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Study of harmonic motion of a liquid in a V shaped tube
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[QUOTE="sumatoken, post: 6815476, member: 730105"] [B]Homework Statement:[/B] Study of harmonic motion of a liquid in a V shaped tube using the Lagrangian method. [B]Relevant Equations:[/B] What is the total potential energy of the system? and why is the restoring force considered to be only the one due to hydrostatic pressure? A V-shaped tube with a cross-section [B]A [/B]contains a perfect liquid with mass density [ATTACH type="full" alt="gif.gif"]316295[/ATTACH] and length [B]L[/B] plus [ATTACH type="full" alt="gif.gif"]316296[/ATTACH] and [ATTACH type="full" alt="gif.gif"]316297[/ATTACH] the angles between the horizontal plane and the tube arms as shown in the attached figure. We displace the liquid from its equilibrium position with a distance [ATTACH type="full" alt="gif.gif"]316298[/ATTACH] and without any initial velocity. I'm interested in applying the Lagrangian method. For that, I need to determine both the system's kinetic energy and potential energy. Kinetic energy is by definition: [ATTACH type="full" alt="gif.gif"]316299[/ATTACH] As for potential energy I need to know which forces to consider. I can see three forces applied to the liquid: - The force due to gravity [ATTACH type="full" alt="gif.gif"]316300[/ATTACH] with a potential energy [ATTACH type="full" alt="gif.gif"]316301[/ATTACH] - The normal force due to the tube reaction. This force will have a null work therefore no potential energy. - The force due to hydrostatic pressure on the liquid by the portion displaced of length [ATTACH type="full" alt="gif.gif"]316302[/ATTACH] with potential energy written in terms of the angles, cross-section A and [ATTACH type="full" alt="gif.gif"]316303[/ATTACH]. I did some research, and some solutions did not consider the potential energy due to gravity and considered the restoring force to be only the one due to hydrostatic pressure which I do not understand why. Please feel free to correct me. Mohammed [ATTACH type="full" width="696px"]316305[/ATTACH] [/QUOTE]
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Study of harmonic motion of a liquid in a V shaped tube
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