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The OP was asking about the physical mechanism responsible for buoyancy. But, to start with, he implied that pressure is caused only by gravity. Dale felt it was necessary to correct the frequent misconception of PF posters that gravity is the only thing that can give rise to pressure, before proceeding to a discussion of the actual physical mechanism. I also felt compelled to set the record straight on this.sophiecentaur said:You could well be right but, in the context of Buoyancy of a floating object (see the title) than the only relevant thing that produces the pressure is the weight of fluid on top and that is not caused by anything other than g (pretty well uniform at any relevant height). After a description around Archimedes' principle, 'other causes' of pressure could have been introduced - after getting some response from the OP.
Pascal's Principle was a good idea to introduce and it links (with a nice authoritative name) the downwards force due to gravity with a force in any other direction.
What is the point of introducing other reasons for the existence of pressure in order to explain flotation, which happens (in virtually any situation that I can think of) in bodies of fluid under the influence of gravity. This is a B QUESTION so why not limit replies appropriately? I am not arguing with any of the Physics that's been quoted here but I think all that stuff may have driven the OP away. Did we want that?
With regard tot he actual physical mechanism, Shreyas Samudra indicated by the buoyant force could be determined simply by integrating the pressure (as a scalar) over the surface area of the body. I felt compelled to correct this, and add that the integration had to be done vectorially, taking into account the normalcy of the pressure force at each location on the surface.