When deriving Bernoulli's equation from Navier Stokes, how do we know it is only valid along a streamline? At the very end of my derivation, assuming Newtonian, incompressible, inviscid, irrotational flow I have ##\nabla(\partial_t \phi + |\vec{u}|^2/2+p/\rho + g z) = \vec{0} \implies \partial_t \phi + |\vec{u}|^2/2+p/\rho + g z = const.## where I think the constant implies something about which streamline you're on. Also, ##\vec{u}=\nabla \phi##.(adsbygoogle = window.adsbygoogle || []).push({});

Thanks!

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# How to show Bernoulli's equation applies on same streamline?

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