I'm at the end of my vector calculus textbook, and there is a section on how vector calculus can be used to derive Euler's for fluid flow. The equations they give are:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\rho\left(\frac{dV}{dt} + \nabla V \cdot V\,\right) + \nabla p = 0[/itex]

and

[itex]\frac{d\rho}{dt} + \nabla \cdot (\rho V) = 0[/itex]

Where p stands for pressure, ρ stands for mass density, and V stands for velocity.

The derivations they give are totally understandable. It took me a few days to fully wrap my head around all of the derivations' nooks and crannies, but I now totally understand them.

Yet, now that I have my head out of the derivations I find myself looking at the equations and noticing that they don't describe how pressure changes with time. It looks to me as if the equations assume some preexisting spatial pressure gradient, and they describe how this gradient causes a fluid to move, but they don't describe how the fluid movement changes the pressure gradient.

Does that imply that this sort of fluid, in a perfect world, would be able to sustain a static pressure gradient? Or does the pressure change with time in some way that my book just has not bothered to mention?

P.S.

Can a moderator change this thread's title to "Is pressure..." instead of "I pressure..." Silly type-o, heh.

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# I pressure constant over time?

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