Continuum Mechanics

Conservation of mass Conservation of momentum Navier-Stokes equations Classical mechanics Stress · Strain · Tensor Solid mechanics Solids · Elasticity Plasticity · Hooke's law Rheology · Viscoelasticity Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ... Image File history File links File links The following pages link to this file: Bernoullis equation ... The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov-Lavoisier law), states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ... Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... Stress is a measure of force per unit area within a body. ... This article is about the deformation of materials. ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ... Solid mechanics is the branch of physics and mathematics that concern the behavior of solid matter under external actions (e. ... This box:      For other uses, see Solid (disambiguation). ... Elasticity is a branch of physics which studies the properties of elastic materials. ... For other uses, see Plasticity. ... Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ... Rheology is the study of the deformation and flow of matter under the influence of an applied stress. ... Viscoelasticity, also known as anelasticity, describes materials that exhibit both viscous and elastic characteristics when undergoing plastic deformation. ... Fluid mechanics Fluids · Fluid statics Fluid dynamics · Viscosity · Newtonian fluids Non-Newtonian fluids Surface tension Scientists Newton · Stokes · Navier · Cauchy· Hooke

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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. 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. 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. This box:      Fluid mechanics is the study of how fluids move and the forces on them. ... Fluid statics (also called hydrostatics) is the science of fluids at rest, and is a sub-field within fluid mechanics. ... Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. ... For other uses, see Viscosity (disambiguation). ... A Newtonian fluid (named for Isaac Newton) is a fluid that flows like water—its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ... A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ... This box:      Surface tension is a property of the surface of a liquid that causes it to behave as an elastic sheet. ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Sir George Gabriel Stokes, 1st Baronet FRS (13 August 1819–1 February 1903), was an Irish mathematician and physicist, who at Cambridge made important contributions to fluid dynamics (including the Navier-Stokes equations), optics, and mathematical physics (including Stokes theorem). ... Claude-Louis Navier (born Claude Louis Marie Henri Navier on February 10, 1785 in Dijon, died August 21, 1836 in Paris) was a French engineer and physicist. ... Augustin Louis Cauchy Augustin Louis Cauchy (August 21, 1789 – May 23, 1857) was a French mathematician. ... Robert Hooke, FRS (July 18, 1635 – March 3, 1703) was an English polymath who played an important role in the scientific revolution, through both experimental and theoretical work. ... Shear stress is a stress state where the stress is parallel or tangential to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ... 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 (i. ... For other uses, see Liquid (disambiguation). ... For other uses, see Gas (disambiguation). ... A Plasma lamp In physics and chemistry, a plasma is an ionized gas, and is usually considered to be a distinct phase of matter. ... For other uses, see Plasticity. ...

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 either a solid or a fluid, depending on the time period over which it is observed. For other uses, see Plasticity. ... For other uses, see Viscosity (disambiguation). ... Silly putty dripping through a hole Silly Putty shown as a solid cube Silly Putty (originally called nutty putty, and also known as Potty Putty) is a silicone plastic, marketed today as a toy for children, but originally created as an accident during the course of research into potential rubber...

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).
  

These properties are typically a function of their inability to support a shear stress in static equilibrium. For other uses, see Viscosity (disambiguation). ... Shear stress is a stress state where the stress is parallel or tangential to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ... A standard definition of mechanical equilibrium is: A system is in mechanical equilibrium when the sum of the forces, and torque, on each particle of the system is zero. ...

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. Compressive stress is the stress applied to materials resulting in their compaction (decrease of volume). ... Tensile stress (or tension) is the stress state leading to expansion; that is, the length of a material tends to increase in the tensile direction. ... This article is about pressure in the physical sciences. ... For other uses, see Viscosity (disambiguation). ... Shear stress is a stress state where the stress is parallel or tangential to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ...

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. This article is about the deformation of materials. ... In the physical sciences, Pascals law or Pascals principle states that for all points at the same absolute height in a connected body of an incompressible fluid at rest, the fluid pressure is the same, even if additional pressure is applied on the fluid at some place. ... This article is about pressure in the physical sciences. ...

Depending on the relationship between shear stress, and the rate of strain and its derivatives, fluids can be characterized as: Stress is a measure of force per unit area within a body. ... This article is about the deformation of materials. ... For other uses, see Derivative (disambiguation). ...

• 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.

The behavior of fluids can be described by the Navier-Stokes equations - a set of partial differential equations which are based on:
A Newtonian fluid (named for Isaac Newton) is a fluid that flows like water—its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ... A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ... In mathematics, and in particular analysis, a partial differential equation (PDE) is an equation involving partial derivatives of an unknown function. ...

• continuity (conservation of mass),
• conservation of linear momentum
• conservation of angular momentum
• conservation of energy.

The study of fluids is fluid mechanics, which is subdivided into fluid dynamics and fluid statics depending on whether the fluid is in motion. All the examples of continuity equations below express the same idea; they are all really examples of the same concept. ... In physics, momentum is a physical quantity related to the velocity and mass of an object. ... This gyroscope remains upright while spinning due to its angular momentum. ... This article is about the law of conservation of energy in physics. ... This box:      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 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