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# Fluid

Continuum mechanics
Conservation of mass
Conservation of momentum
Navier-Stokes equations
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A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of how small the applied stress. All liquids and all gases are fluids. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids.

Liquids form a free surface (that is, a surface not created by the container) while gases do not. The distinction between solids and fluids is not entirely obvious. The distinction is made by evaluating the viscosity of the substance. Silly Putty can be considered either a solid or a fluid, depending on the time period over which it is observed.

Fluids display such properties as:

• not resisting deformation, or resisting it only lightly (viscosity), and
• the ability to flow (also described as the ability to take on the shape of the container).

These properties are typically a function of their inability to support a shear stress in static equilibrium.

Solids can be subjected to shear stresses, and to normal stresses - both compressive and tensile. In contrast, ideal fluids can only be subjected to normal, compressive stress which is called pressure. Real fluids display viscosity and so are capable of being subjected to low levels of shear stress.

In a solid, shear stress is a function of strain, but in a fluid, shear stress is a function of rate of strain. A consequence of this behavior is Pascal's law which describes the role of pressure in characterizing a fluid's state.

Depending on the relationship between shear stress, and 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.

The behavior of fluids can be described by the Navier-Stokes equations - a set of partial differential equations which are based on:

The study of fluids is fluid mechanics, which is subdivided into fluid dynamics and fluid statics depending on whether the fluid is in motion.