condensed matter - Why can, or can not, a perfectly incompressible fluid exist?

Water is normally assumed to be an incompressible fluid - for example in the context of calculations involving water pressure.

I wondered whether that is strictly true, or an approximation? Later I noticed some side note implying water is not fully incompressible.

Of course that makes sense, as there are not many things "perfect" in nature in this sense, like maybe supraconductivity and suprafluidity.

Now, why, or "in what kind of way", is water only almost incompressible - is it caused by impurities like gases and other fluids in the water?

Or is it not completely incompressible in some fundamental way?

Answer

Formally, the incompressibility of a fluid is defined by the compressibility, $$ \beta=\frac1\rho\,\frac{\partial\rho}{\partial p} $$ where $\rho$ is the mass density and $p$ the gas pressure. This means that, the compressibility is the measure of how much the density (volume) changes when a pressure is applied.

For water at standard pressure, this works out to be on the order $10^{-10}\,m^2/N$ which is pretty darn small but definitely non-zero. This value isn't due to impurities in the water, it is due to the properties of H$_2$0 itself. If you look at the $\rho\,{\rm vs}\,p$ plot, you can see how the density changes with both (solid green line):

The left-most end of the chart is standard pressure of 1 atm (roughly 0.1 MPa). As you can see, it is not until very high pressures that the density begins to really change. But at most every-day temperatures the deviations from horizontal are negligible.