flowing

Flowing refers to the continuous movement of matter, typically liquids and gases, from regions of higher potential to lower potential. In physics and engineering, flow describes how a fluid moves through space, around objects, or within a conduit. The state of flow is described by fields such as velocity, pressure, density, and, in some cases, temperature.

Forces such as pressure gradients, gravity, and viscous stresses drive flow. Viscosity resists motion and acts to damp fluctuations in the fluid. Lower viscosity fluids tend to flow more easily than higher viscosity ones. The Reynolds number, defined as Re = rho v L / mu, helps predict whether the flow will be smooth (laminar) or chaotic (turbulent) under given conditions.

Flow can be categorized as laminar or turbulent. Laminar flow features orderly, layered motion with minimal mixing between layers, while turbulent flow is characterized by irregular fluctuations and eddies. Fluids can be Newtonian, with a constant viscosity independent of shear rate, or non-Newtonian, where viscosity changes with shear rate or time. Common examples include water moving through a pipe, air streaming over an aircraft wing, rivers, blood in arteries, and magma flowing in geological settings.

Flow is central to many disciplines and applications, including hydraulics and piping design, meteorology and oceanography, cardiovascular physiology, and environmental science. Measurements of flow include volumetric flow rate and mass flow rate, typically inferred from velocity profiles, pressure differences, or cross-sectional areas.