I've been confused about this point of physics forever. Finally wrote it up and posted it to stack overflow stack exchange:
does water density relate to, or cause, water pressure? Everyone I talk to dismisses the idea that water density substantially affects pressure, and emphasizes that water is nearly completely incompressible.
But I wonder if that "nearly" is a small percentage, but a big deal.
Here's my scenario: we have a hundred-gallon cylindrical water tank, and we poke three holes into it at different heights, stick tubes in the holes, and watch as the water comes pouring out of each tube, with the highest tube producing barely a trickle, and the lowest providing a hard spray. So far, so good, this is a standard grade school experiment.
But lets say we cap each tube from the outside. Lets assume, further, that the tubes are made of incredibly strong and incompressible material, and very narrow, so we can consider only the horizontal pressures and ignore vertical pressures inside of the tube. Now the water pressure will build up inside each tube, ready to spray when we remove the cap.
I'm wondering about the physical state of the molecules closest to the caps. When you remove the caps, those molecules that are now exposed to air are identical within each tube, in terms of velocity and momentum. And they are nearly identical, though not absolutely, in terms of density, which means the next layer of water molecules next to them are essentially the same distance away in each of the tubes.
And yet, once the caps come off, these outermost water molecules will begin to accelerate at very different speeds. The reason, as I understand it, is that there is greater force being applied to all of the nearby water molecules because of the distributed force of gravity on the water higher up in the tank.
So my questions are:
a) if you capped the tubes on the inside before uncapping than on the outside, would the water still spray at different velocities?
b) does the greater density under higher pressure have any effect on the pressure force that nearby molecules feel?
c) how does force transfer from one molecule to an adjacent one? Through nuclear proximity, which engages the weak nuclear forces? Or electromagnetic forces? Or some other force that doesn't want atoms to get too close to each other?
d) if b) is false but c) is true because if proximity, how can greater density NOT affect pressure?
e) Isn't the whole reason that water is difficult to compress that when you bring water molecules into such close proximity, your kinetic energy is converted into potential energy, which is stored in the greater resistance on the atomic level?
f) is water pressure a local phenomenon, like the way gases exhibit pressure by colliding more often, or is it a macro phenomenon, exhibited in the readiness of so many water molecules to for into a space?
g) how can a massive collection of molecules, like in a thin, tall cylinder of water, all be subject to a force applied from above, if not through some observable physical transition like an increase in density? Is there a time consuming process, like a shock wave, by which a newly applied force is effectively communicated to all of the matter which is subject to it?
h) a way of restating g) is to assume that at the same moment that we uncap the tubes in the original example, we add another hundred gallons of water to the tank, by removing a separator at the top of the original tank. How, and when, will the acceleration of the water in the tubes reflect this new gravitational pressure? Surely not immediately, or we've just discovered faster-than-light communication. So then presumably, some information or physical change must spread through the water which triggers a shift in behavior to reflect the greater pressure. Won't this correlate neatly with an increase in density, even if that is inconsequential? What form does this meaningful transition take, if not an increase in density?
Labels: education, science