A careful examination of Archimedes' principle shows that the buoyant force on a body that is either fully or partially immersed in a liquid is unaffected by the external (e.g. atmospheric) pressure, which acts both on the non-immersed part of the body (if any) and on the immersed part via Pascal's principle. The net force on the body due to the external pressure is zero and hence this pressure does not contribute to buoyancy.
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