Water flowing out of a rotating vessel

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The discussion revolves around the dynamics of liquid draining from a rotating vessel shaped like a paraboloid. The initial volume of liquid is given by the formula πR²h, and as liquid flows out, the surface maintains its parabolic shape until it reaches the orifice, at which point the flow stops. Participants debate the application of Bernoulli's principle and the integration needed to find the volume of the liquid above the bottom of the paraboloid. The final volume of liquid that can flow out is calculated as V_out = πR²h - (πω²/4g)(R⁴ - r⁴), where r is the radius of the orifice. The conversation emphasizes the need for careful consideration of the geometry and dynamics involved in the problem.
  • #31
Bling Fizikst said:
It should be 'approximately' true i guess as ##r## is given to be small . Hence , the second order term ##r^2\approx 0## . So , i guess we can only get an approximate answer .
If you just want an approximate answer, you should just send r to zero. The answer you gave contains a term proportional to ##r^4##. This term is negligible compared to the term you are missing due to not including the offset.
 
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