The discussion revolves around a problem involving fluid dynamics in a rotating vessel, specifically focusing on the behavior of water as it drains from a container shaped like a paraboloid due to rotation. The original poster describes the mathematical representation of the fluid surface and the volume of liquid in the vessel.
There is an ongoing exploration of the problem, with participants offering insights into the integration process and questioning the assumptions made about the fluid's behavior. Some guidance has been provided regarding the volume calculations, but no consensus has been reached on the interpretation of the problem statement.
Participants note the potential confusion regarding the initial volume of the liquid and the effects of rotation on the fluid's surface. There is a discussion about the implications of the orifice opening and the steady state of rotation, with some participants expressing uncertainty about the problem's requirements.
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.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 .