# [[Introduction to Fluid Mechanics - Fox, McDonald.pdf#page=85&selection=0,0,2,22|Introduction to Fluid Mechanics, 69 - 73]] If an object is immersed in a liquid, or floating on its surface, net vertical force acting on it due to liquid pressure is termed **buoyancy.** The vertical force on the body due to hydrostatic pressure may be most easily found by considering cylindrical elements. $ dF_{z}=(p_{0}+\rho gh_{2})dA-(p_{0}+\rho gh_{1})dA=\rho g(h_{2}-h_{1}) $ $(h_{2}-h_{1})dA=dV\therefore F_{z}=\int dF_{z}=\int_{V}\rho gdV=\boxed{ \rho gV }$ Submerged object need not be solid. Hydrogen bubbles are positively buoyant; they rise slowly as they are swept by the flow. The line of action of the buoyancy force acts through the centroid of the displaced volume, the location of which determines stability. ![[Pasted image 20260901144931.png|center|600]] The weight of an object acts through its center of gravity. In the figure above, the lines of action of buoyancy & weight are offset in such a way as to produce a couple that tends to right the craft. # Lecture - Buoyant force $F_{B}=\rho_{f}gV_{sub}=W_{disp,fl}$ - Center of buoyancy $x_{CB}=\frac{1}{V_{sub}}\int_{V_{sub}}xdV_{sub}$ - "Center of submerged volume" - Restoring moment created by force couple, $F_{B}$ and $W$