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 Originally Posted by OngBonga
If pressure is simply particle density, why does a large body of an incompressible medium, such as an ocean, have immense pressure at its depths? How are particles more dense when water in incompressible?
TL;DR
AFAIK: Neither water, nor any known thing is actually incompressible.
The reason we say that water is incompressible is because it takes immense pressure to exhibit significant density change.
As ever, being able to set a variable to 0 or "no change" is a great simplification, and if it works... use it.
The particles are more dense (ever so slightly), and water is compressible (if you measure very accurately).
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Pressure is particle density and temperature, this is an important factor.
PV = nRT
Pressure, P, times volume, V, equals number of particles, n, times the gas constant, R, times the temperature, T.
P = nRT/V
P = {R}*(n/V)*T
Pressure equals {ongbonga} times particle density, (n/V) times temperature.
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You may have noticed that {ongbonga} is the GAS constant*, and water is not a gas. Additionally, the equation above is called the Ideal Gas Law, and it's a good approximation for many gasses, but no gas is "ideal". Steam is nowhere ideal, so this equation is useless when it comes to water, or even water vapor.
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(I almost deleted this bit a couple of times, but I think it's really the closest to answering where your questions were coming from.)
Mechanically, particle collisions result in equal and opposite reaction forces. When a force is applied over an area, it is a pressure.
E.g. pounds per square inch or Newtons per meter squared.
Hydraulic pressure is a way of talking about the unbelievably countless amount of tiny bouncy interaction forces between particles by statistically averaging them out over an area.
Since the pressure is capable of expressing that force (since it can push/pull), it must be able to do so over some distance; you can't feel pressure unless it pushes you. The equal and opposite is true for what you're pushing. The application of a force over a distance is one form of energy.
E = F*d
Energy, E, equals force, F, times the distance over which the force is applied, d, (again a simplification, but I need to invoke calculus to be more accurate.)
The energy of the pressure, comes from elastic distortions.
An elastic distortion is one which resumes its original shape when the pressure is removed.
A plastic distortion is one which results in permanent deformation after the pressure is removed.
Plastic deformations transform the energy into a physical distortion, whereas elastic deformations store the energy of the deformation in a spring-like manner.
Drop a sand bag on the floor: no bounce: plastic deformation
Drop a rubber ball on the floor: bounces: elastic deformation
The bounce back comes from the rubber ball undergoing an elastic deformation that acts like a spring to return to its original shape. The "return" causes it to de-deform.
Most materials react in an elastic way when "small" pressures are applied, but will yield to plastic deformation when "large" pressures are applied.
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* cause he's full of hot air. (OK, we can snuggle now, but only if I can call you Ongie during.)
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