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Originally Posted by jrkeller
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This was the first one I thought of too, but then I thought about a little bit larger picture and decided that my favorite was the general conservation law.
The rate of change of something in a control volume = fluxes of something in and out of that volume + sources or sinks of something. Fluxes can be advection or diffusion.
And that's it, that's the basis of the Navier-Stokes equation which is a conservation of linear momentum in Newtonian fluids. But, the overriding conservation equation works with anything: Non-Newtonian fluids, solids, and the conserved quantity can be a lot of different things: mass, both linear and angular momentum, energy, electric charge. Maxwell's equations can be written in conservation form, too.
Conservation looks like a pretty simple statement, but it is an exceptionally powerful tool for solving problems and analyzing situations. And, despite what the perpetual motion machine makers think, there isn't away around it -- at least not in the universe we inhabit.