Definitions

# fluid mechanics

fluid mechanics, branch of mechanics dealing with the properties and behavior of fluids, i.e., liquids and gases. Because of their ability to flow, liquids and gases have many properties in common not shared by solids. The special study of fluids in motion, or fluid dynamics, makes up the larger part of fluid mechanics. Branches of fluid dynamics include hydrodynamics (study of liquids in motion) and aerodynamics (study of gases in motion). Hydrodynamics is often used synonymously with fluid dynamics, since most of the results from the study of liquids also apply to gases. A plasma is also a fluid (see states of matter) and can be described by many of the principles of fluid mechanics, but its electromagnetic properties must also be taken into account. The study of plasmas in motion is known as magnetohydrodynamics and includes principles from several fields.

Study of the effects of forces and energy on liquids and gases. One branch of the field, hydrostatics, deals with fluids at rest; the other, fluid dynamics, deals with fluids in motion and with the motion of bodies through fluids. Liquids and gases are both treated as fluids because they often have the same equations of motion and exhibit the same flow phenomena. The subject has numerous applications in fields varying from aeronautics and marine engineering to the study of blood flow and the dynamics of swimming.

In fluid mechanics, an ensemble is an imaginary collection of notionally identical experiments.

Each member of the ensemble will have nominally identical boundary conditions and fluid properties. If the flow is turbulent, the details of the fluid motion will differ from member to member because the experimental setup will be microscopically different; and these slight differences become magnified as time progresses. Members of an ensemble are, by definition, statistically independent of one another. The concept of ensemble is useful in thought experiments and to improve theoretical understanding of turbulence.

A good image to have in mind is a typical fluid mechanics experiment such as a mixing box. Imagine a million mixing boxes, distributed over the earth; at a predetermined time, a million fluid mechanics engineers each start one experiment, and monitor the flow. Each engineer then sends his or her results to a central database. Such a process would give results that are close to the theoretical ideal of an ensemble.

It is common to speak of Ensemble average or ensemble averaging when considering a fluid mechanical ensemble.

For a completely unrelated type of averaging, see Reynolds-averaged Navier-Stokes equations (the two types of averaging are often confused).

The idea of the ensemble is discussed further in the article Statistical ensemble (mathematical physics).

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