Fluid mechanics

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Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. It can be further subdivided into fluid statics, the study of fluids at rest, and fluid dynamics, the study of fluids in motion.

Relationship to continuum mechanics

Fluid mechanics is often considered a subdiscipline of continuum mechanics, as illustrated in the following table.

Continuum mechanics Solid mechanics: the study of the physics of continuous solids with a defined rest shape. Elasticity: which describes materials that return to their rest shape after an applied stress.
Plasticity: which describes materials that permanently deform after a large enough applied stress. Rheology: the study of materials with both solid and fluid characteristics
Fluid mechanics Non-Newtonian fluids
Newtonian fluids

The continuity assumption

Gases are composed of molecules which collide with one another and solid objects. The continuity assumption, however, considers fluids to be continuous. That is, properties such as density, pressure, temperature, and velocity are taken to be well-defined at infinitely small points, and are assumed to vary continuously from one point to another. The discrete, molecular nature of a fluid is ignored.

Those problems for which the continuity assumption does not allow solutions of desired accuracy are solved using statistical mechanics. In order to determine whether to use conventional fluid dynamics (a subdiscipline of continuum mechanics) or statistical mechanics, the Knudsen number is evaluated for the problem. Problems with Knudsen numbers at or above unity must be evaluated using statistical mechanics for reliable solutions.

References

White, Frank M. 2002 "Fluid Mechanics" (McGraw-Hill Companies, Inc.)