Conservation of Buoyancy: Explained & Applied

AI Thread Summary
The discussion focuses on the relationship between the conservation of energy and the conservation of buoyancy, seeking mathematical connections between the two concepts. The user expresses a need for clarification on how to derive the conservation of buoyancy from energy conservation principles. They are specifically interested in the entrainment coefficient in relation to plume dynamics and background rotation. Additionally, the user requests further resources and assistance regarding a linked presentation. Overall, the conversation emphasizes the need for a deeper understanding of buoyancy principles in environmental fluid mechanics.
Wall
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Hi, all and thanks for your time.

I did read that the conservation of Buoyancy is an "alternative" conservation of energy under some hypothesis.

Can someone explain how do I start from the conservation of energy and find the conservation of buoyancy? Are there some corresponding mathematical passages?

Sorry for my bad English and thanks again!
 
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http://www.ifh.uni-karlsruhe.de/lehre/envflu_III/Downloads/models/IntegralPlumeModel/EFMIII-IntegralPlumeModel.pdf
 
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Thank you SO much! Do you have other documents about this problem? I'm working on plumes and trying to understand the dependence of the entrainment coefficient from the background rotation (but I'm a poor student). I did another post about entrainment.

I'm also trying to understand how to define mathematically the entrainment coefficient.

Thanks a lot!
 
Also, can I ask you some questions about that presentation you linked to me? thanks a lot!
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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