The problem with that is that you see all that because you already have a working knowledge of fluid mechanics. Someone reading this from the intended audience,

The problem with that is that you see all that because you already have a working knowledge of fluid mechanics. Someone reading this from the intended audience, ie someone looking for a gentle introduction, will not realize that absolute statements like “The incompressibility of fluids is the reason why those beautiful curls pop up in fluid bodies.” or “A substance that can not be compressed, can not have areas of higher and lower pressure” are simply and plainly wrong. The result simply is, as I stated, that the interested reader will not have learned anything physical about fluids, and will not even know the vocabulary to dive deeper afterwards. Note also, that the “naive” way still requires you to understand the divergence of a vectorfield, at which point the whole approach collapses and I wonder why they don’t simply give us the equations and then we can see for ourselves.