Fluids

Fluids are substances that deform continuously under shear and consequently flow to fill the shapes of their containers. They include liquids and gases, and in some contexts plasmas and complex fluids like emulsions may be treated as fluids for modeling purposes. The defining feature of fluids is their ability to move and reconfigure under applied forces, making them central to physics, engineering, and the life sciences.

Basic properties used to describe fluids include density (mass per unit volume), viscosity (internal resistance to shear), and compressibility (change in volume with pressure). Surface tension governs the behavior of interfaces, such as air–water surfaces. Fluids can flow smoothly (laminar) or chaotically (turbulent), depending on factors such as viscosity, velocity, and characteristic length scales. The motion of viscous fluids is governed by the Navier–Stokes equations, while ideal, non-viscous fluids follow the Euler equations; the continuity equation expresses mass conservation.

In hydrostatics, fluids at rest support pressure that increases with depth (Pascal’s principle). Buoyancy, described by Archimedes’ principle, explains why objects float or sink. In dynamic settings, Bernoulli’s principle connects fluid speed with pressure along a streamline, though its applicability is limited by assumptions such as steady, incompressible, inviscid flow.

Applications span engineering and science: hydraulics and pneumatics, aircraft and automobile design, weather forecasting, oceanography, cardiovascular physiology, and microfluidics for chemical analysis. Quantities are measured in standard units such as pascals for pressure, kilograms per cubic meter for density, and pascal-second for dynamic viscosity.