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In physics, a fluid is a liquid or gas or other material that continually deforms (flows) under an applied shear stress, or external force.[1] They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force applied to them.

Liquids form a free surface (that is, a surface not created by the container) while gases do not.

Although the term "fluid" generally includes both the liquid and gas phases, its definition varies among branches. Definition of "solid" vary as well, and depending on field, some substances can be both "fluid" and "solid".[2] Viscoelastic fluids like Silly Putty appear to behave similar to a solid when a sudden force is applied.[3] Also substances with a very high viscosity such as pitch appear to behave like a solid (see pitch drop experiment). In particle physics, the concept is extended to include fluidic matters other than liquids or gases.[4] "Fluid" in medicine and biology specifically means any liquid constituent of the body (body fluid),[5][6] whereas "liquid" is not used in this sense. Sometimes liquids to be taken for fluid replacement, either by drinking or by injection, are also called "fluid"[7] ("drink plenty of fluids"). In hydraulics, "fluid" is a term which refers to liquids of certain properties, and is a broader concept than "(hydraulic) oils".[8]


Fluids display properties such as:

  • lack of resistance to permanent deformation, resisting only relative rates of deformation 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 shear stress in static equilibrium. In contrast, solids respond to shear either with a spring-like restoring force, which means 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 normal stresses—both compressive and tensile. In contrast, ideal fluids only respond with restoring forces to normal stresses, called pressure: fluids can be subjected to both compressive stress, corresponding to positive pressure, and to tensile stress, corresponding to negative pressure. Both solids and liquids also have tensile strengths, which when exceeded in solids makes irreversible deformation and fracture, and in liquids causes the onset of cavitation.

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 surface energy, whereas for liquids the same quantity is called surface tension. The ability of liquids to flow results in different behaviour in response to surface tension than in solids, although in equilibrium both will try to minimise their surface energy: liquids tend to form rounded droplets, whereas pure solids tend to form crystals. Gases do not have free surfaces, and freely diffuse.


In a solid, shear stress is a function of strain, but in a fluid, shear stress is a function of strain rate. A consequence of this behavior is Pascal's law which describes the role of pressure 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 fluid mechanics, which is subdivided into fluid dynamics and fluid statics depending on whether the fluid is in motion.

Classification of fluids[edit]

Depending on the relationship between shear stress and the rate of strain and its derivatives, fluids can be characterized as one of the following:

  • Newtonian fluids: 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 viscous fluids.

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 perfect fluids.

See also[edit]


  1. ^ "Fluid | Definition, Models, Newtonian Fluids, Non-Newtonian Fluids, & Facts". Encyclopedia Britannica. Retrieved 2 June 2021.
  2. ^ Thayer, Ann (2000-11-27) [2000]. "What's That Stuff? Silly Putty". C&EN (Chemical & Engineering News). American Chemical Society. 78 (48): 27. Archived from the original on 2021-05-07 – via American Chemical Society.
  3. ^ Kroen, Gretchen Cuda (2012-04-11). "Silly Putty for Potholes". Science. Retrieved 2021-06-23.
  4. ^ Example (in the title): Berdyugin, A. I.; Xu, S. G. (2019-04-12). F. M. D. Pellegrino, R. Krishna Kumar, A. Principi, I. Torre, M. Ben Shalom, T. Taniguchi, K. Watanabe, I. V. Grigorieva, M. Polini, A. K. Geim, D. A. Bandurin. "Measuring Hall viscosity of graphene's electron fluid". Science. 364 (6436): 162–165. doi:10.1126/science.aau0685.
  5. ^ "Fluid (B.1.b.)". Oxford English Dictionary. IV F–G (1978 reprint ed.). Oxford: Oxford university press. 1933 [1901]. p. 358. Retrieved 2021-06-22.
  6. ^ "body fluid". Taber's online – Taber's medical dictionary. Archived from the original on 2021-06-21. Retrieved 2021-06-22.
  7. ^ Usage example: Guppy, Michelle P B; Mickan, Sharon M; Del Mar, Chris B (2004-02-28). ""Drink plenty of fluids": a systematic review of evidence for this recommendation in acute respiratory infections". BMJ. 328 (7438): 499–500. doi:10.1136/bmj.38028.627593.BE. PMC 351843.
  8. ^ "What is Fluid Power?". National Fluid Power Association. Archived from the original on 2021-06-23. Retrieved 2021-06-23. With hydraulics, the fluid is a liquid (usually oil),
  • Bird, Robert Byron; Stewart, Warren E.; Lightfoot, Edward N. (2007). Transport Phenomena. New York: Wiley, Revised Second Edition. p. 912. ISBN 0-471-41077-2.