Is it true that the fundamental difference between the two is that fluid dynamics allows for the compression of a liquid?
I wouldn’t say that. On the one hand, there’s a fairly wide portion of fluid dynamics that deals with incompressible flow (so fluids doesn’t *necessarily *allow for compression). On the other hand, volumetric efficiency of hydraulic machinery, for example, is a function of the compressibility of the liquid.
If you must differentiate, fluid dynamics is more theoretical (the science) and hydraulics is more practical (the engineering). However, the two are closely intertwined, and I’m not sure you can neatly divide fluid-related activity into purely “fluid dynamics” and purely “hydraulics” camps.
(Although “hydraulics” tends to imply liquids only, and “fluid dynamics” includes gasses, so in that sense fluid compressibility plays a greater role in fluid dynamics.)
I’d call hydraulics a subset of fluid dynamics, rather than something distinct. I’d say it’s synonymous with “incompressible fluid dynamics,” in fact.
Fluid dynamics does not require compressibility, like zut says. The study of water flowing around a submarine, for example, is an example of incompressible fluid dynamics. You’d also see this called hydraulics, but IME that term isn’t so widely used these days.
Yes, water is not truly incompressible - hell, nothing is - but its compressibility is so small such a flow that treating the density as a constant will not hurt your results, and will make the calculations much easier. It’s one less equation, generally: conservation of mass and momentum are sufficient to solve incompressible problems, while some kind of equation of state is required (basically dragging conservation of energy in) when the density of the fluid is considered variable.
Any kind of “dynamics” concerns motions. Hydraulics can concern itself with static fluids without considering motion.
On the contrary, Nothing is extremely compressible. If I have a piston cylinder full of Nothing, I can compress it as much as I like :).
Perhaps the OP meant to differentiate between fluid dynamics and fluid statics.
Another way to look at it is: in statics the important property is specific weight, whereas in dynamics the important properties are density and viscosity.
Would this include the vacuum of interstellar space?
Interstellar space is far from Nothing. It’s a darn nice vacuum, but Nothing is Nothing.
Even if it’s just one atom per cubic meter, it’s billions of times more dense than better vaccuums I can imagine & write down. Which are still vastly more dense than Nothing.