Buoyancy

Thrust exerted on a submerged object in a liquid. Direction is vertically upwards. Line of action passes through center of buoyancy.

$$u=\text{weight of displaced fluid}=v\rho{g}$$

Here:

• $u$ - the upthrust
• $v$ - the submerged volume
• $\rho$ - density of the fluid

Center of buoyancy

Center of gravity of the displaced fluid volume. NOT the center of gravity of the submerged object.

Proof

Forces exerted on the submerged object is equivalent to forces exerted on the displaced volume before it was displaced.

Consider the equilibrium of displaced volume before it was displaced:

$$\text{Weight}=W=\text{Resultant force exerted by surrounding liquid}=F$$

$F$ must be equal to $W$, opposite to $W$ and acts through $G$ of the considered volume of fluid.