Continuum mechanics

Conservation of mass Conservation of momentum Navier–Stokes equations

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A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of how small the applied stress. Continuum mechanics is a branch of Mechanics that deals with the analysis of the Kinematics and mechanical behavior of materials modeled as a continuum e The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov - Lavoisier law says that the Mass of In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product The Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous Fluid substances such A shear stress, denoted \tau\ ( Tau) is defined as a stress which is applied Parallel or tangential to a face of a material All liquids and all gases are fluids. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids. In the Physical sciences a phase is a Set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties 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 This page is about the physical properties of gas as a state of matter In Physics and Chemistry, plasma is an Ionized Gas, in which a certain proportion of Electrons are free rather than being bound The term "fluid" is often used as being synonymous with "liquid". This can be erroneous and sometimes clearly inappropriate - such as when referring to a liquid which does not or should not involve the gaseous state. "Brake fluid" is hydraulic oil which will not perform its required function if gas is present. The medical profession relies on the term "fluids" in dietary references ("take plenty of fluids") where the presence of gases is irrelevant or even possibly dangerous.

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. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. Silly Putty can be considered to behave like a solid or a fluid, depending on the time period over which it is observed. Silly Putty (originally called Nutty Putty, and also marketing by other companies as Thinking Putty, Bouncing Putty) is the Crayola owned trademark However Silly Putty is correctly termed a viscoelastic fluid. Silly Putty (originally called Nutty Putty, and also marketing by other companies as Thinking Putty, Bouncing Putty) is the Crayola owned trademark Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation.

Fluids display such properties as:

• not resisting deformation, or resisting it only lightly (viscosity), and
  
• the ability to flow (also described as the ability to take on the shape of the container). Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress.
  

These properties are typically a function of their inability to support a shear stress in static equilibrium. A shear stress, denoted \tau\ ( Tau) is defined as a stress which is applied Parallel or tangential to a face of a material

Solids can be subjected to shear stresses, and to normal stresses - both compressive and tensile. Compressive stress is the stress applied to materials resulting in their compaction (decrease of volume Stress is a measure of the average amount of Force exerted per unit Area. In contrast, ideal fluids can only be subjected to normal, compressive stress which is called pressure. Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface Real fluids display viscosity and so are capable of being subjected to low levels of shear stress. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. A shear stress, denoted \tau\ ( Tau) is defined as a stress which is applied Parallel or tangential to a face of a material

In a solid, shear stress is a function of strain, but in a fluid, shear stress is a function of rate of strain. A consequence of this behavior is Pascal's law which describes the role of pressure in characterizing a fluid's state. Pascal (unitIn the Physical sciences, Pascal's law or Pascal's principle states that "a change in the pressure of an enclosed incompressible fluid is conveyed Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface

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

• Newtonian fluids : where stress is directly proportional to rate of strain, and
• Non-Newtonian fluids : where stress is proportional to rate of strain, its higher powers and derivatives. Stress is a measure of the average amount of Force exerted per unit Area. In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change A Newtonian fluid (named for Isaac Newton) is a Fluid whose stress versus rate of strain curve is linear and passes through the origin A non-Newtonian fluid is a Fluid whose flow properties are not described by a single constant value of Viscosity.

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 momentum
• conservation of energy. The Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous Fluid substances such In Mathematics, partial differential equations ( PDE) are a type of Differential equation, i A continuity equation is a Differential equation that describes the conservative transport of some kind of quantity In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position In Physics, the law of conservation of energy states that the total amount of Energy in an isolated system remains constant and cannot be created although it may

The study of fluids is fluid mechanics, which is subdivided into fluid dynamics and fluid statics depending on whether the fluid is in motion. Fluid mechanics is the study of how Fluids move and the Forces on them Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion Fluid statics (also called hydrostatics) is the Science of Fluids at rest and is a sub-field within Fluid mechanics.

External links

• Fluid mechanics Concept Map from Georgia State University

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