Robert Koslover
Certified Consultant
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Posted:
2 years ago
2022年12月13日 GMT-5 10:46
z and r are simply coordinates. They do not depend on one another. If you compute something that has an actual dependence on a coordinate, then you may then be able to compute its derivative with respect to that coordinate. {Note: You may be able to get some useful help here if you are willing to explain the physical nature of the problem you are trying to solve, which presumably led you to this question.}
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Scientific Applications & Research Associates (SARA) Inc.
www.comsol.com/partners-consultants/certified-consultants/sara
*z* and *r* are simply coordinates. They do not depend on one another. If you compute something that has an actual dependence on a coordinate, then you may then be able to compute its derivative with respect to that coordinate. {Note: You may be able to get some useful help here if you are willing to explain the physical nature of the problem you are trying to solve, which presumably led you to this question.}
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Posted:
2 years ago
2022年12月14日 GMT-5 11:50
Updated:
2 years ago
2022年12月14日 GMT-5 11:53
Dear Mr. Koslover,
Yes, of course I can explain the problem. It is the one described in another forum thread in which you have already answered me :) : volume 2D axi model
My idea, since I am not able to calculate the volume of a hole with axisymmetric 2D geometry, is to use the line integral to calculate the volume by applying the Divergence Theorem or Gauss's Theorem. This theorem can be rewritten mathematically for cylindrical coordinates (2D axisymmetric model) if the COMSOL integral operator can only be applied to line integrals the theorem is rewritten as follows (I omit the mathematical development):
![](data:image/png;base64,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)
In this volume calculation, dS is the arc differential, and z(r) is the cylindrical coordinate as a function of radius for the curve that is shaded blue in the attached pic.
Can I know the "z" coordinate as a function of "r" for a given boundary in COMSOL ?
Thank you very much for your attention again,
Kind Regards,
Andres
Dear Mr. Koslover,
Yes, of course I can explain the problem. It is the one described in another forum thread in which you have already answered me :) : [volume 2D axi model](http://www.comsol.com/forum/thread/317481/how-to-calculate-the-volume-of-a-hole-inside-an-axisymmetric-2d-domain?last=2022-12-14T16:35:01Z)
My idea, since I am not able to calculate the volume of a hole with axisymmetric 2D geometry, is to use the line integral to calculate the volume by applying the Divergence Theorem or Gauss's Theorem. This theorem can be rewritten mathematically for cylindrical coordinates (2D axisymmetric model) if the COMSOL integral operator can only be applied to line integrals the theorem is rewritten as follows (I omit the mathematical development):
V=\int{pi*r^2*\frac{dz(r)}{dr}*\frac{1}{\sqrt{1+\frac{dz(r)^2}{dr}}}}*dS}
In this volume calculation, dS is the arc differential, and z(r) is the cylindrical coordinate as a function of radius for the curve that is shaded blue in the attached pic.
Can I know the "z" coordinate as a function of "r" for a given boundary in COMSOL ?
Thank you very much for your attention again,
Kind Regards,
Andres
Jeff Hiller
COMSOL Employee
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Posted:
2 years ago
2022年12月14日 GMT-5 17:31
Hello Andres,
You're on the right track! See my post in your other thread: [https://www.comsol.com/forum/thread/317481/how-to-calculate-the-volume-of-a-hole-inside-an-axisymmetric-2d-domain?last=2022-12-14T18:20:44Z](https://www.comsol.com/forum/thread/317481/how-to-calculate-the-volume-of-a-hole-inside-an-axisymmetric-2d-domain?last=2022-12-14T18:20:44Z)
Best,
Jeff
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Posted:
2 years ago
2023年1月19日 GMT-5 13:41
>Hello Andres,
>
>You're on the right track! See my post in your other thread: [https://www.comsol.com/forum/thread/317481/how-to-calculate-the-volume-of-a-hole-inside-an-axisymmetric-2d-domain?last=2022-12-14T18:20:44Z](https://www.comsol.com/forum/thread/317481/how-to-calculate-the-volume-of-a-hole-inside-an-axisymmetric-2d-domain?last=2022-12-14T18:20:44Z)
>
>Best,
>
>Jeff
Thank you very much Jeff!
Best,
Andres