Fluid mechanics is the study of the effects of forces and energy on liquids and gases. Like other branches of classical mechanics, the subject subdivides into statics (often called hydrostatics) and dynamics (fluid dynamics, hydrodynamics, or aerodynamics). Hydrostatics is a comparatively elementary subject with a few classical results of importance but little scope for further development. Fluid dynamics, in contrast, is a highly developed branch of science that has been the subject of continuous and expanding research activity since about 1840.

The development of fluid dynamics has been strongly influenced by its numerous applications. Some of the fields of application to engineering, the environmental sciences, and the biological sciences are evident: aeronautical engineering, marine engineering, meteorology, oceanography, and the study of blood flow, the dynamics of swimming, and the flight of creatures. There are also many less immediately obvious applications.

Fluid dynamics is studied both theoretically and experimentally, and the results are described both mathematically and physically. The phenomena of fluid motion are governed by known laws of physics--conservation of mass, the laws of classical mechanics (Newton's laws of motion), and the laws of thermodynamics. These can be formulated as a set of nonlinear partial differential equations, and in principle one might hope to infer all the phenomena from these. In practice, this has not been possible; the mathematical theory is often difficult, and sometimes the equations have more than one solution, so that subtle considerations arise in deciding which one will actually apply. As a result, observations of fluid motion both in the laboratory and in nature are also essential for understanding the motion of fluids.

Liquids and gases are classified together as fluids because, over a wide range of situations, they have identical equations of motion and thus exhibit the same flow phenomena. Scaling analysis makes it possible to infer when two geometrically similar situations--of perhaps quite different size and involving different fluids (either both liquids, both gases, or one of each)--will give rise to the same type of flow. It leads to the formulation of various nondimensional parameters, with names like Reynolds number, Mach number, Froude number, in terms of which fluid-dynamical results are usually presented.

Flow configurations equally applicable to liquids and gases include flow through pipes, flow due to relative motion between a body and ambient fluid, and thermal convection--gravitationally driven flow due to temperature differences. Sometimes the effect of rotation of the whole system (of particular significance in meteorology and oceanography) is included. A common feature of all these flows is their tendency to undergo a spontaneous transition from one type of motion to another. The best-known type of transition is that from laminar flow (a smooth, regular type of flow) to turbulent flow (in which rapid, irregular fluctuations arise). Instability can also lead to a complicated flow with a highly regular structure (such as an orderly array of vortices or of convection cells). Much current research is concerned with gaining an understanding of these various transitions and, in particular, of how a deterministic set of equations can account for the chaotic behaviour of turbulent fluids.

During flow at speeds comparable to the speed of sound, the density of fluids changes significantly. This phenomenon is of practical importance only for gases, in which shock waves may occur. These waves involve an almost discontinuous change in the velocity, temperature, pressure, and density of the fluid.

The main phenomena of importance for liquids but not for gases are those associated with free surfaces, such as the upper boundary of a liquid in a partly filled vessel. The fact that the speed of water waves varies with wavelength and with amplitude leads to a wide variety of effects. These include the hydraulic jump (or bore)--a sudden change in water level, analogous to a shock wave--and the soliton--a single large-amplitude pulse that propagates without change of form.

*Excerpt from the Encyclopedia Britannica without permission.*