physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, a fluid is a

liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...

gas Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...

, or other material that continuously deforms (''flows'') under an applied

shear stress Shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the ot ...

, or external force. They have zero

shear modulus In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: :G \ \stackrel ...

, or, in simpler terms, are substances which cannot resist any

shear force In solid mechanics, shearing forces are unaligned forces acting on one part of a body in a specific direction, and another part of the body in the opposite direction. When the forces are collinear (aligned with each other), they are called t ...

applied to them. Although the term ''fluid'' generally includes both the liquid and gas phases, its definition varies among

branches of science The branches of science, also referred to as sciences, scientific fields or scientific disciplines, are commonly divided into three major groups: *Formal sciences: the study of formal systems, such as those under the branches of logic and mat ...

. Definitions of ''solid'' vary as well, and depending on field, some substances can be both fluid and solid.

Viscoelastic In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly wi ...

fluids like

Silly Putty Silly Putty is a toy based on silicone polymers that have unusual physical properties. It bounces, but it breaks when given a sharp blow, and it can also flow like a liquid. It contains a viscoelastic liquid silicone, a type of non-Newtonian fl ...

appear to behave similar to a solid when a sudden force is applied. Substances with a very high

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

such as pitch appear to behave like a solid (see

pitch drop experiment A pitch drop experiment is a long-term experiment which measures the flow of a piece of pitch over many years. 'Pitch' is the name for any of a number of highly viscous liquids which appear solid, most commonly bitumen, also known as asphalt. ...

) as well. In

particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...

, the concept is extended to include fluidic

matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...

s other than liquids or gases. A fluid in medicine or biology refers any liquid constituent of the body (

body fluid Body fluids, bodily fluids, or biofluids, sometimes body liquids, are liquids within the human body. In lean healthy adult men, the total body water is about 60% (60–67%) of the total Human body weight, body weight; it is usually slightly lower ...

), whereas "liquid" is not used in this sense. Sometimes liquids given for

fluid replacement Fluid replacement or fluid resuscitation is the medical practice of replenishing bodily fluid lost through sweating, bleeding, fluid shifts or other pathologic processes. Fluids can be replaced with oral rehydration therapy (drinking), intravenous ...

, either by drinking or by injection, are also called fluids (e.g. "drink plenty of fluids"). In

hydraulics Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counter ...

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

is a term which refers to liquids with certain properties, and is broader than (hydraulic) oils.

Physics

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

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 Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...

before they deform (see

plasticity Plasticity may refer to: Science * Plasticity (physics), in engineering and physics, the propensity of a solid material to undergo permanent deformation under load * Neuroplasticity, in neuroscience, how entire brain structures, and the brain it ...

). Solids respond with restoring forces to both shear stresses and to

normal stress In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elonga ...

es—both

compressive In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elonga ...

and

tensile In physics, tension is described as the pulling force transmitted axially by the means of a string, a rope, chain, or similar object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as t ...

. In contrast, ideal fluids only respond with restoring forces to normal stresses, called

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...

: fluids can be subjected to both compressive stress, corresponding to positive pressure, and to tensile stress, corresponding to

negative pressure Negative pressure may refer to: * Negative value of a Pressure#Negative pressures, pressure variable * Negative room pressure, a ventilation technique used to avoid contaminating outside areas * Negative pressure ventilator, also known as an iron ...

. 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 Cavitation is a phenomenon in which the static pressure of a liquid reduces to below the liquid's vapour pressure, leading to the formation of small vapor-filled cavities in the liquid. When subjected to higher pressure, these cavities, cal ...

. 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 In surface science, surface free energy (also interfacial free energy or surface energy) quantifies the disruption of intermolecular bonds that occurs when a surface is created. In solid-state physics, surfaces must be intrinsically less energe ...

, whereas for liquids the same quantity is called

surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to f ...

. 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 A drop or droplet is a small column of liquid, bounded completely or almost completely by free surfaces. A drop may form when liquid accumulates at the lower end of a tube or other surface boundary, producing a hanging drop called a pendant d ...

, whereas pure solids tend to form

crystals A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macrosc ...

Gas Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...

es do not have free surfaces, and freely

diffuse Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...

Modelling

In a solid, shear stress is a function of

strain Strain may refer to: Science and technology * Strain (biology), variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes * Strain (chemistry), a chemical stress of a molecule * Strain (injury), an injury to a mu ...

, but in a fluid,

is a function of

strain rate In materials science, strain rate is the change in strain (deformation) of a material with respect to time. The strain rate at some point within the material measures the rate at which the distances of adjacent parcels of the material change wi ...

. A consequence of this behavior is

Pascal's law Pascal's law (also Pascal's principle or the principle of transmission of fluid-pressure) is a principle in fluid mechanics given by Blaise Pascal that states that a pressure change at any point in a confined incompressible fluid is transmitted ...

which describes the role of

in characterizing a fluid's state. The behavior of fluids can be described by the

Navier–Stokes equations In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...

—a set of

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

which are based on: * continuity (

conservation of mass In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass can ...

), * conservation of

linear momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and ...

, * conservation of

angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...

, *

conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means th ...

. The study of fluids is

fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and bio ...

, which is subdivided into

fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

and

fluid statics Fluid statics or hydrostatics is the branch of fluid mechanics that studies the condition of the equilibrium of a floating body and submerged body "fluids at hydrostatic equilibrium and the pressure in a fluid, or exerted by a fluid, on an imme ...

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

derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. F ...

s, fluids can be characterized as one of the following: *

Newtonian fluid A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of chang ...

s: where stress is directly proportional to rate of strain *

Non-Newtonian fluid A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for exa ...

s: 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 fluid In condensed matter physics and physical chemistry, the terms viscous liquid, supercooled liquid, and glassforming liquid are often used interchangeably to designate liquids that are at the same time highly viscous (see Viscosity of amorphous mate ...

s. 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 fluid In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density \rho_m and ''isotropic'' pressure ''p''. Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in whi ...

References

* {{Authority control Fluid dynamics

Physics

Modelling

Classification of fluids

See also

References