|
Stuart Number
The Stuart number (N), also known as magnetic interaction parameter, is a dimensionless number of fluids, i.e. gases or liquids. It is named after mathematician John Trevor Stuart. It is defined as the ratio of electromagnetic to inertial forces, which gives an estimate of the relative importance of a magnetic field on a flow. The Stuart number is relevant for flows of conducting fluids, e.g. in fusion reactors, steel casters or plasmas. Definition : \mathrm = \frac = \frac * ''B'' – magnetic field * ''Lc'' – characteristic length * ''σ'' – electric conductivity * ''U'' – characteristic velocity scale * ''ρ'' – density * Ha – Hartmann number * Re – Reynolds number In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to ... References Further reading * R. More ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
Dimensionless Number
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined Unit of measurement, units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific Unit of volume, units of volume used, such as in milliliters per milliliter (mL/mL). The 1, number one is recognized as a dimensionless Base unit of measurement, base quantity. Radians serve as dimensionless units for Angle, angular measurements, derived from the universal ratio of 2π times the radius of a circle being equal to its circumference. Dimensionless quantities play a crucial role serving as parameters in differential equations in various technical disciplines. In calculus, concepts like the unitless ratios ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
Fluid
In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are Matter, substances which cannot resist any shear force applied to them. Although the term ''fluid'' generally includes both the liquid and gas phases, its definition varies among branches of science. Definitions of ''solid'' vary as well, and depending on field, some substances can have both fluid and solid properties. Non-Newtonian fluids like Silly Putty appear to behave similar to a solid when a sudden force is applied. Substances with a very high viscosity such as Pitch (resin), pitch appear to behave like a solid (see pitch drop experiment) as well. In particle physics, the concept is extended to include fluidic matters other than liquids or gases. A fluid in medicine or biology refers to any liquid constituent of the body (body fluid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
John Trevor Stuart
(John) Trevor Stuart FRS (29 January 1929 – 17 December 2023) was a mathematician and senior research investigator at Imperial College London working in theoretical fluid mechanics, hydrodynamic stability of fluid flows and nonlinear partial differential equations. Education Stuart was educated Gateway Grammar School, Leicester and Imperial College of Science and Technology, London where he was awarded a Bachelor of Science degree in 1949. He continued his study at Imperial College and in 1953 was awarded Ph.D. on the basis of ''Stability of Viscous Motion for Finite Disturbances''. Career Stuart joined the Aeronautics Division of the National Research Laboratory, returning to join the staff of Imperial College after a few years. He was appointed professor of theoretical fluid mechanics in 1966 and was head of the Department of Mathematics from 1974 to 1979 and 1983 to 1986. He was Dean of the Royal College of Science from 1990 to 1993. He was an emeritus professor at Imperi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
 |
Magnetic Field
A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function (mathematics), function assigning a Euclidean vector, vector to each point of space, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
Characteristic Length
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics. In computational mechanics, a characteristic length is defined to force localization of a stress softening constitutive equation. The length is associated with an integration point. For 2D analysis, it is calculated by taking the square root of the area. For 3D analysis, it is calculated by taking the cubic root of the volume associated to the integration point. Examples A characteristic length is usually the volume of a system divided by its surface: L_c = \frac For example, it is used to calculate flow through circular and non-circular tubes in order to examine flow conditions (i.e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
 |
Electric Conductivity
Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter (rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m). For example, if a solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is , then the resistivity of the material is . Electrical conductivity (or specific conductance) is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current. It is commonly signified by the Greek letter (sigma), but (kappa) (especially in electrical engineering) and (gamma) are sometimes used. The SI unit of electrical conductivity is siemens per metre (S/m). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
 |
Density
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be used: \rho = \frac, where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate this quantity is more specifically called specific weight. For a pure substance, the density is equal to its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium is the densest known element at standard conditions for temperature and pressure. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative den ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
 |
Reynolds Number
In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar flow, laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulence, turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (Eddy (fluid dynamics), eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar–turbulent transition, laminar to turbulent flow and is used in the scaling of similar but different-sized fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
Dimensionless Numbers Of Thermodynamics
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific units of volume used, such as in milliliters per milliliter (mL/mL). The number one is recognized as a dimensionless base quantity. Radians serve as dimensionless units for angular measurements, derived from the universal ratio of 2π times the radius of a circle being equal to its circumference. Dimensionless quantities play a crucial role serving as parameters in differential equations in various technical disciplines. In calculus, concepts like the unitless ratios in limits or derivatives often involve dimensionless quantities. In differential geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
 |
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] [Amazon] |