hydrostatique

Hydrostatique, or hydrostatics, is the branch of fluid statics that studies fluids at rest in a gravitational field. It analyzes pressure distribution in liquids and gases when no motion occurs. The central equation, the hydrostatic equation, expresses the change in pressure with depth: dp/dz = -ρ g, where z is the vertical coordinate, ρ is fluid density, and g is the acceleration due to gravity. For a fluid with uniform density and a vertical column of height h with a free surface exposed to atmospheric pressure p0, the pressure at depth h is p = p0 + ρ g h. If the surface is sealed, p0 is the internal reference pressure.

Buoyancy and flotation are key concepts: an object immersed in a fluid experiences an upward buoyant force equal to the weight of displaced fluid (Archimedes' principle). The balance of forces determines whether the object sinks, floats, or remains submerged, depending on densities.

Practical implications include barometry (pressure measurement in the atmosphere), manometry (pressure in liquids), and hydraulic systems. Pascal's principle states that in an enclosed, incompressible fluid at rest, any externally applied pressure is transmitted undiminished to every part of the fluid, enabling hydraulic presses and lifts.

Assumptions commonly used are that the fluid is incompressible, at rest, and in static equilibrium, with weight balanced by pressure forces; surface tension and viscosity effects are neglected in basic analyses. Real fluids may have density variations, compressibility, or temperature effects that modify the simple relations.