Fluid Statics

Fluid statics deals with fluids at rest and the forces and pressures that arise in such conditions.  A fluid is considered to be in a static state when there is no relative motion between its particles, meaning that shear stresses are absent and only normal stresses act within the fluid.  Under these conditions, the behavior of the fluid is governed primarily by the balance between pressure forces and external body forces, most commonly gravity.  The assumption is that the fluid is in mechanical equilibrium, so the net force acting on any fluid element is zero.

A central concept in fluid statics is pressure variation within a fluid.  In a stationary fluid subjected to a gravitational field, pressure increases with depth due to the weight of the overlying fluid.  This relationship is described by the hydrostatic equation, which quantitatively relates the rate of change of pressure with respect to elevation to the fluid’s density and gravitational acceleration.  This principle explains why pressure at the bottom of a container is greater than at the surface and applies universally to liquids and gases under static conditions, provided density variations are appropriately accounted for.

Fluid statics also encompasses the analysis of forces exerted by fluids on submerged or partially submerged surfaces.  This includes the determination of hydrostatic forces on structures such as dams, gates, and tank walls, as well as the location of the center of pressure where the resultant force acts.  Additionally, it includes buoyancy, described by Archimedes' principle, which states that a body immersed in a fluid experiences an upward force equal to the weight of the fluid it displaces.