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Stokes Law
In fluid dynamics, Stokes' law gives the frictional force – also called drag force – exerted on spherical objects moving at very small Reynolds numbers in a viscous fluid. It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations.Batchelor (1967), p. 233. Statement of the law The force of viscosity on a small sphere moving through a viscous fluid is given by: :_ = - 6 \pi \mu R where (in SI units): * _ is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle (newtons, kg m s−2); * (some authors use the symbol ) is the dynamic viscosity ( Pascal-seconds, kg m−1 s−1); * is the radius of the spherical object (meters); * is the flow velocity relative to the object (meters per second). Note the minus sign in the equation, the drag force points in the opposite direction to the relative velocity: drag opposes the motion. Stokes' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stokes' Theorem
Stokes' theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem, is a theorem in vector calculus on \R^3. Given a vector field, the theorem relates the integral of the curl of the vector field over some surface, to the line integral of the vector field around the boundary of the surface. The classical theorem of Stokes can be stated in one sentence: : The line integral of a vector field over a loop is equal to the surface integral of its '' curl'' over the enclosed surface. Stokes' theorem is a special case of the generalized Stokes theorem. In particular, a vector field on \R^3 can be considered as a 1-form in which case its curl is its exterior derivative, a 2-form. Theorem Let \Sigma be a smooth oriented surface in \R^3 with boundary \partial \Sigma \equiv \Gamma . If a vector field \mathbf(x,y,z) = (F_x(x, y, z), F_y(x, y, z), F_z(x, y, z)) is defined and has continuous first ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laminar Flow
Laminar flow () is the property of fluid particles in fluid dynamics to follow smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another smoothly. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface. Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection. When a fluid is flowing through a closed channel such as a pipe or between two flat plates, either of two types of flow may occur depending on the velocity and viscosity of the fluid: laminar flow or turbulent flow. Laminar flow occurs at lower velocities, below a threshold at which the flow becomes turbulent. The thresh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buoyancy
Buoyancy (), or upthrust, is the force exerted by a fluid opposing the weight of a partially or fully immersed object (which may be also be a parcel of fluid). In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus, the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and (as explained by Archimedes' principle) is equivalent to the weight of the fluid that would otherwise occupy the submerged volume of the object, i.e. the Displacement (fluid), displaced fluid. For this reason, an object with average density greater than the surrounding fluid tends to sink because its weight is greater than the weight of the fluid it displaces. If the objec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weight
In science and engineering, the weight of an object is a quantity associated with the gravitational force exerted on the object by other objects in its environment, although there is some variation and debate as to the exact definition. Some standard textbooks define weight as a Euclidean vector, vector quantity, the gravitational force acting on the object. Others define weight as a scalar quantity, the magnitude of the gravitational force. Yet others define it as the magnitude of the reaction (physics), reaction force exerted on a body by mechanisms that counteract the effects of gravity: the weight is the quantity that is measured by, for example, a spring scale. Thus, in a state of free fall, the weight would be zero. In this sense of weight, terrestrial objects can be weightless: so if one ignores Drag (physics), air resistance, one could say the legendary apple falling from the tree, on its way to meet the ground near Isaac Newton, was weightless. The unit of measurement fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terminal Velocity
Terminal velocity is the maximum speed attainable by an object as it falls through a fluid (air is the most common example). It is reached when the sum of the drag force (''Fd'') and the buoyancy is equal to the downward force of gravity (''FG'') acting on the object. Since the net force on the object is zero, the object has zero acceleration. For objects falling through air at normal pressure, the buoyant force is usually dismissed and not taken into account, as its effects are negligible. As the speed of an object increases, so does the drag force acting on it, which also depends on the substance it is passing through (for example air or water). At some speed, the drag or force of resistance will be equal to the gravitational pull on the object. At this point the object stops accelerating and continues falling at a constant speed called the terminal velocity (also called settling velocity). An object moving downward faster than the terminal velocity (for example because it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stokes Sphere
The Stokes parameters are a set of values that describe the Polarization (waves), polarization state of electromagnetic radiation. They were defined by George Gabriel Stokes in 1851, as a mathematically convenient alternative to the more common description of coherence (physics), incoherent or partially polarized radiation in terms of its total Intensity (physics), intensity (''I''), (fractional) degree of polarization (''p''), and the shape parameters of the polarization ellipse. The effect of an optical system on the polarization of light can be determined by constructing the Stokes vector for the input light and applying Mueller calculus, to obtain the Stokes vector of the light leaving the system. They can be determined from directly observable phenomena. The original Stokes paper was discovered independently by Francis Perrin (physicist), Francis Perrin in 1942 and by Subrahamanyan Chandrasekhar in 1947, who named it as the Stokes parameters. Definitions The relationship of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sedimentation
Sedimentation is the deposition of sediments. It takes place when particles in suspension settle out of the fluid in which they are entrained and come to rest against a barrier. This is due to their motion through the fluid in response to the forces acting on them: these forces can be due to gravity, centrifugal acceleration, or electromagnetism. Settling is the falling of suspended particles through the liquid, whereas sedimentation is the final result of the settling process. In geology, sedimentation is the deposition of sediments which results in the formation of sedimentary rock. The term is broadly applied to the entire range of processes that result in the formation of sedimentary rock, from initial erosion through sediment transport and settling to the lithification of the sediments. However, the strict geological definition of sedimentation is the mechanical deposition of sediment particles from an initial suspension in air or water. Sedimentation may pertain to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sperm
Sperm (: sperm or sperms) is the male reproductive Cell (biology), cell, or gamete, in anisogamous forms of sexual reproduction (forms in which there is a larger, female reproductive cell and a smaller, male one). Animals produce motile sperm with a tail known as a flagellum, which are known as spermatozoa, while some red algae and fungi produce non-motile sperm cells, known as spermatia. Flowering plants contain non-motile sperm inside pollen, while some more basal plants like ferns and some gymnosperms have motile sperm. Sperm cells form during the process known as spermatogenesis, which in amniotes (reptiles and mammals) takes place in the seminiferous tubules of the testicles. This process involves the production of several successive sperm cell precursors, starting with spermatogonia, which Cellular differentiation, differentiate into spermatocytes. The spermatocytes then undergo meiosis, reducing their Ploidy, chromosome number by half, which produces spermatids. The sper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microorganism
A microorganism, or microbe, is an organism of microscopic scale, microscopic size, which may exist in its unicellular organism, single-celled form or as a Colony (biology)#Microbial colonies, colony of cells. The possible existence of unseen microbial life was suspected from antiquity, with an early attestation in Jain literature authored in 6th-century BC India. The scientific study of microorganisms began with their observation under the microscope in the 1670s by Anton van Leeuwenhoek. In the 1850s, Louis Pasteur found that microorganisms caused food spoilage, debunking the theory of spontaneous generation. In the 1880s, Robert Koch discovered that microorganisms caused the diseases tuberculosis, cholera, diphtheria, and anthrax. Microorganisms are extremely diverse, representing most unicellular organisms in all three domains of life: two of the three domains, Archaea and Bacteria, only contain microorganisms. The third domain, Eukaryota, includes all multicellular o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymer
A polymer () is a chemical substance, substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeat unit, repeating subunits derived from one or more species of monomers. Due to their broad spectrum of properties, both synthetic and natural polymers play essential and ubiquitous roles in everyday life. Polymers range from familiar synthetic plastics such as polystyrene to natural biopolymers such as DNA and proteins that are fundamental to biological structure and function. Polymers, both natural and synthetic, are created via polymerization of many small molecules, known as monomers. Their consequently large molecular mass, relative to small molecule compound (chemistry), compounds, produces unique physical property, physical properties including toughness, high rubber elasticity, elasticity, viscoelasticity, and a tendency to form Amorphous solid, amorphous and crystallization of polymers, semicrystalline structures rath ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Syrup
Golden syrup or light treacle is a thick, amber-coloured form of inverted sugar syrup made by the process of refining sugar cane or sugar beet juice into sugar. It is used in a variety of baking recipes and desserts. It has an appearance and consistency similar to honey, and is often used as a substitute where honey is unavailable. It is not to be confused with amber corn syrup or amber refined sugar. Regular molasses, or dark treacle (as well as cane syrup found in the southern US, such as Steen's cane syrup), has a richer colour and a strong, distinctive flavour. In Australia, golden syrup was also known as "cocky's joy" or "cocky's delight" through the first half of the 20th century, as it could be easily transported and thus was a favourite of cockys, a name for a small farmer. Golden syrup was first formulated by the chemists Charles Eastick and his brother John Joseph Eastick at the Abram Lyle & Sons (now part of Tate & Lyle) refinery in Plaistow, Newham, London; th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glycerine
Glycerol () is a simple triol compound. It is a colorless, odorless, sweet-tasting, viscous liquid. The glycerol backbone is found in lipids known as glycerides. It is also widely used as a sweetener in the food industry and as a humectant in pharmaceutical formulations. Because of its three hydroxyl groups, glycerol is miscible with water and is hygroscopic in nature. Modern use of the word glycerine (alternatively spelled glycerin) refers to commercial preparations of less than 100% purity, typically 95% glycerol. Structure Although achiral, glycerol is prochiral with respect to reactions of one of the two primary alcohols. Thus, in substituted derivatives, the stereospecific numbering labels the molecule with a ''sn''- prefix before the stem name of the molecule. Production Natural sources Glycerol is generally obtained from plant and animal sources where it occurs in triglycerides, esters of glycerol with long-chain carboxylic acids. The hydrolysis, saponificatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
