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If I have a cylidrical tank with a small hole in the bottom (the surface area of the hole is small in comparison with that from the tank) and I'm filling the tank with water at a constant flow,

**how can I determine the speed of the water both coming from the whole and rising up the tank: (A) with respect to the height of the water in the tank, (B) with respect to time.**

(This is not homework, although it sounds like so)

I know how to determine the maximum height of a system like this one with a specific flow Q. If the surface area of the cylinder is A and that from the hole is S, we have:

[tex]Av_A=Q=Sv_S[/tex] thus [tex]v_S=\frac{Q}{S}[/tex]

And, using Bernouilli's equation:

[tex]P_{at}+\rho g h=p_{at}+ \frac{1}{2}\rho v_S^2[/tex]

[tex]h=\frac{v_S^2}{2g}[/tex]

But that is considering the end point. Where the system is 'at rest' (there's the same amount of fluid in the tank and we can treat it like a pipe), but I don't know how to study the intermediate steps.

Thanks for your help :)