Fundamentals of Hydrostatics in Fluid Mechanics

Hydrostatics is the study of fluids at rest and the forces these fluids exert or experience. It is fundamental for understanding pressure distribution in static fluids and buoyancy effects on submerged or floating bodies. Hydrostatic pressure increases linearly with depth following $p = p_0 + \rho g h$, where $p_0$ is surface pressure, is fluid density, acceleration due to gravity, and depth. Pascal's law states that any pressure applied to an enclosed incompressible fluid transmits undiminished in all directions. The hydrostatic force on submerged vertical surfaces results from the integration of pressure over the surface and acts at the center of pressure, located below the surface's centroid. Buoyancy force equals the weight of the displaced fluid as explained by Archimedes' principle. Stability of floating bodies depends on the metacenter position relative to the center of gravity; stability requires the metacenter to lie above the center of gravity. These principles are essential in engineering applications such as the design of dams, tanks, ship hulls, and medical devices, ensuring safety, functionality, and stability in fluid-related structures and systems.