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From the equation of continuity and Bernoulli's theorem a formula can be derived for the velocity of efflux when it flows from a hole of area "a" such that the cross sectional area of the container is A. The final formula comes out to be:

$v^2 = \frac{2gh}{1-\frac{a^2}{A^2}}$. When the area of the hole approaches the area of the container the velocity becomes infinity which is obviously non sensical. Does some other formula hold for such conditions? If not what happens when I make the area of the hole same as that of the container

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If the area of the hole approaches that of the container's cross-section, the entire fluid just "falls" out of the container in bulk; there is no jet efflux. So, in such a case it is not meaningful to apply Torricelli's theorem.

Torricelli's theorem is based on Bernoulli's Principle, which assumes steady flow. In such a case, the flow is not steady. So, the theorem cannot be applied.

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At that point, you no longer have a hole, you have a pipe

Depending on the circumstances, the isentropic flow will break down. For example, the water at the bottom of the pipe will move faster that the water at the top, creating a funnel of air and breaking Bernoulli’s assumptions.

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