What is the relationship between pressure and fluid dynamics in this problem?

[willworkforfood]

http://portfolio.iu.edu/whoblitz/problem.png
I think Bernoulli's equation is involved in solving this problem, but past that I'm not sure what the pressure of the water inside would be or what it would be outside. Any advice appreciated, as always.

 

[Chi Meson]

Treat the speed of the water inside the bottle as "zero." Treat the gauge pressure outside the nozzle as zero. Treat the water level inside the bottle as "-h." Go Bernoulli.

Edit: Wait, you are solving for the gauge pressure inside the bottle, so it would be more direct to have the height of the nozzle as "+h." It comes to the same thing.

The speed of the fluid inside the bottle is not exactly zero, but it is so small (and the squared value makes it smaller) that it is safe to "call" it zero.

 

[Tide]

The work done on the liquid is P \Delta V and is required to lift the fluid through the height h and impart kinetic energy to the stream.