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Cunningham Correction Factor
In fluid dynamics, the Cunningham correction factor, or Cunningham slip correction factor (denoted ), is used to account for non- continuum effects when calculating the drag on small particles. The derivation of Stokes' law, which is used to calculate the drag force on small particles, assumes a no-slip condition which is no longer correct at high Knudsen numbers. The Cunningham slip correction factor allows predicting the drag force on a particle moving a fluid with Knudsen number between the continuum regime and free molecular flow. The drag coefficient calculated with standard correlations is divided by the Cunningham correction factor, , given below. Ebenezer CunninghamCunningham, E., "On the velocity of steady fall of spherical particles through fluid medium," ''Proc. Roy. Soc. A'' 83(1910)357. derived the correction factor in 1910 and with Robert Andrews Millikan, verified the correction in the same year. :C = 1+ \frac \left(A_1+A_2 e^ \right) where * is the correctio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion) and (the study of water and other liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moment (physics), moments on aircraft, determining the mass flow rate of petroleum through pipeline transport, pipelines, weather forecasting, predicting weather patterns, understanding nebulae in interstellar space, understanding large scale Geophysical fluid dynamics, geophysical flows involving oceans/atmosphere and Nuclear weapon design, modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Mechanics
Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a ''continuous medium'' (also called a ''continuum'') rather than as discrete particles. Continuum mechanics deals with ''deformable bodies'', as opposed to rigid bodies. A continuum model assumes that the substance of the object completely fills the space it occupies. While ignoring the fact that matter is made of atoms, this provides a sufficiently accurate description of matter on length scales much greater than that of inter-atomic distances. The concept of a continuous medium allows for intuitive analysis of bulk matter by using differential equations that describe the behavior of such matter according to physical laws, such as mass conservation, momentum conservation, and energy conservation. Information about the specific material is expressed in constitutive relationships. Continuum mechanics treats the physical properties of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Drag (physics)
In fluid dynamics, drag, sometimes referred to as fluid resistance, is a force acting opposite to the direction of motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers, two solid surfaces, or between a fluid and a solid surface. Drag forces tend to decrease fluid velocity relative to the solid object in the fluid's path. Unlike other resistive forces, drag force depends on velocity. Drag force is proportional to the relative velocity for low-speed flow and is proportional to the velocity squared for high-speed flow. This distinction between low and high-speed flow is measured by the Reynolds number. Drag is instantaneously related to vorticity dynamics through the Josephson-Anderson relation. Examples Examples of drag include: * Net force, Net Aerodynamic force, aerodynamic or Fluid dynamics, hydrodynamic force: Drag acting opposite to the direction of movement of a solid object such as cars, aircraft, and boat hulls. * Viscou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Parcel
In fluid dynamics, a fluid parcel, also known as a fluid element or material element, is an infinitesimal volume of fluid, identifiable throughout its dynamic history while moving with the fluid flow. As it moves, the mass of a fluid parcel remains constant, while—in a compressible flow—its volume may change, and its shape changes due to distortion by the flow. In an incompressible flow, the volume of the fluid parcel is also a constant ( isochoric flow). Material surfaces and material lines are the corresponding notions for surfaces and lines, respectively. The mathematical concept of a fluid parcel is closely related to the description of fluid motion—its kinematics and dynamics—in a Lagrangian frame of reference. In this reference frame, fluid parcels are labelled and followed through space and time. But also in the Eulerian frame of reference the notion of fluid parcels can be advantageous, for instance in defining the material derivative, streamlines, strea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
No-slip Condition
In fluid dynamics, the no-slip condition is a Boundary conditions in fluid dynamics, boundary condition which enforces that at a solid boundary, a viscous fluid attains zero bulk velocity. This boundary condition was first proposed by Osborne Reynolds, who observed this behaviour while performing his influential pipe flow experiments. The form of this boundary condition is an example of a Dirichlet boundary condition. In the majority of fluid flows relevant to fluids engineering, the no-slip condition is generally utilised at solid boundaries. This condition often fails for systems which exhibit non-newtonian fluid, non-Newtonian behaviour. Fluids which this condition fails includes common food-stuffs which contain a high fat content, such as mayonnaise or melted cheese. Physical justification The no-slip condition is an empirical assumption that has been useful in modelling many macroscopic experiments. It was one of three alternatives that were the subject of contention in the 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knudsen Number
The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. This length scale could be, for example, the radius of a body in a fluid. The number is named after Danish physicist Martin Knudsen (1871–1949). The Knudsen number helps determine whether statistical mechanics or the continuum mechanics formulation of fluid dynamics should be used to model a situation. If the Knudsen number is near or greater than one, the mean free path of a molecule is comparable to a length scale of the problem, and the continuum assumption of fluid mechanics is no longer a good approximation. In such cases, statistical methods should be used. Definition The Knudsen number is a dimensionless number defined as :\mathrm\ = \frac , where : \lambda = mean free path [L1], : L = representative physical length scale [L1]. The representative length scale considered, L, may correspond to various physical trai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Molecular Flow
Free molecular flow describes the fluid dynamics of gas where the mean free path of the molecules is larger than the size of the chamber or of the object under test. For tubes/objects of the size of several cm, this means pressures well below 10−3 mbar. This is also called the regime of high vacuum, or even ultra-high vacuum. This is opposed to viscous flow encountered at higher pressures. The presence of free molecular flow can be calculated, at least in estimation, with the Knudsen number (Kn). If Kn > 10, the system is in free molecular flow, also known as Knudsen flow. Knudsen flow has been defined as the transitional range between viscous flow and molecular flow, which is significant in the medium vacuum range where λ ≈ d. Gas flow can be grouped in four regimes: For Kn≤0.001, flow is continuous, and the Navier–Stokes equations are applicable, from 0.001 [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ebenezer Cunningham
Ebenezer Cunningham (7 May 1881 – 12 February 1977) was a British mathematician who is remembered for his research and exposition at the dawn of special relativity. Biography Cunningham was born in Hackney, London, the son of a cabinet maker. He was educated at Owen's School, Islington, before going up to St John's College, Cambridge, in 1899 and graduating as Senior Wrangler in 1902, winning the Smith's Prize in 1904. In 1904, as a lecturer at the University of Liverpool, he began work on a new theorem in relativity with fellow lecturer Harry Bateman. They brought the methods of inversive geometry into electromagnetic theory with their transformations (spherical wave transformation): :Each four-dimensional solution o Maxwell's equationscould then be inverted in a four-dimensional ''hypersphere of pseudo-radius K'' in order to produce a new solution. Central to Cunningham's paper was the demonstration that Maxwell's equations retained their form under these transformatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Andrews Millikan
Robert Andrews Millikan ( ; March 22, 1868 – December 19, 1953) was an American physicist who received the Nobel Prize in Physics in 1923 "for his work on the elementary charge of electricity and on the photoelectric effect". Millikan graduated from Oberlin College in 1891 and obtained his doctorate at Columbia University in 1895. In 1896, he became an assistant at the University of Chicago, where he became a full professor in 1910. In 1909, Millikan began a series of experiments to determine the electric charge carried by a single electron. He began by measuring the course of charged water droplets in an electric field. The results suggested that the charge on the droplets is a multiple of the elementary electric charge, but the experiment was not accurate enough to be convincing. He obtained more precise results in 1910 with his Oil drop experiment, oil-drop experiment in which he replaced water (which tended to evaporate too quickly) with oil. In 1914 Millikan took up wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Free Path
In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a result of one or more successive collisions with other particles. Scattering theory Imagine a beam of particles being shot through a target, and consider an infinitesimally thin slab of the target (see the figure). The atoms (or particles) that might stop a beam particle are shown in red. The magnitude of the mean free path depends on the characteristics of the system. Assuming that all the target particles are at rest but only the beam particle is moving, that gives an expression for the mean free path: :\ell = (\sigma n)^, where is the mean free path, is the number of target particles per unit volume, and is the effective cross-sectional area for collision. The area of the slab is , and its volume is . The typical number of s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
