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If you want to imagine the buoyancy on an object, first imagine a
blob of water with exactly the same shape as the object. That water
is obviously in equilibrium. Integrate the pressure over the surface
area of the blob. If in equilibrium, this must give a force that is
equal and opposite to the weight of the water. Now replace the blob
with the object. The surfaces forces have not changed so they still
add to the weight of the blob. Hence, the buoyant force is the weight
of the water displaced. This definition of buoyancy does not require
water surrounding all surfaces of the blob - the blob could be on the
bottom of a glass beaker.
I think that a negative effect of defining the buoyant force to be an
upward force equal in magnitude to the weight of the water dispaced, is
that I would expect that students who have been taught that definition
would have a greater chance of getting the following problem so wrong
that they come to the conclusion that the piling is in tension rather
than compression ....