Fluid

Encyclopedia

In physics

, a

(flows) under an applied shear stress

. Fluids are a subset of the phases of matter

and include liquid

s, gas

es, plasmas

and, to some extent, plastic solids

.

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 and in nutrition ("take plenty of fluids").

Liquids form a free surface

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

and fluid is not entirely obvious. The distinction is made by evaluating the viscosity

of the substance. Silly Putty

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. There are many examples of substances proving difficult to classify. A particularly interesting one is pitch

, as demonstrated in the pitch drop experiment

currently running at the University of Queensland

.

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.

, 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.

Depending on the relationship between shear stress, and the rate of strain and its derivative

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

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.

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, a

**fluid**is a substance that continually deformsDeformation (mechanics)

Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body...

(flows) under an applied shear stress

Shear stress

A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

. 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, index of refraction, and chemical composition...

and include liquid

Liquid

Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

s, gas

Gas

Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

es, plasmas

Plasma (physics)

In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

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. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the...

.

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 and in nutrition ("take plenty of fluids").

Liquids form a free surface

Free surface

In physics, a free surface is the surface of a fluid that is subject to constant perpendicular normal stress and zero parallel shear stress,such as the boundary between two homogenous fluids,for example liquid water and the air in the Earth's atmosphere...

(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. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the...

and fluid is not entirely obvious. The distinction is made by evaluating the viscosity

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

of the substance. Silly Putty

Silly Putty

Silly Putty , is the Crayola-owned trademark name for a class of silicone polymers. 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. There are many examples of substances proving difficult to classify. A particularly interesting one is pitch

Pitch (resin)

Pitch is the name for any of a number of viscoelastic, solid polymers. Pitch can be made from petroleum products or plants. Petroleum-derived pitch is also called bitumen. Pitch produced from plants is also known as resin. Products made from plant resin are also known as rosin.Pitch was...

, as demonstrated in the pitch drop experiment

Pitch drop experiment

The 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...

currently running at the University of Queensland

University of Queensland

The University of Queensland, also known as UQ, is a public university located in state of Queensland, Australia. Founded in 1909, it is the oldest and largest university in Queensland and the fifth oldest in the nation...

.

## Physics

Fluids display such properties as:- not resisting deformation, or resisting it only lightly (viscosityViscosityViscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

), and - the ability to flow (also described as the ability to take on the shape of the container).This also means that all fluids have the property of fluidity.

These properties are typically a function of their inability to support a shear stress

Shear stress

A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

in static equilibrium

Mechanical equilibrium

A standard definition of static equilibrium 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 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 in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

. Real fluids display viscosity and so are capable of being subjected to low levels of shear stress.

### Modelling

In a solid, shear stress is a function of strainStrain (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 deformations of a continuum body...

, but in a fluid, shear stress

Stress (physics)

In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

is a function of strain rate. A consequence of this behavior is Pascal's law

Pascal's law

In the physical sciences, Pascal's law or the Principle of transmission of fluid-pressure states that "pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the pressure ratio remains the same." The law was established...

which describes the role of pressure

Pressure

Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

in characterizing a fluid's state.

Depending on the relationship between shear stress, and the rate of strain 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 one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...

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

- Newtonian fluidNewtonian fluidA Newtonian fluid is a fluid whose stress versus strain rate curve is linear and passes through the origin. The constant of proportionality is known as the viscosity.-Definition:...

s : where stress is directly proportional to rate of strain

- Non-Newtonian fluidNon-Newtonian fluidA non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Most commonly the viscosity of non-Newtonian fluids is not independent of shear rate or shear rate history...

s : where stress is not 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:

- continuity (conservation of mass),
- conservation of linear momentum,
- conservation of angular momentumAngular momentumIn physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

, - conservation of energyConservation of energyThe nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...

.

The study of fluids is fluid mechanics

Fluid mechanics

Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...

, which is subdivided into fluid dynamics

Fluid dynamics

In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

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. It embraces the study of the conditions under which fluids are at rest in stable equilibrium...

depending on whether the fluid is in motion.