Fluid Dynamics of saltwater in sealed tank

AI Thread Summary
To determine the speed of water flowing out of a small hole in a sealed tank containing seawater, Bernoulli's equation is applicable. The gauge pressure of 2.90 atm at the top of the tank contributes to the pressure difference driving the flow. The equation can be simplified by assuming the velocity of water at the surface (V1) is negligible. The pressure difference between the air above the water and atmospheric pressure can be used to calculate the exit velocity of the water. Understanding these principles will clarify the application of Bernoulli's equation in this scenario.
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Homework Statement


A sealed tank containing seawater to a height of 12.8 m also contains air above the water at a gauge pressure of 2.90 atm. Water flows out from the bottom through a small hole.

How fast is this water moving?


Homework Equations


I believe that Bernoulli's equation is to be applied here somehow.

The Attempt at a Solution


I hate that I don't have more work to show, but I really don't know how to approach this one at all.

p_1 + \frac{1}{2}ρV_{1}^{2} + ρgh_{1}= p_2 + \frac{1}{2}ρV_{2}^{2} + ρgh_{2}

I'm not really sure how to apply this for this type of problem. The gauge pressure air at the top is confusing me. The other questions I have worked on so far were all liquids moving through pipes and such, where the application of the equation is apparent. Can someone just point me in the right direction here?
 
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Guage pressure is, of course, pressure above atmospheric pressure. And the "small hole" is at atmospheric pressure. Whence,

P1 - P2 = 2.9 atm.

And since the problem says the outlet is a small hole, it is reasonable to assume:

V1 ≈ 0.
 
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