When we talk about Archimedes' Principle in an inertial frame, we consider the force on a dipped body being equal to the weight of the fluid being displaced.
If the frame is non-inertial, will the buoyant force be different from the weight of the fluid displaced?
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As ∇ p = − ∇ u , where p is the pressure function and u is the potential energy density function, we can conclude that changing from an inertial frame of reference to a non-inertial frame the pressure will change (since the potential energy will change, due to the existence of inertial forces), resulting in a different value for the buoyant force.