Buoyant force in a nonuniform gravitational eld (Forca de empuxo em um campo gravitacional n~ao-uniforme)

. It is an easy task to apply the divergence theorem to show thatthis force agrees to that predicted by the well-known Archimedes’ principle, namely an upward force whosemagnitude equals the weight of the displaced liquid. Whenever this topic is treated in physics and engineeringtextbooks, a uniform gravitational field is assumed, which is a good approximation near the surface of the Earth.Would this approximation be essential for that law to be valid? In this note, starting from a surface integral ofthe pressure forces exerted by the fluid, we obtain a volume integral for the buoyant force valid for