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Furthermore the "incompressible fluid" they postulate sounds like it enables non-local behavior

It says compressible not incompressible.

Usually a pretty common mistake. Fluid is always compressible (else sound won't travel in STP water). It is whether one chooses to model the flow as compressible or not.

They really ought to stop teaching that fluid is incompressible in middle school.

I think that is a simplification of the model for high school level physics. It's like when we use Hooke's law to describe a spring constant that only holds true for part of the range. Compared with a volume of gas, fluids are "incompressible."

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