Let's say that I have a large soda bottle. I drill a small hole through the side of it, put my finger over it to seal the hole, and fill the bottle up with water. When I let go of the hole, water flows out of the hole. The pressure at the top of the bottle and at the hole is both one atmosphere.
Now, I plug the hole back up and fill it with water. This time, I cap the water bottle tightly (assume the cap perfectly seals the top of the water bottle). When I let go of the hole this time, the water does not flow out of the hole.
The pressure at the top of the bottle is now zero, right? And the velocities at both points is zero. So Bernoulli's equation goes from
$$P_1 + p g h_1 + (1/2)p v_1^2 = P_2 + p g h_2 + (1/2) p v_2^2$$
$$p g h_1 = P_2 + p g h_2$$
where point 1 is at the top of the bottle, and point 2 is at the hole.
It seems to me that because of this, $P_2$ must be less than one atmosphere, right?
But why is the pressure at point 2 reduced because the bottle is capped? Doesn't the atmospheric pressure still act on point 2? Am I doing something wrong conceptually, and/or from the beginning? I just can't wrap my head around it.