Bernoulli Principle of fluid question about velocity

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SUMMARY

The discussion centers on applying the Bernoulli Principle to determine the velocity of water exiting a hole in a circular water trough. Given that the hole is 0.11 m below the water level and the top of the trough is open to the atmosphere, the velocity at the top (v1) is assumed to be zero. The relevant equation used is the Bernoulli equation: p1 + 1/2ρv1² + ρgy1 = p2 + 1/2ρv2² + ρgy2, where the acceleration due to gravity is 9.81 m/s². The key takeaway is that the assumption of v1 being zero does not imply that v2 must also be zero, as the Bernoulli relationship allows for differing velocities.

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Homework Statement


A dairy farmer notices that a circular water trough near the barn has become rusty and now has a hole near the base. The hole is 0.11 m below the level of the water that is in the tank.
If the top of the trough is open to the atmosphere, what is the speed of the water as it leaves the hole? Assume that the trough is large enough that the velocity of the water at the top is zero. The acceleration of gravity is 9.81 m/s^{2}

Homework Equations


p_{1} + \frac{1}{2}ρv_{1}^2 + ρgy_{1} = p_{2} + \frac{1}{2}ρv_{2}^2 + ρgy_{2}


The Attempt at a Solution


In the question, it said I can assume that the certain velocity is 0. But I don't know which one. v_{1} or v_{2}? Even if one of the velocities is 0 because it is so insignificant, shouldn't that make the other velocity 0 as well?
 
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Not necessarily. That is what the Bernoulli relationship explains.
 

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