- #1

joshmccraney

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In fluids I've noticed many authors use the continuity equation with an integral form of conservation of volume (assume density is constant). Is this double counting? Example: let fluid velocity inside an idle bubble be ##\vec u = \nabla \phi##. Conservation of mass implies ##\nabla u = 0 \implies \nabla^2\phi = 0##. Let the surface be perturbed, so conservation of volume requires ##\int_S \nabla \phi \cdot \hat n \, dS = 0## where ##S## is the bubble surface and ##\hat n## is a unit normal to ##S##.

Why use both?