By combining Bernoulli's Equation and equation of continuity, we can derive efflux velocity as:
$$u = \sqrt{2gh\left(\frac{{A_1}^{2}}{{A_1}^{2}-{A_2}^{2}}\right)}$$
where $A_1$ is area of the open surface and $A_2$ is the area of the hole.
But my question is how long does it take to achieve this velocity?
Let's say the hole was initially closed, and suddenly it opened, fluid particles will get pushed and accelerate from initially being at rest till they reach this steady velocity. How long does this take? I don't think it can be assumed to be instantaneous?
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