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In , a fluid is a , , or other material that may continuously and deform ( flow) under an applied , or external force. They have zero , or, in simpler terms, are which cannot resist any applied to them.

Although the term fluid generally includes both the liquid and gas phases, its definition varies among branches of science. Definitions of vary as well, and depending on field, some substances can have both fluid and solid properties. Non-Newtonian fluids like appear to behave similar to a solid when a sudden force is applied. Substances with a very high such as pitch appear to behave like a solid (see pitch drop experiment) as well. In , the concept is extended to include fluidic other than liquids or gases.Example (in the title): A fluid in medicine or biology refers to any liquid constituent of the body (), whereas "liquid" is not used in this sense. Sometimes liquids given for fluid replacement, either by drinking or by injection, are also called fluidsUsage example: (e.g. "drink plenty of fluids"). In , is a term which refers to liquids with certain properties, and is broader than (hydraulic) oils.

Fluids display properties such as:
  • lack of resistance to permanent deformation, resisting only in a dissipative, frictional manner, 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 in static equilibrium. By contrast, solids respond to shear either with a spring-like restoring force—meaning that deformations are reversible—or they require a certain initial stress before they deform (see plasticity).

Solids respond with restoring forces to both shear stresses and to , both compressive and . By contrast, ideal fluids only respond with restoring forces to normal stresses, called : fluids can be subjected both to compressive stress—corresponding to positive pressure—and to tensile stress, corresponding to negative pressure. Solids and liquids both have tensile strengths, which when exceeded in solids creates irreversible deformation and fracture, and in liquids cause the onset of .

Both solids and liquids have free surfaces, which cost some amount of free energy to form. In the case of solids, the amount of free energy to form a given unit of surface area is called , whereas for liquids the same quantity is called . In response to surface tension, the ability of liquids to flow results in behaviour differing from that of solids, though at equilibrium both tend to minimise their surface energy: liquids tend to form rounded , whereas pure solids tend to form . , lacking free surfaces, freely diffuse.

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

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 , which is subdivided into and depending on whether the fluid is in motion.

Classification of fluids
Depending on the relationship between shear stress and the rate of strain and its , fluids can be characterized as one of the following:
  • : where stress is directly proportional to rate of strain
  • Non-Newtonian fluids: where stress is not proportional to rate of strain, its higher powers and derivatives.

Newtonian fluids follow Newton's law of viscosity and may be called .

Fluids may be classified by their compressibility:

  • Compressible fluid: A fluid that causes volume reduction or density change when pressure is applied to the fluid or when the fluid becomes supersonic.
  • Incompressible fluid: A fluid that does not vary in volume with changes in pressure or flow velocity (i.e., ρ=constant) such as water or oil.

Newtonian and incompressible fluids do not actually exist, but are assumed to be for theoretical settlement. Virtual fluids that completely ignore the effects of viscosity and compressibility are called .

See also

  • (2024). 9780471410775, Wiley, Revised Second Edition.

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