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For most plumbing applications, each obstruction has a $C_V$ value and the flow is $C_V \Delta p^2$, where $\Delta p$ is the pressure drop across the obstruction. As you need to flow more water through the hole, you need more pressure behind it, which means more depth of water in the bucket. In this approximation, as long as the bucket is tall enough, you ...

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Bernoulli's principle and conservation of mass can give you a simple approximation to an equilibrium solution to the problem: $$\frac{1}{2}v^2+gh+\frac{p}{\rho} = constant$$ and $$\dot{m}_{in} = \rho A_{hole} v_{hole}$$ Where $\dot{m}_{in}$ is the mass flux of fluid into the bucket. Assuming zero velocity at the fill point of the bucket and pressure at ...

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There is some subtle terminology that may help in answering this question. First, the saturated vapor pressure is the pressure at which the number of water molecules evaporating from the surface of a liquid equals the number of water vapor particles condensing back to the liquid phase. The saturated vapor pressure is also non-linearly dependent on the ...

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No, you should not refer to molecules coming out or going in, unless there is more than one phase (such as in evaporation, sublimation, condensation, etc.). The volume decreases (or increases) because the space between molecules or atoms decreases (or increases), even though the number of molecules or atoms is constant.

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