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According to Archimedes' principle, the buoyancy force on a submerged object is given by the product of the mass of the displace fluid and the gravitational acceleration. Effectively, it is determined by the net pressure difference of the fluid between the bottom and the top of the object, or in other words the weight difference of the corresponding columns of fluid. However, if we have a weight placed on a scale for instance, this weight will change if we accelerate the scale upwards or downwards. As scale in freefall for instance will register zero weight. Now as the buoyancy force will accelerate an object initially at rest, should it not be reduced as a result of this (the buoyant object can be considered the scale here and the fluid column the weight being measured)?

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    $\begingroup$ Technically the usual buoyant force formula only applies to hydrostatics, and in general you need to solve for the fluid's full pressure field and integrate that to find the force on the object. But yeah, in this case, if the acceleration isn't too big you can patch up the buoyant force by adding additional contributions due to the "virtual mass effect" and the "Basset force", both of which you can find if you google the terms. $\endgroup$
    – knzhou
    Commented Sep 14, 2023 at 21:41
  • $\begingroup$ It seems that your questions is based on the assumption that the weight is changed by acceleration of the object. This is a wrong assumption. The acceleration in you example changes the force on the scale but does not change the weight of the object. $\endgroup$
    – nasu
    Commented Sep 14, 2023 at 21:43

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Archimedes principle is only valid for objects in equilibrium. Likewise, Pascal's law is only valid for stationary fluids. There is no simple correction that can be applied to accelerating objects to find a useful buoyancy force on accelerating objects in the absence of other information.

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You are right. For example, a system in free fall is equivalent to it being inside a gravitation-free space (Equivalence principle) in which case there will be no buoyancy force on any submerged object. This doesn't mean that the pressure inside the fluid will become zero; instead it will take on some finite uniform value. However, buoyancy effect is a consequence of the variation of pressure (in the direction of gravity) over the submerged object (i.e. the pressure on the "bottom" of the submerged object is higher than that at its "top").

Any acceleration of the system modifies the effective gravity it experiences.

In fact you can always switch to an accelerating reference frame and do hydrostatics, provided you introduce suitable pseudo-forces. Only when different parts of the fluid are in relative motion w.r.t. each other (i.e. when the shear stress is non-zero inside the fluid) will you need something more than the laws of hydrostatics.

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  • $\begingroup$ (sorry about the late reply). I was actually not assuming the whole system is accelerating but only the submerged object within the fluid due to buoyant acceleration $a$. Would it be correct to assume that this would cause an increase of pressure on the object at the top (assuming upward acceleration) corresponding to $g+a$ and a decrease of pressure at the bottom corresponding to $g-a$, hence reducing the buoyant force compared to the stationary case? $\endgroup$
    – Thomas
    Commented Nov 12, 2023 at 17:12

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