What is the pressure in a container which contains fluid which is accelerated upwards?
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Archimedes' principle tells us that the upthrust on a body immersed in a fluid is equal to the weight of the fluid displaced, where the weight is the force given by F=ma i.e. the mass of fluid displaced, m, multiplied by the acceleration, a, experienced by the fluid.
In this context there is no difference between gravitational acceleration and inertial acceleration - this is one example of Einstein's equivalence principle - so:
a=agravity+ainertial
And the upthrust is therefore:
F=m(agravity+ainertial)=Vρ(agravity+ainertial)
as you said in your question.
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