# 412B Proof that Upthrust is the Weight of Fluid Displaced

The upthrust exerted by a fluid on a submerged object is actually the resultant of all the pressure forces acting perpendicularly into each point on the surface of the object. Since the pressure force at each point is only dependent on the fluid pressure and the orientation of the surface at each point, it does not matter what the object is made of. If we swap the object with an identically shaped one made of a different material, that object will still experience the same pressure force at each point and thus the same upthrust.

So why don’t we imagine that the foreign body is replaced by a body of fluid identically shaped as the foreign body, but made of the surrounding fluid. We should all agree that this imaginary body of fluid, together with the surrounding fluid, should be at equilibrium. This means that the weight of this body of fluid is exactly balanced by the upthrust exerted by the surrounding fluid. With this simple reasoning, we have proven that the upthrust is always equal to the weight of the displaced fluid!