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Just thinking about liquids and Pascal's law when, this question came. Ideal liquids, I understand, are deemed to be incompressible, which simplifies our problems while decently holding good for some real-life situations.

But, is there some deeper underlying meaning behind the incompressiblity of liquids? Can we arrive at this indepensible property of ideal liquids rather than just assuming it?

My thoughts:

  1. Is it because we assume that the liquid is already occupying the minimum possible volume?
  2. Or because it we assume replusive forces which are generated when we try to compress the liquid which prevent any compression?
  3. Is something else the matter?

Note that these are just naive speculations and I would be really grateful if my doubts could be clarified.

Edit: The scope of this question is restricted strictly to conditions where the approximation of incompressiblity of liquids holds good.

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  • $\begingroup$ If the pressure is enough then liquids are compressible... $\endgroup$
    – user207455
    Commented May 25, 2019 at 19:59
  • $\begingroup$ @SolarMike Thanks for pointing that out. Edited it $\endgroup$
    – user79161
    Commented May 25, 2019 at 20:00
  • $\begingroup$ Have a search for bulk modulus... $\endgroup$
    – user207455
    Commented May 25, 2019 at 20:04

2 Answers 2

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The concept of incompressibility is centrally connected to the concept of pressure, and so incompressibility almost always holds because of the high "default" pressure present in our environment.

In essence, what we call the density of a fluid comes about through a statistical mechanics process where the random internal motion of the molecules making up the fluid settles each molecule into possessing an average "volume range" of motion, balancing the desire of a test molecule to move around and spread out with the repulsive forces of the neighboring molecules keeping it in (usually called a mean free path/volume).

Because the internal energy of our liquids in pretty high due to atmospheric pressure/nontrivial temperatures, most liquids with meaningful densities (a.k.a. small mean free volumes) will experience massive molecular repulsion forces under compression. As a result, humongous amounts of energy need to be dumped into a "typical" liquid to compress it (hence why it only pops up in normal liquids near the speed of sound), and in most cases this kind of energy dump will result in pressure gradients that drive macroscale motion (flow) instead.

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  • $\begingroup$ Thanks, it is actually pretty interesting to think like that:) $\endgroup$
    – user79161
    Commented May 28, 2019 at 9:17
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Usually liquids are hard to compress. Compressibility only causes small effects. It can be handy to ignore these by assuming the liquid is ideal.

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  • $\begingroup$ The point of the question is that is there an alternative way to reach the same conclusion and if yes, then how? $\endgroup$
    – user79161
    Commented May 25, 2019 at 20:22
  • $\begingroup$ "Handy to ignore.." hmm not a good idea if you work with some fuel injection systems - fuel injected under the skin can kill or disfigure... $\endgroup$
    – user207455
    Commented May 25, 2019 at 20:57
  • $\begingroup$ No liquid is incompressible. Hence to ignore compressibility is an idealisation. It is a useful idealisation because compression only has a limited effect. $\endgroup$
    – my2cts
    Commented May 25, 2019 at 21:05
  • $\begingroup$ @SolarMike What does this have to do with liquid compressibility? $\endgroup$
    – my2cts
    Commented May 25, 2019 at 21:07
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    $\begingroup$ @SolarMike Ignoring small effects is essential in physics. $\endgroup$
    – my2cts
    Commented May 25, 2019 at 21:13

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