Fluid Dynamics of saltwater in sealed tank

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SUMMARY

The discussion centers on calculating the velocity of water flowing out of a small hole in a sealed tank containing seawater at a height of 12.8 m and a gauge pressure of 2.90 atm. The relevant equation is Bernoulli's equation, which relates pressure, velocity, and height in fluid dynamics. The user expresses confusion regarding the application of gauge pressure in this context, particularly how it affects the calculation of water velocity at the outlet. The assumption that the inlet velocity (V1) is approximately zero is also noted as a simplification for this problem.

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  • Understanding of Bernoulli's equation in fluid dynamics
  • Knowledge of gauge pressure and its implications
  • Familiarity with the concept of fluid flow through orifices
  • Basic principles of hydrostatics and fluid statics
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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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