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Fluid mechanics is the study of fluids and the forces on them. (Fluids include liquids , gases , and plasmas .) Fluid mechanics can be divided into fluid statics , the study of fluids at rest; fluid kinematics , the study of fluids in motion; and fluid dynamics , the study of the effect of forces on fluid motion. It is a branch of continuum mechanics , a subject which models matter without usingthe information that it is made out of atoms, that is, it models matter from a macroscopic viewpoint rather than from a microscopic viewpoint. Fluid mechanics, especially fluid dynamics, is an active field of research with many unsolved or partly solved problems. Fluid mechanics can be mathematically complex. Sometimes it can best be solved by numerical methods , typically using computers. Amodern discipline, called computational fluid dynamics (CFD), is devoted to this approach to solving fluid mechanics problems. Also taking advantage of the highly visual nature of fluid flow is particle image velocimetry , an experimental method for visualizing and analyzing fluid flow.
Contents

1 Brief history
2 Relationship to continuum mechanics
3 Assumptions
3.1 Continuumhypothesis
4 Navier–Stokes equations
4.1 General form of the equation
5 Newtonian versus non-Newtonian fluids
5.1 Equations for a Newtonian fluid
6 See also
7 Notes
8 References
9 External links

Brief history
Main article: History of fluid mechanics

The study of fluid mechanics goes back at least to the days of ancient Greece , whenArchimedes investigated fluid statics and buoyancy and formulated his famous law known now as the Archimedes' Principle . Rapid advancement in fluid mechanics began with Leonardo da Vinci (observation and experiment), Evangelista Torricelli ( barometer ), Isaac Newton ( viscosity ) and Blaise Pascal ( hydrostatics ), and was continued by Daniel Bernoulli with the introduction of mathematical fluiddynamics in Hydrodynamica (1738). Inviscid flow was further analyzed by various mathematicians ( Leonhard Euler , d'Alembert , Lagrange , Laplace , Poisson ) and viscous flow was explored by a multitude of engineers including Poiseuille and Gotthilf Heinrich Ludwig Hagen . Further mathematical justification was provided by Claude-Louis Navier and George Gabriel Stokes in the Navier–Stokes equations ,and boundary layers were investigated ( Ludwig Prandtl , Theodore von Kármán ), while various scientists ( Osborne Reynolds , Andrey Kolmogorov , Geoffrey Ingram Taylor ) advanced the understanding of fluid viscosity and turbulence .
Relationship to continuum mechanics

Fluid mechanics is a subdiscipline of continuum mechanics , as illustrated in the following table.
Continuum mechanics
Thestudy of the physics of continuous materials Solid mechanics
The study of the physics of continuous materials with a defined rest shape. Elasticity
Describes materials that return to their rest shape after an applied stress .
Plasticity
Describes materials that permanently deform after a sufficient applied stress. Rheology
The study of materials with both solid and fluid characteristics.Fluid mechanics
The study of the physics of continuous materials which take the shape of their container. Non-Newtonian fluids
Newtonian fluids

In a mechanical view, a fluid is a substance that does not support shear stress ; that is why a fluid at rest has the shape of its containing vessel. A fluid at rest has no shear stress.
Assumptions
Balance for some integrated fluid quantity in acontrol volume enclosed by a control surface .

Like any mathematical model of the real world, fluid mechanics makes some basic assumptions about the materials being studied. These assumptions are turned into equations that must be satisfied if the assumptions are to be held true.

For example, consider an fluid in three dimensions. The assumption that mass is conserved means that for any...