I How Do I Symbolically Evaluate a Double Integral with an Offset Circle?

[Mark_ca_101]

Hello,
I am new to the forum and need some help understanding how to evaluate this integral symbolically.

∫∫ r dA

The differential element lies within a circle that is offset from the y-axis by some value R_2, and the radius of the circle is R₁. Again, the circle center location is (0,R₂).

Any help would be greatly appreciated.

 

[berkeman]

Hello,
I am new to the forum and need some help understanding how to evaluate this integral symbolically.

∫∫ r dA

The differential element lies within a circle that is offset from the y-axis by some value R_2, and the radius of the circle is R₁. Again, the circle center location is (0,R₂).

Any help would be greatly appreciated.

Welcome to the PF, Mark.

Can you please explain this question a bit better and Upload a diagram of the geometry? Also, is this a question for your schoolwork? If so, I can move it to the Homework Help forums as long as you show your initial work toward the solution.

 

[Mark_ca_101]

Welcome to the PF, Mark.

Can you please explain this question a bit better and Upload a diagram of the geometry? Also, is this a question for your schoolwork? If so, I can move it to the Homework Help forums as long as you show your initial work toward the solution.

berkeman,

This is not a homework problem, this is for research.

I want to calculate the angular momentum induced by introducing flow into a cylinder by an offset, inclined tube. I have referenced a journal paper regarding this method, but I'm not clear on how they are integrating this area. Please see the diagram below.

For simplicity reasons, the S1 area is shown as a circle, while it would actually be an ellipse.[PLAIN]https://www.physicsforums.com/attachments/da-png.113264/[PLAIN]https://www.physicsforums.com/attachments/inflow-angular-momentum-png.113265/

 

[Mark_ca_101]

berkeman,

This is not a homework problem, this is for research.

I want to calculate the angular momentum induced by introducing flow into a cylinder by an offset, inclined tube. I have referenced a journal paper regarding this method, but I'm not clear on how they are integrating this area. Please see the diagram below.

For simplicity reasons, the S1 area is shown as a circle, while it would actually be an ellipse.[PLAIN]https://www.physicsforums.com/attachments/da-png.113264/[PLAIN]https://www.physicsforums.com/attachments/inflow-angular-momentum-png.113265/[/QUOTE]