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fluid

Continuum mechanics
General

Classical mechanics

Stress

Tensor

Conservation of mass

Conservation of momentum

Solid mechanics

Solids

Elasticity

Plasticity

Hooke's law

Rheology

Fluid mechanics

Fluids

Fluid statics

Fluid dynamics

Navier-Stokes equations

Viscosity

Newtonian fluids

Non-Newtonian fluids

A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. It is a subset of the phases of matter and includes liquids, gases, plasmas and, to some extent, plastic solids.

Fluids are also divided into liquids and gases. Liquids form a free surface (that is, a surface not created by their container) while gases do not. The distinction between solids and fluids is not so obvious. The distinction is made by evaluating the viscosity of the matter: for example silly putty can be considered either a solid or a fluid, depending on the time period over which it is observed.

Fluids share the properties of not resisting deformation and the ability to flow (also described as their ability to take on the shape of their containers). These properties are typically a function of their inability to support a shear stress in static equilibrium. While in a solid, stress is a function of strain, in a fluid, stress is a function of rate of strain. A consequence of this behavior is Pascal's law which entails the important role of pressure in characterizing a fluid's state.

Based on how the stress depends on the rate of strain and its derivatives, fluids can be characterized as:

Newtonian fluids : where stress is directly proportional to rate of strain, and
Non-Newtonian fluids : where stress is proportional to rate of strain, its higher powers and derivatives (basically everything other than Newtonian fluid).

The behavior of fluids can be described by a set of partial differential equations, which are based on the conservation of mass, linear and angular momentum (Navier-Stokes equations) and energy.

The study of fluids is fluid mechanics, which is subdivided into fluid dynamics and fluid statics depending on whether the fluid is in motion or not.

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