Fluid Statics Fundamentals

Concept

Fluid statics is the branch of fluid mechanics that analyzes fluids at rest. In a stationary fluid, there are no shear stresses present; the only forces acting are normal surface forces (pressure) and body forces (gravity). The fundamental principle of hydrostatics states that the pressure in a continuous, stationary fluid of constant density increases linearly with depth due to the weight of the overlying fluid.

Formula & Method

The fundamental hydrostatic equation relating a change in pressure to a change in elevation in an incompressible fluid is:

Expressing pressure at a depth $h$ below a free liquid surface (where $P = P_{atm}$):

Engineering Meaning

The hydrostatic principle is vital for the design of dams, storage tanks, submarines, and manometers. In manometry, this linear relationship allows engineers to measure pressure differences in complex piping systems simply by measuring differences in fluid column heights.

Engineering Check

Always ensure that the elevation difference is measured strictly vertically. The shape or width of a container does not affect the hydrostatic pressure at a given depth. Furthermore, clearly distinguish between absolute and gage pressures when performing calculations, as mixing them up is a frequent source of errors.

Explicit Exclusions

This fundamental article only covers basic hydrostatic pressure and manometry. It does not cover forces on submerged curved surfaces, center of pressure calculations, buoyancy, stability of floating bodies, and rigid-body translation/rotation of fluids.