Fluid Statics is the study of fluids at rest relative to a chosen reference frame and the pressure distributions and forces that exist when there is no relative fluid motion. In a stationary fluid, shear stresses are absent under ordinary equilibrium conditions, while pressure acts normal to surfaces. The central relation is the hydrostatic pressure gradient, which states that pressure increases with depth in a fluid of appropriate density under gravity. Fluid Statics applies to liquids and gases, although density variations with height are usually much more significant for gases. Applications include reservoirs, dams, tanks, hydraulic systems, pressure measurement and buoyancy.
Hydrostatic equilibrium results from a balance between pressure forces and body forces such as gravity. For a fluid with constant density rho in a uniform gravitational field, pressure increases with depth according to P equals P0 plus rho g h, where P0 is the pressure at a reference surface and h is vertical depth below that surface. The pressure difference between two points depends on their vertical separation and density, not on the shape of the container. This explains why containers with very different geometries can produce the same pressure at equal depths when they contain the same fluid under equivalent conditions.
Pressure in a static fluid has important directional properties. At a point in a fluid at rest, pressure is isotropic, meaning that the normal stress has the same magnitude in every direction. If different normal stresses existed at a point without balancing forces, the fluid would accelerate and cease to be static. Pressure therefore acts perpendicular to submerged surfaces. The total force on a surface is obtained by integrating pressure over its area, and because pressure can vary with depth, the resultant force generally does not act through the geometric centre of the surface. Its point of application is known as the centre of pressure.
Manometers are important applications of Fluid Statics because they measure pressure differences through differences in fluid column height. A simple liquid column can relate pressure to rho g h, while differential manometers compare pressures at two locations using one or more fluids of known density. Barometers use the hydrostatic balance of a liquid column to measure atmospheric pressure. These instruments demonstrate that pressure measurements depend on reference conditions. Absolute pressure is measured relative to a vacuum, gauge pressure is measured relative to local atmospheric pressure, and pressure differences can be measured directly without choosing either as the zero reference.
Fluid Statics provides the basis for analysing forces on submerged structures. A vertical wall, gate, dam or tank surface experiences a pressure that increases with depth, producing a resultant force and corresponding moment. Engineers calculate these quantities to determine structural loads and ensure stability against sliding, overturning and deformation. Curved surfaces require additional treatment because pressure forces have horizontal and vertical components whose magnitudes depend on the geometry and fluid above or below the surface. These analyses are particularly important for dams, lock gates, retaining systems and underwater structures.
Buoyancy is directly connected to Fluid Statics because pressure increases with depth and therefore produces a net upward force on an immersed body when the pressure on its lower surfaces exceeds the pressure on its upper surfaces. The resulting buoyant force equals the weight of the displaced fluid under the assumptions of Archimedes' Principle. Whether a body floats, sinks or remains neutrally buoyant depends on the relationship between its average density and the surrounding fluid density, together with the body's geometry and mass distribution. Fluid Statics therefore provides the pressure field from which buoyancy emerges as a force consequence.
Fluid Statics also applies to gases, although atmospheric pressure varies with altitude because air density and temperature vary. Under hydrostatic equilibrium, pressure decreases with increasing elevation, and atmospheric models can use the hydrostatic equation together with an equation of state such as the Ideal Gas Law. The constant density approximation is usually much more appropriate for liquids than for gases over substantial vertical distances. In specialised settings, centrifugal acceleration or other body forces can replace or supplement gravity, producing corresponding pressure gradients in rotating fluids.
The assumptions of Fluid Statics should be stated explicitly. A fluid can be considered static relative to one reference frame while moving relative to another, and a fluid undergoing rigid body rotation can be in equilibrium relative to the rotating frame while exhibiting a pressure gradient in both radial and vertical directions. Static fluid analysis does not describe viscous drag, turbulence or ordinary flow acceleration because those phenomena require relative fluid motion. Nevertheless, hydrostatic relationships remain fundamental throughout Fluid Mechanics and provide essential boundary conditions and reference states for many dynamic problems.
