Physical Examples of Divergence Theorem

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The discussion focuses on finding real-life applications of the divergence theorem, specifically in demonstrating the equivalence between integral and differential forms of conservation laws. The user has successfully applied the theorem to Gauss' law for electric charge but seeks additional examples beyond gravity. Suggestions for relevant fields include fluid mechanics, which extensively utilizes integral theorems from vector analysis. The user is looking for diverse applications in physics to fulfill their homework requirements. Exploring other areas like electromagnetism or heat transfer may also yield useful examples.
Diracster
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Homework Statement


This problem I have been set is to find real life applications of divergence theorem. I have to show the equivalence between the integral and differential forms of conservation laws using it.

2. The attempt at a solution

I have used div theorem to show the equivalence between Gauss' law for electric charge enclosed by a surface S. But can't think or find of another example other than that for Gravity. The problem is that I need to find a different example to Gravity as that is the next question and I can't imagine they would ask the same question twice!
Any suggestions of fields of physics that I can look into would be really helpful. Thanks in advance.




Homework Equations





The Attempt at a Solution

 
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iirc, Fluid Mechanics heavily uses these integral theorems from Vector Analysis.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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