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A fluid is defined as a substance that continually deforms (flows) under an applied shear stress
Shear stress

File:Shear stress.JPGA shear stress, denoted , is defined as a stress which is applied parallel or tangent to a face of a material, as opposed to a normal stress which is applied perpendicularly....
. All liquids and all gases are fluids. Fluids are a subset of the phases of matter
Phase (matter)

In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, refractive index, and chemical composition....
 and include liquid
Liquid

Liquid is one of the principal states of matter. A liquid is a fluid that has the particles loose and can freely form a distinct surface at the boundaries of its bulk material....
s, gases
Gas

In physics, a gas is a state of matter, consisting of a collection of particles without a definite shape or volume that are in more or less random motion....
, plasmas and, to some extent, plastic solids
Plasticity (physics)

In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces....
.

In common usage, "fluid" is often used as a synonym for "liquid", with no implication that gas could also be present. For example, "brake fluid" is hydraulic oil and will not perform its required function if there is gas in it.






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A fluid is defined as a substance that continually deforms (flows) under an applied shear stress
Shear stress

File:Shear stress.JPGA shear stress, denoted , is defined as a stress which is applied parallel or tangent to a face of a material, as opposed to a normal stress which is applied perpendicularly....
. All liquids and all gases are fluids. Fluids are a subset of the phases of matter
Phase (matter)

In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, refractive index, and chemical composition....
 and include liquid
Liquid

Liquid is one of the principal states of matter. A liquid is a fluid that has the particles loose and can freely form a distinct surface at the boundaries of its bulk material....
s, gases
Gas

In physics, a gas is a state of matter, consisting of a collection of particles without a definite shape or volume that are in more or less random motion....
, plasmas and, to some extent, plastic solids
Plasticity (physics)

In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces....
.

In common usage, "fluid" is often used as a synonym for "liquid", with no implication that gas could also be present. For example, "brake fluid" is hydraulic oil and will not perform its required function if there is gas in it. This colloquial usage of the term is also common in medicine ("take plenty of fluids"), and in nutrition.

Liquids form a free surface (that is, a surface not created by the container) while gases do not. The distinction between solids
Plasticity (physics)

In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces....
 and fluid is not entirely obvious. The distinction is made by evaluating the viscosity
Viscosity

Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
 of the substance. Silly Putty
Silly Putty

Silly Putty is the Crayola owned trademark name for a class of silicone polymers known as Bouncing Putty. It is marketed today as a toy for children, but was originally created by accident during research into potential rubber substitutes for use by the United States in World War II....
 can be considered to behave like a solid or a fluid, depending on the time period over which it is observed. It is best described as a viscoelastic fluid.

Fluids display such properties as:
  • not resisting deformation, or resisting it only lightly (viscosity
    Viscosity

    Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
    ), 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
Shear stress

File:Shear stress.JPGA shear stress, denoted , is defined as a stress which is applied parallel or tangent to a face of a material, as opposed to a normal stress which is applied perpendicularly....
 in static equilibrium
Mechanical equilibrium

A standard definition of is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....
.

Solids can be subjected to shear stresses, and to normal stresses - both compressive
Compressive stress

Compressive stress is the stress applied to materials resulting in their compaction . When a material is subjected to compressive stress, then this material is under physical compression....
 and tensile. In contrast, ideal fluids can only be subjected to normal, compressive stress which is called pressure
Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
. Real fluids display viscosity
Viscosity

Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
 and so are capable of being subjected to low levels of shear stress
Shear stress

File:Shear stress.JPGA shear stress, denoted , is defined as a stress which is applied parallel or tangent to a face of a material, as opposed to a normal stress which is applied perpendicularly....
.

In a solid, shear stress is a function of strain
Strain (materials science)

In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal Deformation s of a Continuum mechanics....
, but in a fluid, shear stress is a function of rate of strain. A consequence of this behavior is Pascal's law
Pascal's law

In the physical sciences, Pascal's law or Pascal's principle states that "a change in the pressure of an enclosed incompressible fluid is conveyed undiminished to every part of the fluid and to the surfaces of its container."...
 which describes the role of pressure
Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
 in characterizing a fluid's state.

Depending on the relationship between shear stress
Stress (physics)

In continuum mechanics, stress is a measure of the average amount of force exerted per unit area. It is a measure of the intensity of the total internal forces acting within a body across imaginary internal surfaces, as a reaction to external applied forces and body forces....
, and the rate of strain
Strain (materials science)

In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal Deformation s of a Continuum mechanics....
 and its derivative
Derivative

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point....
s, fluids can be characterized as:
  • Newtonian fluid
    Newtonian fluid

    A Newtonian fluid is a fluid whose shear stress versus rate of strain curve is linear and passes through the Origin . The constant of proportionality is known as the viscosity....
    s : where stress is directly proportional to rate of strain, and
  • Non-Newtonian fluid
    Non-Newtonian fluid

    A non-Newtonian fluid is a fluid whose flow properties are not described by a single constant value of viscosity. Many polymer solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as ketchup, starch suspensions, paint, blood and shampoo....
    s : 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
Navier-Stokes equations

The Navier?Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances, that is substances which can flow....
—a set of partial differential equations which are based on:
  • continuity (conservation of mass
    Continuity equation

    A continuity equation is a differential equation that describes the conservative transport of some kind of quantity. Since mass, energy, momentum, and other natural quantities are conserved, a vast variety of physics may be described with continuity equations....
    ),
  • conservation of linear momentum
  • conservation of angular momentum
    Angular momentum

    In physics, the angular momentum of a particle about an origin is a vector quantity related to rotation, equal to the mass of the particle multiplied by the cross product of the position vector of the particle with its velocity vector....
  • conservation of energy
    Conservation of energy

    The law of conservation of energy states that the total amount of energy in an isolated system remains constant. A consequence of this law is that energy cannot be created or destroyed....
    .


The study of fluids is fluid mechanics
Fluid mechanics

Fluid mechanics is the study of how fluids move and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest, and fluid dynamics, the study of fluids in motion....
, which is subdivided into fluid dynamics
Fluid dynamics

In physics, fluid dynamics is the sub-discipline of fluid mechanics dealing with fluid flow — the natural science of fluids in motion....
 and fluid statics
Fluid statics

Fluid statics is the science of fluids at rest, and is a sub-field within fluid mechanics. The term usually refers to the mathematical treatment of the subject....
 depending on whether the fluid is in motion.

See also

  • Matter
    Matter

    In common usage, matter is anything that has both mass and volume . A more rigorous definition is used in science: matter is what atoms and molecules are made of....