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vlehner1-Visitor
1-Visitor
November 17, 2016
Solved

Center of gravity

  • November 17, 2016
  • 11 replies
  • 5968 views

Hello,

Has somebody an Idea, how to calculate the center of gravity (zs1) in zylindrical koordinates (The boundarys of the 3-Integrals are not really clear for me)?

See attached Files-sheet two of Kugelspeicher.mcdx.


Thank you very much!

Volker

Best answer by Fred_Kohlhepp

Okay.

  • The 2 pi is the integral around the angle (full circle.)  There is no dependence of radius (or height) with azimuth, so a true integral with angle is not required.  (That's why there are only two integrals to get volume.)
  • The variable "s" is a variable of integration.  It does not appear outside the integral.  The inner integral above is the integral over the radius.  the limits of integration (for V3) are the radius of the center pipe (d/2) to the outside of the sphere (defined by the function r(z):
  • The outside integral is the vertical integral (z), the limits of integration are the bottom and top of the water.

This is equivalent to your integral above except that the outer bound for radial integral is a function of height "rr(z).

Your integral has height as function of radius; I don't know how to write those functions.

11 replies

F
Fred_Kohlhepp23-Emerald I
23-Emerald I
November 17, 2016

I get CG's of odd shapes by integrating.  Attached is integration in cylindrical coordinates.

V
vlehner1-VisitorAuthor
1-Visitor
November 18, 2016

Fred, I understand the integration of zylinders, etc.

But this is not the answer of my question.

I want to have the integration limits of the Integral concerning to the sketch:

This is a water-reservoir (shaded Area) of whitch i only want to know the integration limits for Integration to get the Volume.

Thank you

F
Fred_Kohlhepp23-Emerald I
23-Emerald I
November 18, 2016

Sorry!

Mis-read the problem.

V
ValeryOchkov24-Ruby IV
24-Ruby IV
November 17, 2016

See please my try to calculate a center of mass (gravity)

Re: Bug in Prime?

V
vlehner1-VisitorAuthor
1-Visitor
November 18, 2016

Valery,


sorry, but this doesn't solve my problem.

I wanted the correct limits for the Integration of a volume concerning to the upper shown sketch in my origin post.


Yes-It is necessary for finding the center of gravity


Thanks, anyway

Volker

F
Fred_Kohlhepp23-Emerald I
23-Emerald I
November 21, 2016

Added

Z centers of gravity on page 2

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