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## Main Question or Discussion Point

Hello everyone,

According to Archimedes' principle, a solid body immersed in fluid (gas or liquid) always experiences a net upward buoyant force due to pressure variations occurring within he hosting fluid. Pressure calculations show that the buoyant force magnitude is equal to the magnitude of the weight of the fluid displaced by the solid body regardless of the overall shape of the body itself. I believe Archimedes empirically discovered that impressive and not intuitive result. The body immersed in the host fluid does not have to be a solid and can be a liquid or a gas.

If the body has uniform density, the buoyancy force acts exactly at the body's center of mass CM. But if the body is NOT uniform in density, the net buoyancy force acts at a different point called center of buoyancy CB. The CB is the center of mass of the displaced fluid (say water). We can calculate the location of CB by knowing the weight and shape of the volume of water displaced by the body.

Does anyone know where I can find a mathematical derivation of this interesting result, i.e. the fact that the net buoyant force acts at the CM of the displaced fluid? That does not seem to be an intuitive result. The magnitude of the buoyant force only depends on the weight of the displaced water but the point of application of the force depends both on the shape of the displaced volume of water and its weight...

thanks!

According to Archimedes' principle, a solid body immersed in fluid (gas or liquid) always experiences a net upward buoyant force due to pressure variations occurring within he hosting fluid. Pressure calculations show that the buoyant force magnitude is equal to the magnitude of the weight of the fluid displaced by the solid body regardless of the overall shape of the body itself. I believe Archimedes empirically discovered that impressive and not intuitive result. The body immersed in the host fluid does not have to be a solid and can be a liquid or a gas.

If the body has uniform density, the buoyancy force acts exactly at the body's center of mass CM. But if the body is NOT uniform in density, the net buoyancy force acts at a different point called center of buoyancy CB. The CB is the center of mass of the displaced fluid (say water). We can calculate the location of CB by knowing the weight and shape of the volume of water displaced by the body.

Does anyone know where I can find a mathematical derivation of this interesting result, i.e. the fact that the net buoyant force acts at the CM of the displaced fluid? That does not seem to be an intuitive result. The magnitude of the buoyant force only depends on the weight of the displaced water but the point of application of the force depends both on the shape of the displaced volume of water and its weight...

thanks!