Krotov problem: how to write Energy conservation for this fluid?

AI Thread Summary
The discussion centers on the Krotov problem and the challenges of writing energy conservation equations for fluid dynamics. A participant acknowledges errors in their calculations related to the radius of the fluid, specifically using the formula r = √(S/π) incorrectly. The relevance of this radius is questioned, as it is not provided in the problem data, leading to confusion about its necessity. Another participant points out that S represents the cross-sectional area, defined as S = πr², but questions the need for assuming a circular cross-section. The conversation highlights the importance of clear assumptions and accurate calculations in fluid dynamics problems.
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Homework Statement
I uploaded the problem. when I want to write the potential energy of the fluid in the initial and final state I don't find the right answer. I know the rest of the problem.
Relevant Equations
$$ U=\rho g h A h_{cm} $$
I wrote some potentials but they were wrong. I used the cm of all fluid parts and I used the radius which is $$ \sqrt S/ \pi $$ .
 

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That equation for radius has a "type" error.
$$r =\sqrt \frac{S}{\pi} $$
 
Per forum rules, please post your working. Otherwise we have no way to know where you are going wrong.
 
Could you explain how is that radius, which is not shown as data in the problem, relevant?
 
Lnewqban said:
Could you explain how is that radius, which is not shown as data in the problem, relevant?
S is the cross sectional area, so ##S=\pi r^2##. But if you are asking why bother calculating the radius (you don't even have to assume it is a circular cross section) then I agree.
 
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