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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク List of dimensionless quantities ： ウィキペディア英語版 List of dimensionless quantities A dimensionless quantity is any number or defined expression which is either unitless or has composite dimensions which cancel out to unity. These are found in numerous fields such as mathematics, physics, engineering, and economics. In contrast, quantities containing dimensions include length, time, mass, luminosity, and electric charge, and products of these fundamental quantities such as volume, speed, and voltage. In mathematics, numbers do not have a dimension; this includes 1, , , , and others. Physics often uses dimensionless quantities to simplify the characterization of systems with multiple interacting physical phenomena. These may be found by applying the Buckingham π theorem or otherwise may emerge from making partial differential equations unitless by the process of nondimensionalization. Furthermore, dimensionless physical constants allow systems of units such as natural units to be constructed based on the known fundamental physical constants. Engineering, economics, and other fields often extend these ideas in design and analysis of the relevant systems. == List of dimensionless quantities == All pure numbers are dimensionless quantities by definition. The list below shows many of the well known dimensionless quantities to illustrate their variety of forms and applications. The table does not include dimensionless units such as percentage (%) and dozen or dimensionless physical constants such as the proton-to-electron mass ratio; these topics are discussed in the article on dimensionless quantities. || optics (dispersion in optical materials) |- | Activity coefficient || $\backslash gamma$ || $\backslash gamma=\; \backslash frac$|| chemistry (Proportion of "active" molecules or atoms) |- | Albedo || $\backslash alpha$ ||$\backslash alpha=\; (1-D)\; \backslash bar\; \backslash alpha(\backslash theta\_i)\; +\; D\; \backslash bar$|| climatology, astronomy (reflectivity of surfaces or bodies) |- | Archimedes number || Ar || $\backslash mathrm\; =\; \backslash frac$|| fluid mechanics (motion of fluids due to density differences) |- | Arrhenius number || $\backslash alpha$ || $\backslash alpha\; =\; \backslash frac$ || chemistry (ratio of activation energy to thermal energy)〔 |- | Atomic weight || ''M'' || || chemistry (mass of atom over one atomic mass unit, u, where carbon-12 is exactly 12 u) |- | Atwood number || A || $\backslash mathrm\; =\; \backslash frac$ || fluid mechanics (onset of instabilities in fluid mixtures due to density differences) |- | Bagnold number || Ba ||$\backslash mathrm\; =\; \backslash frac$|| fluid mechanics, geology (ratio of grain collision stresses to viscous fluid stresses in flow of a granular material such as grain and sand)〔(Bagnold number )〕 |- | Bejan number (fluid mechanics)|| Be || $\backslash mathrm\; =\; \backslash frac$ || fluid mechanics (dimensionless pressure drop along a channel) |- | Bejan number (thermodynamics)|| Be || $\backslash mathrm\; =\; \backslash frac\}+\; \backslash dot\; S\text{'}\_\}$ || thermodynamics (ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction) |- | Bingham number || Bm ||$\backslash mathrm\; =\; \backslash frac$|| fluid mechanics, rheology (ratio of yield stress to viscous stress)〔 |- | Biot number || Bi ||$\backslash mathrm\; =\; \backslash frac$|| heat transfer (surface vs. volume conductivity of solids) |- | Blake number || Bl or B ||$\backslash mathrm\; =\; \backslash frac$ || geology, fluid mechanics, porous media (inertial over viscous forces in fluid flow through porous media) |- | Bodenstein number || Bo or Bd || $\backslash mathrm\; =\; vL/\backslash mathcal\; =\; \backslash mathrm\backslash ,\; \backslash mathrm$ || chemistry (residence-time distribution; similar to the axial mass transfer Peclet number) |- | Bond number || Bo ||$\backslash mathrm\; =\; \backslash frac$|| geology, fluid mechanics, porous media (buoyant versus capillary forces, similar to the Eötvös number) 〔(Bond number )〕 |- | Brinkman number || Br ||$\backslash mathrm\; =\; \backslash frac$|| heat transfer, fluid mechanics (conduction from a wall to a viscous fluid) |- | Brownell–Katz number || NBK || $\backslash mathrm\_\backslash mathrm\; =\; \backslash frac$ || fluid mechanics (combination of capillary number and Bond number) |- | Capillary number || Ca || $\backslash mathrm\; =\; \backslash frac$ || porous media, fluid mechanics (viscous forces versus surface tension) |- | Chandrasekhar number || Q ||$\backslash mathrm\; =\; \backslash frac\; =\; \backslash dfrac\backslash ,\; ,$ || aeronautics, fluid dynamics (resistance to fluid motion) |- | Dukhin number || Du || $\backslash mathrm\; =\; \backslash frac$ || optics (slit diffraction)〔(Fresnel number )〕 |- | Froude number || Fr || $\backslash mathrm\; =\; \backslash frac\; =\; \backslash frac$ || fluid mechanics (gravitational over viscous forces) |- | Golden ratio || $\backslash varphi$ || $\backslash varphi\; =\; \backslash frac\; \backslash approx\; 1.61803$ || mathematics, aesthetics (long side length of self-similar rectangle) |- | Görtler number || G || $\backslash mathrm\; =\; \backslash frac\; \backslash left(\; \backslash frac\; \backslash right)^$ || fluid dynamics (boundary layer flow along a concave wall) |- | Graetz number || Gz || $\backslash mathrm\; =\; \backslash mathrm\backslash ,\; \backslash mathrm$ || heat transfer, fluid mechanics (laminar flow through a conduit; also used in mass transfer) |- | Grashof number || Gr || $\backslash mathrm\_L\; =\; \backslash frac$ || heat transfer, natural convection (ratio of the buoyancy to viscous force) |- | Gravitational coupling constant || $\backslash alpha\_G$ ||$\backslash alpha\_G=\backslash frac$|| gravitation (attraction between two massy elementary particles; analogous to the Fine structure constant) |- | Hatta number || Ha || $\backslash mathrm\; =\; \backslash frac\}^$ || chemical engineering (adsorption enhancement due to chemical reaction) |- | Hagen number || Hg || $\backslash mathrm\; =\; -\backslash frac\backslash frac\backslash frac$ || heat transfer (ratio of the buoyancy to viscous force in forced convection) |- | Hydraulic gradient || ''i'' || $i\; =\; \backslash frac\; =\; \backslash frac\; =\; \backslash frac\; =\; \backslash frac)\; \}$|| chemistry (ratio of sensible to latent energy absorbed during liquid-vapor phase change) |- | Karlovitz number || Ka || $\backslash mathrm\; =\; k\; t\_c$ || turbulent combustion (characteristic flow time times flame stretch rate) |- | Keulegan–Carpenter number || KC || $\backslash mathrm\; =\; \backslash frac$ || fluid dynamics (ratio of drag force to inertia for a bluff object in oscillatory fluid flow) |- | Knudsen number || Kn || $\backslash mathrm\; =\; \backslash frac$ || gas dynamics (ratio of the molecular mean free path length to a representative physical length scale) |- | Kt/V || ''Kt''/''V'' || || medicine (hemodialysis and peritoneal dialysis treatment; dimensionless time) |- | Kutateladze number || Ku || $\backslash mathrm\; =\; \backslash frac\backslash right)^\}$ || fluid mechanics (counter-current two-phase flow) |- | Laplace number || La || $\backslash mathrm\; =\; \backslash frac$ || fluid dynamics (free convection within immiscible fluids; ratio of surface tension to momentum-transport) |- | Lewis number || Le || $\backslash mathrm\; =\; \backslash frac\; =\; \backslash frac\}$ || heat and mass transfer (ratio of thermal to mass diffusivity) |- | Lift coefficient || ''C''L || $C\_\backslash mathrm\; =\; \backslash frac$ || aerodynamics (lift available from an airfoil at a given angle of attack) |- | Lockhart–Martinelli parameter || $\backslash chi$ || $\backslash chi\; =\; \backslash frac\; \backslash sqrt\}$ || two-phase flow (flow of wet gases; liquid fraction)〔(Lockhart–Martinelli parameter )〕 |- | Love numbers || ''h'', ''k'', ''l'' || || geophysics (solidity of earth and other planets) |- | Lundquist number || ''S'' || $S\; =\; \backslash frac$ || plasma physics (ratio of a resistive time to an Alfvén wave crossing time in a plasma) |- | Mach number || M or Ma ||$\backslash mathrm\; =\; \backslash frac\}$ || gas dynamics (compressible flow; dimensionless velocity) |- | Magnetic Reynolds number || Rm || $\backslash mathrm\_\backslash mathrm\; =\; \backslash frac$ || magnetohydrodynamics (ratio of magnetic advection to magnetic diffusion) |- | Manning roughness coefficient || ''n'' || || open channel flow (flow driven by gravity) |- | Marangoni number || Mg || $\backslash mathrm\; =\; -\; \}\backslash frac$ || fluid mechanics (Marangoni flow; thermal surface tension forces over viscous forces) |- | Morton number || Mo || $\backslash mathrm\; =\; \backslash frac$ || fluid dynamics (determination of bubble/drop shape) |- | Nusselt number || Nu ||$\backslash mathrm\; =\backslash frac$ || heat transfer (forced convection; ratio of convective to conductive heat transfer) |- | Ohnesorge number || Oh || $\backslash mathrm\; =\; \backslash frac\}\}\; =\; \backslash frac\; =\; \backslash mathrm\backslash ,\; \backslash mathrm$|| heat transfer (advection–diffusion problems; total momentum transfer to molecular heat transfer) |- | Peel number || ''N''P || $N\_\backslash mathrm\; =\; \backslash frac\}$ || coating (adhesion of microstructures with substrate) |- | Perveance || ''K'' || $=\; \backslash frac\backslash ,\backslash frac\}$ || elasticity (load in transverse and longitudinal direction) |- | Porosity || $\backslash phi$ || $\backslash phi\; =\; \backslash frac\}$ || geology, porous media (void fraction of the medium) |- | Power factor || ''P''/''S'' || || electronics (real power to apparent power) |- | Power number || ''N''''p'' || $N\_p\; =$ || electronics (power consumption by agitators; resistance force versus inertia force) |- | Prandtl number || Pr ||$\backslash mathrm\; =\; \backslash frac\; =\; \backslash frac$|| heat transfer (ratio of viscous diffusion rate over thermal diffusion rate) |- | Prater number || ''β'' || $\backslash beta\; =\; \backslash frac\}$ || reaction engineering (ratio of heat evolution to heat conduction within a catalyst pellet) |- | Pressure coefficient || ''CP'' || $C\_p\; =\; \backslash rho\_\backslash infty\; V\_\backslash infty^2\}$ || aerodynamics, hydrodynamics (pressure experienced at a point on an airfoil; dimensionless pressure variable) |- | Q factor || ''Q'' || $Q\; =\; 2\; \backslash pi\; f\_r\; \backslash frac\}$ || physics, engineering (damping of oscillator or resonator; energy stored versus energy lost) |- | Radian measure || rad ||$\backslash text/\backslash text$ || mathematics (measurement of planar angles, 1 radian = 180/π degrees) |- | Rayleigh number || Ra || $\backslash mathrm\_\; =\; \backslash frac\; (T\_s\; -\; T\_\backslash infin)\; x^3$ || heat transfer (buoyancy versus viscous forces in free convection) |- | Refractive index || ''n'' || $n=\backslash frac$ || electromagnetism, optics (speed of light in a vacuum over speed of light in a material) |- | Relative density || ''RD'' || $RD\; =\; \backslash frac\}$ || hydrometers, material comparisons (ratio of density of a material to a reference material—usually water) |- | Relative permeability || $\backslash mu\_r$ || $\backslash mu\_r\; =\; \backslash frac$ || magnetostatics (ratio of the permeability of a specific medium to free space) |- | Relative permittivity || $\backslash varepsilon\_r$ || $\backslash varepsilon\_\; =\; \backslash frac\}$ || electrostatics (ratio of capacitance of test capacitor with dielectric material versus vacuum) |- | Reynolds number || Re || $\backslash mathrm\; =\; \backslash frac$ || fluid mechanics (ratio of fluid inertial and viscous forces)〔(【引用サイトリンク】format=PDF )〕 |- | Richardson number || Ri || $\backslash mathrm\; =\; \backslash frac\; =\; \backslash frac$ || fluid dynamics (effect of buoyancy on flow stability; ratio of potential over kinetic energy)〔(Richardson number )〕 |- | Rockwell scale || – || || mechanical hardness (indentation hardness of a material) |- | Rolling resistance coefficient || ''Crr'' ||$C\_\; =\; \backslash frac$|| vehicle dynamics (ratio of force needed for motion of a wheel over the normal force) |- | Roshko number || Ro || $\backslash mathrm\; =\; =\backslash mathrm\backslash ,\backslash mathrm$ || fluid dynamics (oscillating flow, vortex shedding) |- | Rossby number || Ro || $\backslash mathrm=\backslash frac$ || geophysics (ratio of inertial to Coriolis force) |- | Rouse number || P or Z || $\backslash mathrm\; =\; \backslash frac$ || sediment transport (ratio of the sediment fall velocity and the upwards velocity of grain) |- | Schmidt number || Sc || $\backslash mathrm\; =\; \backslash frac$ || mass transfer (viscous over molecular diffusion rate)〔(Schmidt number )〕 |- | Shape factor || ''H'' || $H\; =\; \backslash frac$ || boundary layer flow (ratio of displacement thickness to momentum thickness) |- | Sherwood number || Sh || $\backslash mathrm\; =\; \backslash frac$ || mass transfer (forced convection; ratio of convective to diffusive mass transport) |- | Shields parameter || $\backslash tau\_$ * or $\backslash theta$ || $\backslash tau\_\; =\; \backslash frac$ || sediment transport (threshold of sediment movement due to fluid motion; dimensionless shear stress) |- | Sommerfeld number || S || $\backslash mathrm\; =\; \backslash left(\; \backslash frac\; \backslash right)^2\; \backslash frac$ || hydrodynamic lubrication (boundary lubrication)〔(Sommerfeld number )〕 |- | Specific gravity || ''SG'' || || (same as Relative density) |- | Stanton number || St || $\backslash mathrm\; =\; \backslash frac\; =\; \backslash frac\backslash ,\backslash mathrm\}$ || heat transfer and fluid dynamics (forced convection) |- | Stefan number || Ste ||$\backslash mathrm\; =\; \backslash frac$|| phase change, thermodynamics (ratio of sensible heat to latent heat) |- | Stokes number || Stk or Sk ||$\backslash mathrm\; =\; \backslash frac$|| particles suspensions (ratio of characteristic time of particle to time of flow) |- | Strain || $\backslash epsilon$ ||$\backslash epsilon\; =\; \backslash cfrac\}\; -\; 1$|| materials science, elasticity (displacement between particles in the body relative to a reference length) |- | Strouhal number || St or Sr ||$\backslash mathrm\; =$|| fluid dynamics (continuous and pulsating flow; nondimensional frequency)〔(Strouhal number ), Engineering Toolbox〕 |- | Stuart number || N || $\backslash mathrm\; =\; \backslash frac\; =\; \backslash frac\; =\; \backslash frac$|| fluid dynamics (rotating fluid flows; inertial forces due to rotation of a fluid versus viscous forces) |- | Transmittance || ''T'' ||$T\; =\; \backslash frac$|| optics, spectroscopy (the ratio of the intensities of radiation exiting through and incident on a sample) |- | Ursell number || U ||$\backslash mathrm\; =\; \backslash frac$|| wave mechanics (nonlinearity of surface gravity waves on a shallow fluid layer) |- | Vadasz number || Va ||$\backslash mathrm\; =\; \backslash frac\}$|| porous media (governs the effects of porosity $\backslash phi$, the Prandtl number and the Darcy number on flow in a porous medium) |- | van 't Hoff factor || ''i'' ||$i\; =\; 1\; +\; \backslash alpha\; (n\; -\; 1)$|| quantitative analysis (''K''f and ''K''b) |- | Wallis parameter || ''j'' * ||$j^$ * = R \left( \frac \right)^\frac|| multiphase flows (nondimensional superficial velocity) |- | Weaver flame speed number || Wea ||$\backslash mathrm\; =\; \backslash frac\; =\; \backslash frac$|| multiphase flow (strongly curved surfaces; ratio of inertia to surface tension) |- | Weissenberg number || Wi ||$\backslash mathrm\; =\; \backslash dot\; \backslash lambda$|| viscoelastic flows (shear rate times the relaxation time)〔(Weissenberg number )〕 |- | Womersley number || $\backslash alpha$ ||$\backslash alpha\; =\; R\; \backslash left(\; \backslash frac\; \backslash right)^\backslash frac$|| biofluid mechanics (continuous and pulsating flows; ratio of pulsatile flow frequency to viscous effects)〔(Womersley number )〕 |} 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「List of dimensionless quantities」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. 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