• word_count: 200

Fluid statics deals with fluids at rest. The fundamental equation is $P = P_0 + \rho gh$, which gives pressure at depth $h$ below the surface. This pressure depends only on depth — not on the container's shape, size, or the total volume of fluid (hydrostatic paradox). Atmospheric pressure $P_0 \approx 1.013 \times 10^5$ Pa supports a 10.3 m water column or a 760 mm mercury column.

Pascal's Law states that pressure changes in an enclosed incompressible fluid are transmitted undiminished throughout. This enables hydraulic machines: a small force on a small piston creates a proportionally larger force on a larger piston, with mechanical advantage $= A_2/A_1$. Energy is conserved — the larger force acts over a smaller distance.

Archimedes' Principle provides the buoyant force: $F_B = \rho_f V_{\text{sub}} g$ (weight of displaced fluid). A body floats when its density is less than the fluid's, with fraction submerged $= \rho_{\text{body}}/\rho_{\text{fluid}}$. Apparent weight = true weight minus buoyant force. These principles govern floating bodies, submarines, hot air balloons, and hydrometers.