Center of mass of fluid in rotating cylinder

  • Thread starter homedoc
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  • #1
homedoc
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Homework Statement


A closed cylindrical canister with central axis coincident with the Z axis has a height H and a radius R. It is suspended by a rod coincident with the Y axis that passes through the canister, transecting its central axis at a height h above the bottom surface of the canister with h > 0.5H.
A volume V of a uniform fluid with density d is placed in the canister (V ≤ 0.2∏R^2H). Derive the equation describing the locus in the XZ plane of the center of mass of the fluid as the cylinder pivots around the rod such that the axis of the cylinder with respect to the Z axis varies from -80 to +80 degrees.


Homework Equations


V=∏R^2H
For other equations see http://mathworld.wolfram.com/CylindricalWedge.html
and http://mathworld.wolfram.com/CylindricalSegment.html.



The Attempt at a Solution


I have been working on this for a week and cannot seem to conceptualize a method for solving the problem. I would greatly appreciate any help and/or suggestions.
 

Answers and Replies

  • #2
voko
6,054
391
I think you need to assume that the fluid is stationary at any position of the cylinder. Meaning that the cylinder moves very very slowly. Because if not, arbitrary motions of the cylinder could produce very violent motions in the fluid, which one could model only numerically.

Assuming the fluid is stationary at every angle of tilt, its surface must be horizontal. That's enough to determine its shape and with the shape its center of mass. Then you do this for all the possible angles of tilt, and you get the locus.
 

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