I have a text that writes a pressure balance for a cylindrical shape of fluid, where the linearized Bernoulli gives the pressure field ##p = p_0+\rho\partial_t \phi : \vec{v} = -\nabla \phi## where ##\vec{v}## is the velocity vector. ##p_0## is the static pressure required to maintain the fluid's static interface shape.(adsbygoogle = window.adsbygoogle || []).push({});

Evidently gravity and kinetic energy are neglected. My question is, how is it simply ##p## equates to both the transient and ##p_0## quantity? Wouldn't there have to be a transient quantity corresponding to ##p## (wherever it's located?)

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# I Fluids Bernoulli and a pressure field

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