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125-528: SAE J306 is a standard that defines the viscometric properties of automotive gear oils . It is maintained by SAE International . Key parameters for this standard are the kinematic viscosity of the gear oil, the maximum temperature at which the oil has a viscosity of 150,000 cP , and a measure of its shear stability through the KRL test. This engineering-related article is a stub . You can help Misplaced Pages by expanding it . Viscometric Viscosity quantifies

250-422: A Standard Model to describe forces between particles smaller than atoms. The Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong , electromagnetic , weak , and gravitational . High-energy particle physics observations made during

375-435: A magnetic field , possibly to the point of behaving like a solid. The viscous forces that arise during fluid flow are distinct from the elastic forces that occur in a solid in response to shear, compression, or extension stresses. While in the latter the stress is proportional to the amount of shear deformation, in a fluid it is proportional to the rate of deformation over time. For this reason, James Clerk Maxwell used

500-464: A constant mass m {\displaystyle m} to then have any predictive content, it must be combined with further information. Moreover, inferring that a force is present because a body is accelerating is only valid in an inertial frame of reference. The question of which aspects of Newton's laws to take as definitions and which to regard as holding physical content has been answered in various ways, which ultimately do not affect how

625-436: A constant viscosity ( non-Newtonian fluids ) cannot be described by a single number. Non-Newtonian fluids exhibit a variety of different correlations between shear stress and shear rate. One of the most common instruments for measuring kinematic viscosity is the glass capillary viscometer. In coating industries, viscosity may be measured with a cup in which the efflux time is measured. There are several sorts of cup—such as

750-580: A different set of mathematical rules than physical quantities that do not have direction (denoted scalar quantities). For example, when determining what happens when two forces act on the same object, it is necessary to know both the magnitude and the direction of both forces to calculate the result . If both of these pieces of information are not known for each force, the situation is ambiguous. Historically, forces were first quantitatively investigated in conditions of static equilibrium where several forces canceled each other out. Such experiments demonstrate

875-502: A fluid, just as thermal conductivity characterizes heat transport, and (mass) diffusivity characterizes mass transport. This perspective is implicit in Newton's law of viscosity, τ = μ ( ∂ u / ∂ y ) {\displaystyle \tau =\mu (\partial u/\partial y)} , because the shear stress τ {\displaystyle \tau } has units equivalent to

1000-482: A force is applied in the direction of motion while the kinetic friction force exactly opposes the applied force. This results in zero net force, but since the object started with a non-zero velocity, it continues to move with a non-zero velocity. Aristotle misinterpreted this motion as being caused by the applied force. When kinetic friction is taken into consideration it is clear that there is no net force causing constant velocity motion. Some forces are consequences of

1125-474: A force that existed intrinsically between two charges . The properties of the electrostatic force were that it varied as an inverse square law directed in the radial direction , was both attractive and repulsive (there was intrinsic polarity ), was independent of the mass of the charged objects, and followed the superposition principle . Coulomb's law unifies all these observations into one succinct statement. Subsequent mathematicians and physicists found

1250-582: A frame of reference if it at rest and not accelerating, whereas a body in dynamic equilibrium is moving at a constant speed in a straight line, i.e., moving but not accelerating. What one observer sees as static equilibrium, another can see as dynamic equilibrium and vice versa. Static equilibrium was understood well before the invention of classical mechanics. Objects that are not accelerating have zero net force acting on them. The simplest case of static equilibrium occurs when two forces are equal in magnitude but opposite in direction. For example, an object on

1375-459: A key principle of Newtonian physics. In the early 17th century, before Newton's Principia , the term "force" ( Latin : vis ) was applied to many physical and non-physical phenomena, e.g., for an acceleration of a point. The product of a point mass and the square of its velocity was named vis viva (live force) by Leibniz . The modern concept of force corresponds to Newton's vis motrix (accelerating force). Sir Isaac Newton described

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1500-479: A level surface is pulled (attracted) downward toward the center of the Earth by the force of gravity. At the same time, a force is applied by the surface that resists the downward force with equal upward force (called a normal force ). The situation produces zero net force and hence no acceleration. Pushing against an object that rests on a frictional surface can result in a situation where the object does not move because

1625-415: A momentum flux , i.e., momentum per unit time per unit area. Thus, τ {\displaystyle \tau } can be interpreted as specifying the flow of momentum in the y {\displaystyle y} direction from one fluid layer to the next. Per Newton's law of viscosity, this momentum flow occurs across a velocity gradient, and the magnitude of the corresponding momentum flux

1750-416: A specific fluid state. To standardize comparisons among experiments and theoretical models, viscosity data is sometimes extrapolated to ideal limiting cases, such as the zero shear limit, or (for gases) the zero density limit. Transport theory provides an alternative interpretation of viscosity in terms of momentum transport: viscosity is the material property which characterizes momentum transport within

1875-432: A straight line will see it continuing to do so. According to the first law, motion at constant speed in a straight line does not need a cause. It is change in motion that requires a cause, and Newton's second law gives the quantitative relationship between force and change of motion. Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time . If

2000-745: A surface up to the limit specified by the coefficient of static friction ( μ s f {\displaystyle \mu _{\mathrm {sf} }} ) multiplied by the normal force ( F N {\displaystyle \mathbf {F} _{\text{N}}} ). In other words, the magnitude of the static friction force satisfies the inequality: 0 ≤ F s f ≤ μ s f F N . {\displaystyle 0\leq \mathbf {F} _{\mathrm {sf} }\leq \mu _{\mathrm {sf} }\mathbf {F} _{\mathrm {N} }.} The kinetic friction force ( F k f {\displaystyle F_{\mathrm {kf} }} )

2125-413: A system with an arbitrary number of particles. In general, as long as all forces are due to the interaction of objects with mass, it is possible to define a system such that net momentum is never lost nor gained. Some textbooks use Newton's second law as a definition of force. However, for the equation F = m a {\displaystyle \mathbf {F} =m\mathbf {a} } for

2250-484: A unidirectional force or a force that acts on only one body. In a system composed of object 1 and object 2, the net force on the system due to their mutual interactions is zero: F 1 , 2 + F 2 , 1 = 0. {\displaystyle \mathbf {F} _{1,2}+\mathbf {F} _{2,1}=0.} More generally, in a closed system of particles, all internal forces are balanced. The particles may accelerate with respect to each other but

2375-649: Is 1 cP divided by 1000 kg/m^3, close to the density of water. The kinematic viscosity of water at 20 °C is about 1 cSt. The most frequently used systems of US customary, or Imperial , units are the British Gravitational (BG) and English Engineering (EE). In the BG system, dynamic viscosity has units of pound -seconds per square foot (lb·s/ft ), and in the EE system it has units of pound-force -seconds per square foot (lbf·s/ft ). The pound and pound-force are equivalent;

2500-457: Is a linear combination of the shear and bulk viscosities that describes the reaction of a solid elastic material to elongation. It is widely used for characterizing polymers. In geology , earth materials that exhibit viscous deformation at least three orders of magnitude greater than their elastic deformation are sometimes called rheids . Viscosity is measured with various types of viscometers and rheometers . Close temperature control of

2625-462: Is a calculation derived from tests performed on drilling fluid used in oil or gas well development. These calculations and tests help engineers develop and maintain the properties of the drilling fluid to the specifications required. Nanoviscosity (viscosity sensed by nanoprobes) can be measured by fluorescence correlation spectroscopy . The SI unit of dynamic viscosity is the newton -second per square meter (N·s/m ), also frequently expressed in

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2750-550: Is a viscosity tensor that maps the velocity gradient tensor ∂ v k / ∂ r ℓ {\displaystyle \partial v_{k}/\partial r_{\ell }} onto the viscous stress tensor τ i j {\displaystyle \tau _{ij}} . Since the indices in this expression can vary from 1 to 3, there are 81 "viscosity coefficients" μ i j k l {\displaystyle \mu _{ijkl}} in total. However, assuming that

2875-421: Is actually conducted, the cannonball always falls at the foot of the mast, as if the cannonball knows to travel with the ship despite being separated from it. Since there is no forward horizontal force being applied on the cannonball as it falls, the only conclusion left is that the cannonball continues to move with the same velocity as the boat as it falls. Thus, no force is required to keep the cannonball moving at

3000-532: Is called the rate of shear deformation or shear velocity , and is the derivative of the fluid speed in the direction parallel to the normal vector of the plates (see illustrations to the right). If the velocity does not vary linearly with y {\displaystyle y} , then the appropriate generalization is: where τ = F / A {\displaystyle \tau =F/A} , and ∂ u / ∂ y {\displaystyle \partial u/\partial y}

3125-453: Is derived from the Latin viscum (" mistletoe "). Viscum also referred to a viscous glue derived from mistletoe berries. In materials science and engineering , there is often interest in understanding the forces or stresses involved in the deformation of a material. For instance, if the material were a simple spring, the answer would be given by Hooke's law , which says that

3250-448: Is determined by the viscosity. The analogy with heat and mass transfer can be made explicit. Just as heat flows from high temperature to low temperature and mass flows from high density to low density, momentum flows from high velocity to low velocity. These behaviors are all described by compact expressions, called constitutive relations , whose one-dimensional forms are given here: where ρ {\displaystyle \rho }

3375-417: Is equal in magnitude and direction to the transversal of the parallelogram. The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action. Free-body diagrams can be used as a convenient way to keep track of forces acting on a system. Ideally, these diagrams are drawn with the angles and relative magnitudes of

3500-534: Is equal to the SI millipascal second (mPa·s). The SI unit of kinematic viscosity is square meter per second (m /s), whereas the CGS unit for kinematic viscosity is the stokes (St, or cm ·s = 0.0001 m ·s ), named after Sir George Gabriel Stokes . In U.S. usage, stoke is sometimes used as the singular form. The submultiple centistokes (cSt) is often used instead, 1 cSt = 1 mm ·s  = 10  m ·s . 1 cSt

3625-576: Is in terms of the standard (scalar) viscosity μ {\displaystyle \mu } and the bulk viscosity κ {\displaystyle \kappa } such that α = κ − 2 3 μ {\displaystyle \alpha =\kappa -{\tfrac {2}{3}}\mu } and β = γ = μ {\displaystyle \beta =\gamma =\mu } . In vector notation this appears as: where δ {\displaystyle \mathbf {\delta } }

3750-658: Is not a fundamental law of nature, but rather a constitutive equation (like Hooke's law , Fick's law , and Ohm's law ) which serves to define the viscosity μ {\displaystyle \mu } . Its form is motivated by experiments which show that for a wide range of fluids, μ {\displaystyle \mu } is independent of strain rate. Such fluids are called Newtonian . Gases , water , and many common liquids can be considered Newtonian in ordinary conditions and contexts. However, there are many non-Newtonian fluids that significantly deviate from this behavior. For example: Trouton 's ratio

3875-481: Is taken from sea level and may vary depending on location), and points toward the center of the Earth. This observation means that the force of gravity on an object at the Earth's surface is directly proportional to the object's mass. Thus an object that has a mass of m {\displaystyle m} will experience a force: F = m g . {\displaystyle \mathbf {F} =m\mathbf {g} .} For an object in free-fall, this force

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4000-397: Is taken to be massless, frictionless, unbreakable, and infinitely stretchable. Such springs exert forces that push when contracted, or pull when extended, in proportion to the displacement of the spring from its equilibrium position. This linear relationship was described by Robert Hooke in 1676, for whom Hooke's law is named. If Δ x {\displaystyle \Delta x}

4125-515: Is the coefficient of kinetic friction . The coefficient of kinetic friction is normally less than the coefficient of static friction. Tension forces can be modeled using ideal strings that are massless, frictionless, unbreakable, and do not stretch. They can be combined with ideal pulleys , which allow ideal strings to switch physical direction. Ideal strings transmit tension forces instantaneously in action–reaction pairs so that if two objects are connected by an ideal string, any force directed along

4250-581: Is the dynamic viscosity of the fluid, often simply referred to as the viscosity . It is denoted by the Greek letter mu ( μ ). The dynamic viscosity has the dimensions ( m a s s / l e n g t h ) / t i m e {\displaystyle \mathrm {(mass/length)/time} } , therefore resulting in the SI units and the derived units : The aforementioned ratio u / y {\displaystyle u/y}

4375-432: Is the mass and v {\displaystyle \mathbf {v} } is the velocity . If Newton's second law is applied to a system of constant mass , m may be moved outside the derivative operator. The equation then becomes F = m d v d t . {\displaystyle \mathbf {F} =m{\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}.} By substituting

4500-418: Is the newton (N) , and force is often represented by the symbol F . Force plays an important role in classical mechanics. The concept of force is central to all three of Newton's laws of motion . Types of forces often encountered in classical mechanics include elastic , frictional , contact or "normal" forces , and gravitational . The rotational version of force is torque , which produces changes in

4625-408: Is the density, J {\displaystyle \mathbf {J} } and q {\displaystyle \mathbf {q} } are the mass and heat fluxes, and D {\displaystyle D} and k t {\displaystyle k_{t}} are the mass diffusivity and thermal conductivity. The fact that mass, momentum, and energy (heat) transport are among

4750-410: Is the displacement, the force exerted by an ideal spring equals: F = − k Δ x , {\displaystyle \mathbf {F} =-k\Delta \mathbf {x} ,} where k {\displaystyle k} is the spring constant (or force constant), which is particular to the spring. The minus sign accounts for the tendency of the force to act in opposition to

4875-410: Is the distance between the two objects' centers of mass and r ^ {\displaystyle {\hat {\mathbf {r} }}} is the unit vector pointed in the direction away from the center of the first object toward the center of the second object. This formula was powerful enough to stand as the basis for all subsequent descriptions of motion within the solar system until

5000-468: Is the electromagnetic force, E {\displaystyle \mathbf {E} } is the electric field at the body's location, B {\displaystyle \mathbf {B} } is the magnetic field, and v {\displaystyle \mathbf {v} } is the velocity of the particle. The magnetic contribution to the Lorentz force is the cross product of the velocity vector with

5125-488: Is the force of body 1 on body 2 and F 2 , 1 {\displaystyle \mathbf {F} _{2,1}} that of body 2 on body 1, then F 1 , 2 = − F 2 , 1 . {\displaystyle \mathbf {F} _{1,2}=-\mathbf {F} _{2,1}.} This law is sometimes referred to as the action-reaction law , with F 1 , 2 {\displaystyle \mathbf {F} _{1,2}} called

SAE J306 - Misplaced Pages Continue

5250-425: Is the local shear velocity. This expression is referred to as Newton's law of viscosity . In shearing flows with planar symmetry, it is what defines μ {\displaystyle \mu } . It is a special case of the general definition of viscosity (see below), which can be expressed in coordinate-free form. Use of the Greek letter mu ( μ {\displaystyle \mu } ) for

5375-581: Is the magnitude of the hypothetical test charge. Similarly, the idea of the magnetic field was introduced to express how magnets can influence one another at a distance. The Lorentz force law gives the force upon a body with charge q {\displaystyle q} due to electric and magnetic fields: F = q ( E + v × B ) , {\displaystyle \mathbf {F} =q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right),} where F {\displaystyle \mathbf {F} }

5500-591: Is the momentum of object 1 and p 2 {\displaystyle \mathbf {p} _{2}} the momentum of object 2, then d p 1 d t + d p 2 d t = F 1 , 2 + F 2 , 1 = 0. {\displaystyle {\frac {\mathrm {d} \mathbf {p} _{1}}{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {p} _{2}}{\mathrm {d} t}}=\mathbf {F} _{1,2}+\mathbf {F} _{2,1}=0.} Using similar arguments, this can be generalized to

5625-438: Is the momentum of the system, and F {\displaystyle \mathbf {F} } is the net ( vector sum ) force. If a body is in equilibrium, there is zero net force by definition (balanced forces may be present nevertheless). In contrast, the second law states that if there is an unbalanced force acting on an object it will result in the object's momentum changing over time. In common engineering applications

5750-606: Is the ratio of extensional viscosity to shear viscosity . For a Newtonian fluid, the Trouton ratio is 3. Shear-thinning liquids are very commonly, but misleadingly, described as thixotropic. Viscosity may also depend on the fluid's physical state (temperature and pressure) and other, external , factors. For gases and other compressible fluids , it depends on temperature and varies very slowly with pressure. The viscosity of some fluids may depend on other factors. A magnetorheological fluid , for example, becomes thicker when subjected to

5875-554: Is the unit tensor. This equation can be thought of as a generalized form of Newton's law of viscosity. The bulk viscosity (also called volume viscosity) expresses a type of internal friction that resists the shearless compression or expansion of a fluid. Knowledge of κ {\displaystyle \kappa } is frequently not necessary in fluid dynamics problems. For example, an incompressible fluid satisfies ∇ ⋅ v = 0 {\displaystyle \nabla \cdot \mathbf {v} =0} and so

6000-449: Is the velocity of the object and r {\displaystyle r} is the distance to the center of the circular path and r ^ {\displaystyle {\hat {\mathbf {r} }}} is the unit vector pointing in the radial direction outwards from the center. This means that the net force felt by the object is always directed toward the center of the curving path. Such forces act perpendicular to

6125-437: Is typically independent of both the forces applied and the movement of the object. Thus, the magnitude of the force equals: F k f = μ k f F N , {\displaystyle \mathbf {F} _{\mathrm {kf} }=\mu _{\mathrm {kf} }\mathbf {F} _{\mathrm {N} },} where μ k f {\displaystyle \mu _{\mathrm {kf} }}

6250-442: Is unopposed and the net force on the object is its weight. For objects not in free-fall, the force of gravity is opposed by the reaction forces applied by their supports. For example, a person standing on the ground experiences zero net force, since a normal force (a reaction force) is exerted by the ground upward on the person that counterbalances his weight that is directed downward. Newton's contribution to gravitational theory

6375-464: The Aristotelian theory of motion . He showed that the bodies were accelerated by gravity to an extent that was independent of their mass and argued that objects retain their velocity unless acted on by a force, for example friction . Galileo's idea that force is needed to change motion rather than to sustain it, further improved upon by Isaac Beeckman , René Descartes , and Pierre Gassendi , became

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6500-577: The Zahn cup and the Ford viscosity cup —with the usage of each type varying mainly according to the industry. Also used in coatings, a Stormer viscometer employs load-based rotation to determine viscosity. The viscosity is reported in Krebs units (KU), which are unique to Stormer viscometers. Vibrating viscometers can also be used to measure viscosity. Resonant, or vibrational viscometers work by creating shear waves within

6625-400: The action and − F 2 , 1 {\displaystyle -\mathbf {F} _{2,1}} the reaction . Newton's Third Law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are interactions between different bodies. and thus that there is no such thing as

6750-476: The center of mass of the system will not accelerate. If an external force acts on the system, it will make the center of mass accelerate in proportion to the magnitude of the external force divided by the mass of the system. Combining Newton's Second and Third Laws, it is possible to show that the linear momentum of a system is conserved in any closed system . In a system of two particles, if p 1 {\displaystyle \mathbf {p} _{1}}

6875-425: The density of the fluid ( ρ ). It is usually denoted by the Greek letter nu ( ν ): and has the dimensions ( l e n g t h ) 2 / t i m e {\displaystyle \mathrm {(length)^{2}/time} } , therefore resulting in the SI units and the derived units : In very general terms, the viscous stresses in a fluid are defined as those resulting from

7000-431: The shear viscosity . However, at least one author discourages the use of this terminology, noting that μ {\displaystyle \mu } can appear in non-shearing flows in addition to shearing flows. In fluid dynamics, it is sometimes more appropriate to work in terms of kinematic viscosity (sometimes also called the momentum diffusivity ), defined as the ratio of the dynamic viscosity ( μ ) over

7125-409: The 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines . The mechanical advantage given by a simple machine allowed for less force to be used in exchange for that force acting over a greater distance for

7250-425: The 20th century. During that time, sophisticated methods of perturbation analysis were invented to calculate the deviations of orbits due to the influence of multiple bodies on a planet , moon , comet , or asteroid . The formalism was exact enough to allow mathematicians to predict the existence of the planet Neptune before it was observed. The electrostatic force was first described in 1784 by Coulomb as

7375-491: The BG and EE systems. Nonstandard units include the reyn (lbf·s/in ), a British unit of dynamic viscosity. In the automotive industry the viscosity index is used to describe the change of viscosity with temperature. The reciprocal of viscosity is fluidity , usually symbolized by ϕ = 1 / μ {\displaystyle \phi =1/\mu } or F = 1 / μ {\displaystyle F=1/\mu } , depending on

7500-463: The Couette flow, a fluid is trapped between two infinitely large plates, one fixed and one in parallel motion at constant speed u {\displaystyle u} (see illustration to the right). If the speed of the top plate is low enough (to avoid turbulence), then in steady state the fluid particles move parallel to it, and their speed varies from 0 {\displaystyle 0} at

7625-486: The acceleration of the Moon around the Earth could be ascribed to the same force of gravity if the acceleration due to gravity decreased as an inverse square law . Further, Newton realized that the acceleration of a body due to gravity is proportional to the mass of the other attracting body. Combining these ideas gives a formula that relates the mass ( m ⊕ {\displaystyle m_{\oplus }} ) and

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7750-399: The applied force is opposed by static friction , generated between the object and the table surface. For a situation with no movement, the static friction force exactly balances the applied force resulting in no acceleration. The static friction increases or decreases in response to the applied force up to an upper limit determined by the characteristics of the contact between the surface and

7875-430: The applied load. For an object in uniform circular motion , the net force acting on the object equals: F = − m v 2 r r ^ , {\displaystyle \mathbf {F} =-{\frac {mv^{2}}{r}}{\hat {\mathbf {r} }},} where m {\displaystyle m} is the mass of the object, v {\displaystyle v}

8000-473: The arithmetic and the reference table provided in ASTM D 2161. Force (physics) A force is an influence that can cause an object to change its velocity unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. The SI unit of force

8125-502: The atoms in an object is able to flow, contract, expand, or otherwise change shape, the theories of continuum mechanics describe the way forces affect the material. For example, in extended fluids , differences in pressure result in forces being directed along the pressure gradients as follows: F V = − ∇ P , {\displaystyle {\frac {\mathbf {F} }{V}}=-\mathbf {\nabla } P,} where V {\displaystyle V}

8250-425: The bottom to u {\displaystyle u} at the top. Each layer of fluid moves faster than the one just below it, and friction between them gives rise to a force resisting their relative motion. In particular, the fluid applies on the top plate a force in the direction opposite to its motion, and an equal but opposite force on the bottom plate. An external force is therefore required in order to keep

8375-428: The constant application of a force needed to keep a cart moving, had conceptual trouble accounting for the behavior of projectiles , such as the flight of arrows. An archer causes the arrow to move at the start of the flight, and it then sails through the air even though no discernible efficient cause acts upon it. Aristotle was aware of this problem and proposed that the air displaced through the projectile's path carries

8500-406: The constant forward velocity. Moreover, any object traveling at a constant velocity must be subject to zero net force (resultant force). This is the definition of dynamic equilibrium: when all the forces on an object balance but it still moves at a constant velocity. A simple case of dynamic equilibrium occurs in constant velocity motion across a surface with kinetic friction . In such a situation,

8625-515: The construct of the electric field to be useful for determining the electrostatic force on an electric charge at any point in space. The electric field was based on using a hypothetical " test charge " anywhere in space and then using Coulomb's Law to determine the electrostatic force. Thus the electric field anywhere in space is defined as E = F q , {\displaystyle \mathbf {E} ={\mathbf {F} \over {q}},} where q {\displaystyle q}

8750-597: The convention used, measured in reciprocal poise (P , or cm · s · g ), sometimes called the rhe . Fluidity is seldom used in engineering practice. At one time the petroleum industry relied on measuring kinematic viscosity by means of the Saybolt viscometer , and expressing kinematic viscosity in units of Saybolt universal seconds (SUS). Other abbreviations such as SSU ( Saybolt seconds universal ) or SUV ( Saybolt universal viscosity ) are sometimes used. Kinematic viscosity in centistokes can be converted from SUS according to

8875-408: The crucial properties that forces are additive vector quantities : they have magnitude and direction. When two forces act on a point particle , the resulting force, the resultant (also called the net force ), can be determined by following the parallelogram rule of vector addition : the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector that

9000-417: The definition of acceleration , the algebraic version of Newton's second law is derived: F = m a . {\displaystyle \mathbf {F} =m\mathbf {a} .} Whenever one body exerts a force on another, the latter simultaneously exerts an equal and opposite force on the first. In vector form, if F 1 , 2 {\displaystyle \mathbf {F} _{1,2}}

9125-461: The dynamic viscosity (sometimes also called the absolute viscosity ) is common among mechanical and chemical engineers , as well as mathematicians and physicists. However, the Greek letter eta ( η {\displaystyle \eta } ) is also used by chemists, physicists, and the IUPAC . The viscosity μ {\displaystyle \mu } is sometimes also called

9250-406: The early 20th century, Einstein developed a theory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light and also provided insight into the forces produced by gravitation and inertia . With modern insights into quantum mechanics and technology that can accelerate particles close to the speed of light, particle physics has devised

9375-428: The elements earth and water, were in their natural place when on the ground, and that they stay that way if left alone. He distinguished between the innate tendency of objects to find their "natural place" (e.g., for heavy bodies to fall), which led to "natural motion", and unnatural or forced motion, which required continued application of a force. This theory, based on the everyday experience of how objects move, such as

9500-403: The equivalence of constant velocity and rest were correct. For example, if a mariner dropped a cannonball from the crow's nest of a ship moving at a constant velocity, Aristotelian physics would have the cannonball fall straight down while the ship moved beneath it. Thus, in an Aristotelian universe, the falling cannonball would land behind the foot of the mast of a moving ship. When this experiment

9625-407: The equivalent forms pascal - second (Pa·s), kilogram per meter per second (kg·m ·s ) and poiseuille (Pl). The CGS unit is the poise (P, or g·cm ·s = 0.1 Pa·s), named after Jean Léonard Marie Poiseuille . It is commonly expressed, particularly in ASTM standards, as centipoise (cP). The centipoise is convenient because the viscosity of water at 20 °C is about 1 cP, and one centipoise

9750-409: The fluid do not depend on the distance the fluid has been sheared; rather, they depend on how quickly the shearing occurs. Viscosity is the material property which relates the viscous stresses in a material to the rate of change of a deformation (the strain rate). Although it applies to general flows, it is easy to visualize and define in a simple shearing flow, such as a planar Couette flow . In

9875-459: The fluid is essential to obtain accurate measurements, particularly in materials like lubricants, whose viscosity can double with a change of only 5 °C. A rheometer is used for fluids that cannot be defined by a single value of viscosity and therefore require more parameters to be set and measured than is the case for a viscometer. For some fluids, the viscosity is constant over a wide range of shear rates ( Newtonian fluids ). The fluids without

10000-424: The force directly between them is called the normal force, the component of the total force in the system exerted normal to the interface between the objects. The normal force is closely related to Newton's third law. The normal force, for example, is responsible for the structural integrity of tables and floors as well as being the force that responds whenever an external force pushes on a solid object. An example of

10125-426: The force experienced by a spring is proportional to the distance displaced from equilibrium. Stresses which can be attributed to the deformation of a material from some rest state are called elastic stresses. In other materials, stresses are present which can be attributed to the deformation rate over time . These are called viscous stresses. For instance, in a fluid such as water the stresses which arise from shearing

10250-417: The force of gravity is proportional to volume for objects of constant density (widely exploited for millennia to define standard weights); Archimedes' principle for buoyancy; Archimedes' analysis of the lever ; Boyle's law for gas pressure; and Hooke's law for springs. These were all formulated and experimentally verified before Isaac Newton expounded his Three Laws of Motion . Dynamic equilibrium

10375-400: The force vectors preserved so that graphical vector addition can be done to determine the net force. As well as being added, forces can also be resolved into independent components at right angles to each other. A horizontal force pointing northeast can therefore be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields

10500-405: The friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is negligible in certain cases. For example,

10625-401: The fundamental ones. In such situations, idealized models can be used to gain physical insight. For example, each solid object is considered a rigid body . What we now call gravity was not identified as a universal force until the work of Isaac Newton. Before Newton, the tendency for objects to fall towards the Earth was not understood to be related to the motions of celestial objects. Galileo

10750-410: The interactions of the fields themselves. This led Maxwell to discover that electric and magnetic fields could be "self-generating" through a wave that traveled at a speed that he calculated to be the speed of light . This insight united the nascent fields of electromagnetic theory with optics and led directly to a complete description of the electromagnetic spectrum . When objects are in contact,

10875-409: The internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's center line than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome

11000-456: The laws governing motion are revised to rely on fundamental interactions as the ultimate origin of force. However, the understanding of force provided by classical mechanics is useful for practical purposes. Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines , but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part, this

11125-529: The liquid. In this method, the sensor is submerged in the fluid and is made to resonate at a specific frequency. As the surface of the sensor shears through the liquid, energy is lost due to its viscosity. This dissipated energy is then measured and converted into a viscosity reading. A higher viscosity causes a greater loss of energy. Extensional viscosity can be measured with various rheometers that apply extensional stress . Volume viscosity can be measured with an acoustic rheometer . Apparent viscosity

11250-404: The load. Such machines allow a mechanical advantage for a corresponding increase in the length of displaced string needed to move the load. These tandem effects result ultimately in the conservation of mechanical energy since the work done on the load is the same no matter how complicated the machine. A simple elastic force acts to return a spring to its natural length. An ideal spring

11375-427: The magnetic field. The origin of electric and magnetic fields would not be fully explained until 1864 when James Clerk Maxwell unified a number of earlier theories into a set of 20 scalar equations, which were later reformulated into 4 vector equations by Oliver Heaviside and Josiah Willard Gibbs . These " Maxwell's equations " fully described the sources of the fields as being stationary and moving charges, and

11500-432: The magnitude or direction of the other. Choosing a set of orthogonal basis vectors is often done by considering what set of basis vectors will make the mathematics most convenient. Choosing a basis vector that is in the same direction as one of the forces is desirable, since that force would then have only one non-zero component. Orthogonal force vectors can be three-dimensional with the third component being at right angles to

11625-440: The mass in a system remains constant allowing as simple algebraic form for the second law. By the definition of momentum, F = d p d t = d ( m v ) d t , {\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}={\frac {\mathrm {d} \left(m\mathbf {v} \right)}{\mathrm {d} t}},} where m

11750-551: The mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object. A modern statement of Newton's second law is a vector equation: F = d p d t , {\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}},} where p {\displaystyle \mathbf {p} }

11875-435: The most relevant processes in continuum mechanics is not a coincidence: these are among the few physical quantities that are conserved at the microscopic level in interparticle collisions. Thus, rather than being dictated by the fast and complex microscopic interaction timescale, their dynamics occurs on macroscopic timescales, as described by the various equations of transport theory and hydrodynamics. Newton's law of viscosity

12000-438: The motion of all objects using the concepts of inertia and force. In 1687, Newton published his magnum opus, Philosophiæ Naturalis Principia Mathematica . In this work Newton set out three laws of motion that have dominated the way forces are described in physics to this day. The precise ways in which Newton's laws are expressed have evolved in step with new mathematical approaches. Newton's first law of motion states that

12125-644: The natural behavior of an object at rest is to continue being at rest, and the natural behavior of an object moving at constant speed in a straight line is to continue moving at that constant speed along that straight line. The latter follows from the former because of the principle that the laws of physics are the same for all inertial observers , i.e., all observers who do not feel themselves to be in motion. An observer moving in tandem with an object will see it as being at rest. So, its natural behavior will be to remain at rest with respect to that observer, which means that an observer who sees it moving at constant speed in

12250-566: The normal force in action is the impact force on an object crashing into an immobile surface. Friction is a force that opposes relative motion of two bodies. At the macroscopic scale, the frictional force is directly related to the normal force at the point of contact. There are two broad classifications of frictional forces: static friction and kinetic friction . The static friction force ( F s f {\displaystyle \mathbf {F} _{\mathrm {sf} }} ) will exactly oppose forces applied to an object parallel to

12375-466: The object by either slowing it down or speeding it up, and the radial (centripetal) force, which changes its direction. Newton's laws and Newtonian mechanics in general were first developed to describe how forces affect idealized point particles rather than three-dimensional objects. In real life, matter has extended structure and forces that act on one part of an object might affect other parts of an object. For situations where lattice holding together

12500-446: The object. A static equilibrium between two forces is the most usual way of measuring forces, using simple devices such as weighing scales and spring balances . For example, an object suspended on a vertical spring scale experiences the force of gravity acting on the object balanced by a force applied by the "spring reaction force", which equals the object's weight. Using such tools, some quantitative force laws were discovered: that

12625-481: The original force. Resolving force vectors into components of a set of basis vectors is often a more mathematically clean way to describe forces than using magnitudes and directions. This is because, for orthogonal components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors. Orthogonal components are independent of each other because forces acting at ninety degrees to each other have no effect on

12750-409: The other two. When all the forces that act upon an object are balanced, then the object is said to be in a state of equilibrium . Hence, equilibrium occurs when the resultant force acting on a point particle is zero (that is, the vector sum of all forces is zero). When dealing with an extended body, it is also necessary that the net torque be zero. A body is in static equilibrium with respect to

12875-503: The projectile to its target. This explanation requires a continuous medium such as air to sustain the motion. Though Aristotelian physics was criticized as early as the 6th century, its shortcomings would not be corrected until the 17th century work of Galileo Galilei , who was influenced by the late medieval idea that objects in forced motion carried an innate force of impetus . Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove

13000-414: The radius ( R ⊕ {\displaystyle R_{\oplus }} ) of the Earth to the gravitational acceleration: g = − G m ⊕ R ⊕ 2 r ^ , {\displaystyle \mathbf {g} =-{\frac {Gm_{\oplus }}{{R_{\oplus }}^{2}}}{\hat {\mathbf {r} }},} where

13125-515: The relative velocity of different fluid particles. As such, the viscous stresses must depend on spatial gradients of the flow velocity. If the velocity gradients are small, then to a first approximation the viscous stresses depend only on the first derivatives of the velocity. (For Newtonian fluids, this is also a linear dependence.) In Cartesian coordinates, the general relationship can then be written as where μ i j k ℓ {\displaystyle \mu _{ijk\ell }}

13250-473: The rotational speed of an object. In an extended body, each part often applies forces on the adjacent parts; the distribution of such forces through the body is the internal mechanical stress . In equilibrium these stresses cause no acceleration of the body as the forces balance one another. If these are not in equilibrium they can cause deformation of solid materials, or flow in fluids . In modern physics , which includes relativity and quantum mechanics ,

13375-621: The same laws of motion , his law of gravity had to be universal. Succinctly stated, Newton's law of gravitation states that the force on a spherical object of mass m 1 {\displaystyle m_{1}} due to the gravitational pull of mass m 2 {\displaystyle m_{2}} is F = − G m 1 m 2 r 2 r ^ , {\displaystyle \mathbf {F} =-{\frac {Gm_{1}m_{2}}{r^{2}}}{\hat {\mathbf {r} }},} where r {\displaystyle r}

13500-547: The same amount of work . Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was especially famous for formulating a treatment of buoyant forces inherent in fluids . Aristotle provided a philosophical discussion of the concept of a force as an integral part of Aristotelian cosmology . In Aristotle's view, the terrestrial sphere contained four elements that come to rest at different "natural places" therein. Aristotle believed that motionless objects on Earth, those composed mostly of

13625-400: The string by the first object is accompanied by a force directed along the string in the opposite direction by the second object. By connecting the same string multiple times to the same object through the use of a configuration that uses movable pulleys, the tension force on a load can be multiplied. For every string that acts on a load, another factor of the tension force in the string acts on

13750-555: The term fugitive elasticity for fluid viscosity. However, many liquids (including water) will briefly react like elastic solids when subjected to sudden stress. Conversely, many "solids" (even granite ) will flow like liquids, albeit very slowly, even under arbitrarily small stress. Such materials are best described as viscoelastic —that is, possessing both elasticity (reaction to deformation) and viscosity (reaction to rate of deformation). Viscoelastic solids may exhibit both shear viscosity and bulk viscosity. The extensional viscosity

13875-715: The term containing κ {\displaystyle \kappa } drops out. Moreover, κ {\displaystyle \kappa } is often assumed to be negligible for gases since it is 0 {\displaystyle 0} in a monatomic ideal gas . One situation in which κ {\displaystyle \kappa } can be important is the calculation of energy loss in sound and shock waves , described by Stokes' law of sound attenuation , since these phenomena involve rapid expansions and compressions. The defining equations for viscosity are not fundamental laws of nature, so their usefulness, as well as methods for measuring or calculating

14000-410: The theory is used in practice. Notable physicists, philosophers and mathematicians who have sought a more explicit definition of the concept of force include Ernst Mach and Walter Noll . Forces act in a particular direction and have sizes dependent upon how strong the push or pull is. Because of these characteristics, forces are classified as " vector quantities ". This means that forces follow

14125-583: The top plate moving at constant speed. In many fluids, the flow velocity is observed to vary linearly from zero at the bottom to u {\displaystyle u} at the top. Moreover, the magnitude of the force, F {\displaystyle F} , acting on the top plate is found to be proportional to the speed u {\displaystyle u} and the area A {\displaystyle A} of each plate, and inversely proportional to their separation y {\displaystyle y} : The proportionality factor

14250-507: The two systems differ only in how force and mass are defined. In the BG system the pound is a basic unit from which the unit of mass (the slug ) is defined by Newton's Second Law , whereas in the EE system the units of force and mass (the pound-force and pound-mass respectively) are defined independently through the Second Law using the proportionality constant g c . Kinematic viscosity has units of square feet per second (ft /s) in both

14375-487: The vector direction is given by r ^ {\displaystyle {\hat {\mathbf {r} }}} , is the unit vector directed outward from the center of the Earth. In this equation, a dimensional constant G {\displaystyle G} is used to describe the relative strength of gravity. This constant has come to be known as the Newtonian constant of gravitation , though its value

14500-412: The velocity vector associated with the motion of an object, and therefore do not change the speed of the object (magnitude of the velocity), but only the direction of the velocity vector. More generally, the net force that accelerates an object can be resolved into a component that is perpendicular to the path, and one that is tangential to the path. This yields both the tangential force, which accelerates

14625-403: The viscosity depends only space- and time-dependent macroscopic fields (such as temperature and density) defining local equilibrium. Nevertheless, viscosity may still carry a non-negligible dependence on several system properties, such as temperature, pressure, and the amplitude and frequency of any external forcing. Therefore, precision measurements of viscosity are only defined with respect to

14750-609: The viscosity of a Newtonian fluid does not vary significantly with the rate of deformation. Zero viscosity (no resistance to shear stress ) is observed only at very low temperatures in superfluids ; otherwise, the second law of thermodynamics requires all fluids to have positive viscosity. A fluid that has zero viscosity (non-viscous) is called ideal or inviscid . For non-Newtonian fluid 's viscosity, there are pseudoplastic , plastic , and dilatant flows that are time-independent, and there are thixotropic and rheopectic flows that are time-dependent. The word "viscosity"

14875-571: The viscosity rank-2 tensor is isotropic reduces these 81 coefficients to three independent parameters α {\displaystyle \alpha } , β {\displaystyle \beta } , γ {\displaystyle \gamma } : and furthermore, it is assumed that no viscous forces may arise when the fluid is undergoing simple rigid-body rotation, thus β = γ {\displaystyle \beta =\gamma } , leaving only two independent parameters. The most usual decomposition

15000-500: The viscosity, must be established using separate means. A potential issue is that viscosity depends, in principle, on the full microscopic state of the fluid, which encompasses the positions and momenta of every particle in the system. Such highly detailed information is typically not available in realistic systems. However, under certain conditions most of this information can be shown to be negligible. In particular, for Newtonian fluids near equilibrium and far from boundaries (bulk state),

15125-521: Was due to an incomplete understanding of the sometimes non-obvious force of friction and a consequently inadequate view of the nature of natural motion. A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton . With his mathematical insight, Newton formulated laws of motion that were not improved for over two hundred years. By

15250-521: Was first described by Galileo who noticed that certain assumptions of Aristotelian physics were contradicted by observations and logic . Galileo realized that simple velocity addition demands that the concept of an "absolute rest frame " did not exist. Galileo concluded that motion in a constant velocity was completely equivalent to rest. This was contrary to Aristotle's notion of a "natural state" of rest that objects with mass naturally approached. Simple experiments showed that Galileo's understanding of

15375-436: Was instrumental in describing the characteristics of falling objects by determining that the acceleration of every object in free-fall was constant and independent of the mass of the object. Today, this acceleration due to gravity towards the surface of the Earth is usually designated as g {\displaystyle \mathbf {g} } and has a magnitude of about 9.81 meters per second squared (this measurement

15500-459: Was to unify the motions of heavenly bodies, which Aristotle had assumed were in a natural state of constant motion, with falling motion observed on the Earth. He proposed a law of gravity that could account for the celestial motions that had been described earlier using Kepler's laws of planetary motion . Newton came to realize that the effects of gravity might be observed in different ways at larger distances. In particular, Newton determined that

15625-450: Was unknown in Newton's lifetime. Not until 1798 was Henry Cavendish able to make the first measurement of G {\displaystyle G} using a torsion balance ; this was widely reported in the press as a measurement of the mass of the Earth since knowing G {\displaystyle G} could allow one to solve for the Earth's mass given the above equation. Newton realized that since all celestial bodies followed

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