What is the effect on gravity underwater?

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Sphyrna:
Perhaps a little factoid will help... it takes the same pressure to pump water (or blood) out the top of a vertical pipe eight feet long that has six of those feet above water as it does to pump water (or blood) out the top of a vertical pipe that is twenty feet long that has six of those feet above water. There'll be a tiny bit less flow in the longer pipe due to friction, but the pressure to get the water to the top of either pipe will be the same. This is true for the same reason that blood in the body doesn't seek "down" when submerged.
S
That would be Bernouli's equation:
E=(pressure/density)+(velocity^2/2*gravity const)+elevation [E=p/r+v^2/2g+z]
All these taken relative to a datum would indeed prove your point out - assuming the flow is negligble takes out the velocity term which leaves you with the pressure and elevation terms equally the same elevation where they hit the air pressure meaning they have the same energy - without the pumping the blood or water would come back down and be level with the top of the water surface as you would have taken out the pressure term - however that means some of it would have to flow out the bottom of the system (assuming it can here) - if it isnt an open system then the energy previously used to pump the water/blood up to the top of the pipe would continue to be a positive pressure when measured relative to the water pressure surrounding the pipe until such time as a change in the restraint of that pipe and its contents - ie it leaked or allowed the pressure to equalise with the surrounding water.

This would all assume an inflexible pipe, i would think a flexible pipe that allows the influence of water pressure to act on the fluid inside the pipe might change this result - at least in my theory (no i havent found proof of this, but i also havent looked), the pipe would bulge at the base and decrease the pressure above the water until the maximum elevation of the fluid equalled that of the surrounding environment (ie the water surface) and the pressure of the liquid inside the pipe would therefore equal that of the surrounding water. This would be more of a buoyancy/Archimedes thing then as the walls of the pipe would not hold a force and pressure differential as they would with a solid/inflexible pipe as had been considered above. However you probably wouldnt be able to pump using this flexible pipe, so you would just have to aim to start this kind of experiment with the same conditions as just turning the pump off of the original case.

In the human body, we are somewhere between the rigid and flexible case but i do believe that we are more of an open system than the first rigid closed system of the first case. Absent the pressure of the heart beating and with the ability for the blood to equalize with the water surrounding it in that environment, given our semi-flexible body, this would mean that the when the heart stops pumping the blood will want to achieve an equal pressure with that surrounding it. Now we are left with where will the blood flow to achieve equality, given its slightly higher SG we can only conclude that it is downwards below the water - hence the reason blood doesnt stay on the surface when you bleed in the water. Assuming that the blood can flow there it will find the lowest point and have a pressure equal to the water around it, depending on the amount of blood and water in the body (from what i gather dead people UW are often bloated full of water - showing its an open system) the blood will be below the water all things being equal.
 
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