Water pressure in free fall The increasing water pressure as you go deeper is generally explained in terms of the weight of the water column above the observation point pressing down. The question, then, is what would happen if you had a big blob of water in free fall, say 100m in diameter-- not big enough to produce large gravitational forces on its own-- and swam to the center of it. I'm imagining some sort of contained environment, here-- a giant space station, or the planet-sized envelope of air in Karl Schroeder's Virga novels, that sort of thing-- so you don't worry about the water boiling off into vacuum or freezing solid, or whatever. 
Would there be any pressure differential between the surface of the blob and the center of the blob? At first glance, it would seem not, or at least not beyond whatever fairly trivial difference you would get from the self-gravity of the water. But it's conceivable that there might be some other fluid dynamics thing going on that would give you a difference.
For that matter, what difference would you expect between the pressure inside the water and outside the water? We know from shots of astronauts goofing around that water in free fall tends to stay together in discrete blobs. This is presumably some sort of surface tension effect. Does that lead to a higher pressure inside the water than out? How much of a difference would that be? Or would you not particularly notice a change from sticking your head into a blob of free-falling water? (Other than, you know, being wet...)
(This is just an idle question, brought on by thinking about the equivalence principle, and thus free-falling frames. It occurred to me that somebody here might know something about this kind of scenario, so why not post it?)
 A: The same pressure throughout.
By the same argument used to show that horizontal bands under a gravitational field must be at equal pressure: if they weren't there would be a net flow.
A: indeed there would be a (very small) and homogenous pressure 
within the blob, coming from surface tension. 
This pressure is calculated by the Kelvin Equation
and is significant in small droplets (reason for small 
droplets to have  a higher vapour pressure than bulk liquid) 
In Your 100 m blob, this extra pressure is negligible of course. 
There is another thing in liquids the so called internal 
pressure, caused by the cohesion forces. (more theoretical)
But this You cannot sense in Your blob, because 
Your body per se always has this internal pressure. 
A: I know less about this than you do, and I think you answered your own question correctly;
The only significant force is the self gravity of the water.
Just for fun, I calculated the acceleration at the surface and got approximately 10^-6 g.
Therefore the pressure at the center should be approximately 10^-5 atmospheres.
A: I'm not sure how it would behave if the internal pressure is less than the vapor pressure of water at that temperature. If the absolute pressure is lower than that thermodynamics would tend to favor the formation/growth of steam bubbles. You bubble would be (nonlinearly) unstable to boiling. I used the term nonlinear, because surface tension increases the internal pressure in bubbles, and only bubbles that exceed a certain critical size would grow. So your liquid very much resembles soda water, provide some surfaces or bubbles on which the vapor phase can grow and it woul start fizzing.
