/vi/9eVMuPIJh0k/mqdefault.jpg "Explained: Bring Data To Front In Chart [Excel]
This video explains how to bring line data in front of scatter data in an Excel plot. Plots with only scatter data can be brought to the front by moving them up or down in the Select Data Source window. However, its not as easy for mixed data.
Update 11/12/15 - Thanks to comments from Eric Almquist and Robert Patrick
1) I was not careful enough with resetting my secondary axis, and the vertical scale for the primary and secondary axes are actually different (exactly what I was warning you about, ironically).
2) An easier way to hide the secondary axis is to either simply click on the axis and delete it (Robert Patrick), or to click on the + sign (Chart Elements) at the top right of the plot, click on the right-arrow next to axes, and uncheck Secondary Vertical (Eric Almquist).")
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A static text field can be used to provide information on how your code is running. In this video, I describe how to blink a message in a static text field in a MATLAB GUI.
How To Make a MATLAB GUI:
https://www.youtube.com/watch?v=42xLYuMIexg")
![Explained: Static Discharge Wicks [Airplanes]](https://i.ytimg.com/vi/B8K_JeZQNNk/mqdefault.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/mqdefault.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/mqdefault.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/mqdefault.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")
