Does Pascal's law only hold for fluids that obey the Bernoulli's Principle?
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Are you referring to Pascal's law of constant pressure in a static fluid?
Bernoulli's principle is about moving fluids, so I don't think they are necessarily related.
I was shown that Pascal's law still hold even when the liquid is in motion, i.e. in a piston, so I was thinking if there was a relationship between them.
that small movement of piston is just transmitted motion from molecule to molecule level and cant be brought under fluid dynamics
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Isn't fluid dynamics the study of dynamics of fluids, i.e. free moving molecules exactly?
Fluid dynamics are bulk properties of the whole system in motion. Statistical mechanics and thermodynamics are needed for internal molecular actions.
Is Pascal's law contained within the realm of fluid mechanics?
Yes. Pascal's law is for fluids (usually liquids) in a closed system (pistons, etc.).
I was mixing it up with Archimedes' principle earlier when I said static fluid.
The mechanics of it are still based on characteristics when the fluid is at rest.
I'm sorry I'm still not able to satisfactorily answer your question. I'm trying to think of a fluid that does not obey Bernoulli's principle in order to find a counter-example.
When the velocity term in Bernoulli's equation is zero, it shows that the fliud is not flowing, and the fluid is static?