Fluid Statics: Pressure and Buoyancy

Hydrostatic Pressure

Water does not care what is above it: pressure at depth depends only on depth, not the container's shape.

Pressure is force per unit area: $P = F/A$ in pascals ($Pa$).

Hydrostatic pressure at depth $h$ is:

$$P = P_0 + \rho g h$$

where $P_0$ is atmospheric pressure and $\rho$ is density.

Pascal's principle: Confined fluid pressure transmits equally. Thus $\frac{F_1}{A_1} = \frac{F_2}{A_2}$ runs hydraulics.

Buoyancy & Archimedes

Archimedes' principle: The buoyant force equals the weight of displaced fluid:

$$F_b = \rho_{\text{fluid}}\,g\,V_{\text{displaced}}$$

Floating condition: An object floats when $\rho_{\text{object}} < \rho_{\text{fluid}}$. The submerged fraction is:

$$\frac{V_{\text{sub}}}{V_{\text{total}}} = \frac{\rho_{\text{object}}}{\rho_{\text{fluid}}}$$

Common pitfall: Buoyancy depends on the displaced fluid's weight, not the object's. A steel ship floats because its hollow shape displaces a huge volume of water; solid steel sinks.