All numbers are dimensionless quantities. Certain dimensionless quantities of some accent are accustomed below:
Name Standard symbol Definition Field of application
Abbe number V V = \frac{ n_d - 1 }{ n_F - n_C } optics (dispersion in optical materials)
Activity coefficient \gamma \gamma= \frac {{a}}{{x}} chemistry (Proportion of "active" molecules or atoms)
Albedo \alpha \alpha= (1-D) \bar \alpha(\theta_i) + D \bar{ \bar \alpha} climatology, astrochemistry (reflectivity of surfaces or bodies)
Archimedes number Ar \mathrm{Ar} = \frac{g L^3 \rho_\ell (\rho - \rho_\ell)}{\mu^2} fluid mechanics (motion of fluids due to physique differences)
Arrhenius number \alpha \alpha = \frac{E_a}{RT} chemistry (ratio of activation activity to thermal energy)[5]
Atomic weight M chemistry (mass of atom over one diminutive accumulation unit, u, breadth carbon-12 is absolutely 12 u)
Atwood number A \mathrm{A} = \frac{\rho_1 - \rho_2} {\rho_1 + \rho_2} fluid mechanics (onset of instabilities in aqueous mixtures due to physique differences)
Bagnold number Ba \mathrm{Ba} = \frac{\rho d^2 \lambda^{1/2} \gamma}{\mu} fluid mechanics, cartography (ratio of atom blow stresses to adhesive aqueous stresses in breeze of a diminutive actual such as atom and sand)[6]
Bejan number
(fluid mechanics) Be \mathrm{Be} = \frac{\Delta P L^2} {\mu \alpha} fluid mechanics (dimensionless burden bead forth a channel)[7]
Bejan number
(thermodynamics) Be \mathrm{Be} = \frac{\dot S'_{\mathrm{gen},\, \Delta T}}{\dot S'_{\mathrm{gen},\, \Delta T}+ \dot S'_{\mathrm{gen},\, \Delta p}} thermodynamics (ratio of calefaction alteration irreversibility to absolute irreversibility due to calefaction alteration and aqueous friction)[8]
Bingham number Bm \mathrm{Bm} = \frac{ \tau_y L }{ \mu V } fluid mechanics, rheology (ratio of crop accent to adhesive stress)[5]
Biot number Bi \mathrm{Bi} = \frac{h L_C}{k_b} heat alteration (surface vs. aggregate application of solids)
Blake number Bl or B \mathrm{B} = \frac{u \rho}{\mu (1 - \epsilon) D} geology, aqueous mechanics, absorptive media (inertial over adhesive armament in aqueous breeze through absorptive media)
Bodenstein number Bo or Bd \mathrm{Bo} = vL/\mathcal{D} = \mathrm{Re}\, \mathrm{Sc} chemistry (residence-time distribution; agnate to the axial accumulation alteration Peclet number)[9]
Bond number Bo \mathrm{Bo} = \frac{\rho a L^2}{\gamma} geology, aqueous mechanics, absorptive media (buoyant against capilary forces, agnate to the Eötvös number) [10]
Brinkman number Br \mathrm{Br} = \frac {\mu U^2}{\kappa (T_w - T_0)} heat transfer, aqueous mechanics (conduction from a bank to a adhesive fluid)
Brownell–Katz number NBK \mathrm{N}_\mathrm{BK} = \frac{u \mu}{k_\mathrm{rw}\sigma} fluid mechanics (combination of capillary amount and Bond number) [11]
Capillary number Ca \mathrm{Ca} = \frac{\mu V}{\gamma} porous media, aqueous mechanics (viscous armament against credible tension)
Chandrasekhar number Q \mathrm{Q} = \frac{{B_0}^2 d^2}{\mu_0 \rho \nu \lambda} magnetohydrodynamics (ratio of the Lorentz force to the bendability in alluring convection)
Colburn J factors JM, JH, JD turbulence; heat, mass, and drive alteration (dimensionless alteration coefficients)
Coefficient of active friction \mu_k mechanics (friction of solid bodies in translational motion)
Coefficient of changeless friction \mu_s mechanics (friction of solid bodies at rest)
Coefficient of determination R^2 statistics (proportion of about-face explained by a statistical model)
Coefficient of variation \frac{\sigma}{\mu} \frac{\sigma}{\mu} statistics (ratio of accepted aberration to expectation)
Correlation ПЃ or r \frac{{\mathbb E}[(X-\mu_X)(Y-\mu_Y)]}{\sigma_X \sigma_Y} or \frac{\sum_{k=1}^n (x_k-\bar x)(y_k-\bar y)}{\sqrt{\sum_{k=1}^n (x_k-\bar x)^2 \sum_{k=1}^n (y_k-\bar y)^2}} breadth \bar x = \sum_{k=1}^n x_k/n and analogously for \bar y statistics (measure of beeline dependence)
Courant–Friedrich–Levy number C or 𝜈 C = \frac {u\,\Delta t} {\Delta x} mathematics (numerical solutions of abstract PDEs)[12]
Damkohler number Da \mathrm{Da} = k \tau chemistry (reaction time scales vs. abode time)
Damping ratio \zeta \zeta = \frac{c}{2 \sqrt{km}} mechanics (the akin of damping in a system)
Darcy abrasion factor Cf or fD fluid mechanics (fraction of burden losses due to abrasion in a pipe; four times the Fanning abrasion factor)
Darcy number Da \mathrm{Da} = \frac{K}{d^2} porous media (ratio of permeability to cross-sectional area)
Dean number D \mathrm{D} = \frac{\rho V d}{\mu} \left( \frac{d}{2 R} \right)^{1/2} turbulent breeze (vortices in arced ducts)
Deborah number De \mathrm{De} = \frac{t_\mathrm{c}}{t_\mathrm{p}} rheology (viscoelastic fluids)
Decibel dB acoustics, electronics, ascendancy approach (ratio of two intensities or admiral of a wave)
Drag coefficient cd c_\mathrm{d} = \dfrac{2 F_\mathrm{d}}{\rho v^2 A}\, , aeronautics, aqueous dynamics (resistance to aqueous motion)
Dukhin number Du \mathrm{Du} = \frac{\kappa^{\sigma}}{{\Kappa_m} a} colloid science (ratio of electric credible application to the electric aggregate application in amalgamate systems)
Eckert number Ec \mathrm{Ec} = \frac{V^2}{c_p\Delta T} convective calefaction alteration (characterizes amusement of energy; arrangement of active activity to enthalpy)
Ekman number Ek \mathrm{Ek} = \frac{\nu}{2D^2\Omega\sin\varphi} geophysics (viscous against Coriolis forces)
Elasticity
(economics) E E_{x,y} = \frac{\partial ln(x)}{\partial ln(y)} = \frac{\partial x}{\partial y}\frac{y}{x} economics (response of appeal or accumulation to amount changes)
Eötvös number Eo \mathrm{Eo}=\frac{\Delta\rho \,g \,L^2}{\sigma} fluid mechanics (shape of bubbles or drops)
Ericksen number Er \mathrm{Er}=\frac{\mu v L}{K} fluid dynamics (liquid clear breeze behavior; adhesive over adaptable forces)
Euler number Eu \mathrm{Eu}=\frac{\Delta{}p}{\rho V^2} hydrodynamics (stream burden against apathy forces)
Euler's number e e = \displaystyle\sum\limits_{n = 0}^{ \infty} \dfrac{1}{n!} = \approx 2.71828 mathematics (base of the accustomed logarithm)
Excess temperature coefficient \Theta_r \Theta_r = \frac{c_p (T-T_e)}{U_e^2/2} heat transfer, aqueous dynamics (change in centralized activity against active energy)[13]
Fanning abrasion factor f fluid mechanics (fraction of burden losses due to abrasion in a pipe; 1/4th the Darcy abrasion factor)[14]
Feigenbaum constants \alpha, \delta \alpha \approx 2.50290,
\ \delta \approx 4.66920 chaos approach (period doubling)[15]
Fine anatomy constant \alpha \alpha = \frac{e^2}{2\varepsilon_0 hc} quantum electrodynamics (QED) (coupling connected anecdotic the backbone of the electromagnetic interaction)
f-number f f = \frac {{\ell}}{{D}} optics, photography (ratio of focal breadth to bore of aperture)
Föppl–von Kármán number \gamma \gamma = \frac{Y r^2}{\kappa} virology, solid mechanics (thin-shell buckling)
Fourier number Fo \mathrm{Fo} = \frac{\alpha t}{L^2} heat transfer, accumulation alteration (ratio of deviating amount against accumulator rate)
Fresnel number F \mathit{F} = \frac{a^{2}}{L \lambda} optics (slit diffraction)[16]
Froude number Fr \mathrm{Fr} = \frac{v}{\sqrt{g\ell}} fluid mechanics (wave and credible behaviour; arrangement of a body's apathy to gravitational forces)
Gain – electronics (signal achievement to arresting input)
Gain ratio – bicycling (system of apery gearing; breadth catholic over breadth pedaled)[17]
Galilei number Ga \mathrm{Ga} = \frac{g\, L^3}{\nu^2} fluid mechanics (gravitational over adhesive forces)
Golden ratio \varphi \varphi = \frac{1+\sqrt{5}}{2} \approx 1.61803 mathematics, aesthetics (long ancillary breadth of self-similar rectangle)
Görtler number G \mathrm{G} = \frac{U_e \theta}{\nu} \left( \frac{\theta}{R} \right)^{1/2} fluid dynamics (boundary band breeze forth a biconcave wall)
Graetz number Gz \mathrm{Gz} = {D_H \over L} \mathrm{Re}\, \mathrm{Pr} heat transfer, aqueous mechanics (laminar breeze through a conduit; aswell acclimated in accumulation transfer)
Grashof number Gr \mathrm{Gr}_L = \frac{g \beta (T_s - T_\infty ) L^3}{\nu ^2} heat transfer, accustomed alteration (ratio of the airiness to adhesive force)
Gravitational coupling constant \alpha_G \alpha_G=\frac{Gm_e^2}{\hbar c} gravitation (attraction amid two massy elementary particles; akin to the Fine anatomy constant)
Hatta number Ha \mathrm{Ha} = \frac{N_{\mathrm{A}0}}{N_{\mathrm{A}0}^{\mathrm{phys}}} chemical engineering (adsorption accessory due to actinic reaction)
Hagen number Hg \mathrm{Hg} = -\frac{1}{\rho}\frac{\mathrm{d} p}{\mathrm{d} x}\frac{L^3}{\nu^2} heat alteration (ratio of the airiness to adhesive force in affected convection)
Hydraulic gradient i i = \frac{\mathrm{d}h}{\mathrm{d}l} = \frac{h_2 - h_1}{\mathrm{length}} fluid mechanics, groundwater breeze (pressure arch over distance)
Iribarren number Ir \mathrm{Ir} = \frac{\tan \alpha}{\sqrt{H/L_0}} wave mechanics (breaking credible force after-effects on a slope)
Jakob number Ja \mathrm{Ja} = \frac{c_p (T_\mathrm{s} - T_\mathrm{sat}) }{\Delta H_{\mathrm{f}} } chemistry (ratio of alive to abeyant activity captivated during liquid-vapor appearance change)[18]
Karlovitz number Ka \mathrm{Ka} = k t_c turbulent agitation (characteristic breeze time times blaze amplitude rate)
Keulegan–Carpenter number KC \mathrm{K_C} = \frac{V\,T}{L} fluid dynamics (ratio of annoyance force to apathy for a barefaced article in oscillatory aqueous flow)
Knudsen number Kn \mathrm{Kn} = \frac {\lambda}{L} gas dynamics (ratio of the atomic beggarly chargeless aisle breadth to a adumbrative concrete breadth scale)
Kt/V Kt/V medicine (hemodialysis and peritoneal dialysis treatment; dimensionless time)
Kutateladze number Ku \mathrm{Ku} = \frac{U_h \rho_g^{1/2}}{\left({\sigma g (\rho_l - \rho_g)}\right)^{1/4}} fluid mechanics (counter-current two-phase flow)[19]
Laplace number La \mathrm{La} = \frac{\sigma \rho L}{\mu^2} fluid dynamics (free alteration aural immiscible fluids; arrangement of credible astriction to momentum-transport)
Lewis number Le \mathrm{Le} = \frac{\alpha}{D} = \frac{\mathrm{Sc}}{\mathrm{Pr}} heat and accumulation alteration (ratio of thermal to accumulation diffusivity)
Lift coefficient CL C_\mathrm{L} = \frac{L}{q\,S} aerodynamics (lift accessible from an airfoil at a accustomed bend of attack)
Lockhart–Martinelli parameter \chi \chi = \frac{m_\ell}{m_g} \sqrt{\frac{\rho_g}{\rho_\ell}} two-phase breeze (flow of wet gases; aqueous fraction)[20]
Love numbers h, k, l geophysics (solidity of apple and added planets)
Lundquist number S S = \frac{\mu_0LV_A}{\eta} plasma physics (ratio of a arresting time to an AlfvГ©n beachcomber bridge time in a plasma)
Mach number M or Ma \mathrm{M} = \frac{{v}}{{v_\mathrm{sound}}} gas dynamics (compressible flow; dimensionless velocity)
Magnetic Reynolds number Rm \mathrm{R}_\mathrm{m} = \frac{U L}{\eta} magnetohydrodynamics (ratio of alluring advection to alluring diffusion)
Manning acerbity coefficient n open approach breeze (flow apprenticed by gravity)[21]
Marangoni number Mg \mathrm{Mg} = - {\frac{\mathrm{d}\sigma}{\mathrm{d}T}}\frac{L \Delta T}{\eta \alpha} fluid mechanics (Marangoni flow; thermal credible astriction armament over adhesive forces)
Morton number Mo \mathrm{Mo} = \frac{g \mu_c^4 \, \Delta \rho}{\rho_c^2 \sigma^3} fluid dynamics (determination of bubble/drop shape)
Nusselt number Nu \mathrm{Nu} =\frac{hd}{k} heat alteration (forced convection; arrangement of convective to conductive calefaction transfer)
Ohnesorge number Oh \mathrm{Oh} = \frac{ \mu}{ \sqrt{\rho \sigma L }} = \frac{\sqrt{\mathrm{We}}}{\mathrm{Re}} fluid dynamics (atomization of liquids, Marangoni flow)
Péclet number Pe \mathrm{Pe} = \frac{du\rho c_p}{k} = \mathrm{Re}\, \mathrm{Pr} heat alteration (advection–diffusion problems; absolute drive alteration to atomic calefaction transfer)
Peel number NP N_\mathrm{P} = \frac{\text{Restoring force}}{\text{Adhesive force}} coating (adhesion of microstructures with substrate)[22]
Perveance K {K} = \frac{{I}}{{I_0}}\,\frac{{2}}{{\beta}^3{\gamma}^3} (1-\gamma^2f_e) charged atom carriage (measure of the backbone of amplitude allegation in a answerable atom beam)
pH \mathrm{pH} \mathrm{pH} = - \log_{10}(a_{\textrm{H}^+}) = \log_{10}\left(\frac{1}{a_{\textrm{H}^+}}\right) the admeasurement of the acidity or basicity of an aqueous solution
Pi \pi \pi = \frac{C}{d} \approx 3.14159 mathematics (ratio of a circle's ambit to its diameter)
Pixel px digital imaging (smallest addressable unit)
Poisson's ratio \nu \nu = -\frac{\mathrm{d}\varepsilon_\mathrm{trans}}{\mathrm{d}\varepsilon_\mathrm{axial}} elasticity (load in axle and longitudinal direction)
Porosity \phi \phi = \frac{V_\mathrm{V}}{V_\mathrm{T}} geology, absorptive media (void atom of the medium)
Power factor P/S electronics (real ability to credible power)
Power number Np N_p = {P\over \rho n^3 d^5} electronics (power afire by agitators; attrition force against apathy force)
Prandtl number Pr \mathrm{Pr} = \frac{\nu}{\alpha} = \frac{c_p \mu}{k} heat alteration (ratio of adhesive circulation amount over thermal circulation rate)
Prater number ОІ \beta = \frac{-\Delta H_r D_{TA}^e C_{AS}}{\lambda^e T_s} reaction engineering (ratio of calefaction change to calefaction advice aural a agitator pellet)[23]
Pressure coefficient CP C_p = {p - p_\infty \over \frac{1}{2} \rho_\infty V_\infty^2} aerodynamics, hydrodynamics (pressure accomplished at a point on an airfoil; dimensionless burden variable)
Q factor Q physics, engineering (damping of oscillator or resonator; activity stored against activity lost)
Radian measure rad \text{arc length}/\text{radius} mathematics (measurement of collapsed angles, 1 radian = 180/ПЂ degrees)
Rayleigh number Ra \mathrm{Ra}_{x} = \frac{g \beta} {\nu \alpha} (T_s - T_\infin) x^3 heat alteration (buoyancy against adhesive armament in chargeless convection)
Refractive index n n=\frac{c}{v} electromagnetism, eyes (speed of ablaze in a exhaustion over acceleration of ablaze in a material)
Relative density RD RD = \frac{\rho_\mathrm{substance}}{\rho_\mathrm{reference}} hydrometers, actual comparisons (ratio of physique of a actual to a advertence material—usually water)
Relative permeability \mu_r \mu_r = \frac{\mu}{\mu_0} magnetostatics (ratio of the permeability of a specific average to chargeless space)
Relative permittivity \varepsilon_r \varepsilon_{r} = \frac{C_{x}} {C_{0}} electrostatics (ratio of capacitance of assay capacitor with dielectric actual against vacuum)
Reynolds number Re \mathrm{Re} = \frac{vL\rho}{\mu} fluid mechanics (ratio of aqueous inertial and adhesive forces)[5]
Richardson number Ri \mathrm{Ri} = \frac{gh}{u^2} = \frac{1}{\mathrm{Fr}^2} fluid dynamics (effect of airiness on breeze stability; arrangement of abeyant over active energy)[24]
Rockwell scale – mechanical acerbity (indentation acerbity of a material)
Rolling attrition coefficient Crr C_{rr} = \frac{F}{N_f} vehicle dynamics (ratio of force bare for motion of a caster over the accustomed force)
Roshko number Ro \mathrm{Ro} = {f L^{2}\over \nu} =\mathrm{St}\,\mathrm{Re} fluid dynamics (oscillating flow, amphitheater shedding)
Rossby number Ro \mathrm{Ro}=\frac{U}{Lf} geophysics (ratio of inertial to Coriolis force)
Rouse number P or Z \mathrm{P} = \frac{w_s}{\kappa u_*} sediment carriage (ratio of the debris abatement acceleration and the upwards acceleration of grain)
Schmidt number Sc \mathrm{Sc} = \frac{\nu}{D} mass alteration (viscous over atomic circulation rate)[25]
Shape factor H H = \frac {\delta^*}{\theta} boundary band breeze (ratio of displacement array to drive thickness)
Sherwood number Sh \mathrm{Sh} = \frac{K L}{D} mass alteration (forced convection; arrangement of convective to deviating accumulation transport)
Shields parameter \tau_* or \theta \tau_{\ast} = \frac{\tau}{(\rho_s - \rho) g D} sediment carriage (threshold of debris movement due to aqueous motion; dimensionless microburst stress)
Sommerfeld number S \mathrm{S} = \left( \frac{r}{c} \right)^2 \frac {\mu N}{P} hydrodynamic lubrication (boundary lubrication)[26]
Specific gravity SG (same as About density)
Stanton number St \mathrm{St} = \frac{h}{c_p \rho V} = \frac{\mathrm{Nu}}{\mathrm{Re}\,\mathrm{Pr}} heat alteration and aqueous dynamics (forced convection)
Stefan number Ste \mathrm{Ste} = \frac{c_p \Delta T}{L} phase change, thermodynamics (ratio of alive calefaction to abeyant heat)
Stokes number Stk or Sk \mathrm{Stk} = \frac{\tau U_o}{d_c} particles suspensions (ratio of appropriate time of atom to time of flow)
Strain \epsilon \epsilon = \cfrac{\partial{F}}{\partial{X}} - 1 materials science, animation (displacement amid particles in the physique about to a advertence length)
Strouhal number St or Sr \mathrm{St} = {\omega L\over v} fluid dynamics (continuous and pulsating flow; nondimensional frequency)[27]
Stuart number N \mathrm{N} = \frac {B^2 L_{c} \sigma}{\rho U} = \frac{\mathrm{Ha}^2}{\mathrm{Re}} magnetohydrodynamics (ratio of electromagnetic to inertial forces)
Taylor number Ta \mathrm{Ta} = \frac{4\Omega^2 R^4}{\nu^2} fluid dynamics (rotating aqueous flows; inertial armament due to circling of a aqueous against adhesive forces)
Ursell number U \mathrm{U} = \frac{H\, \lambda^2}{h^3} wave mechanics (nonlinearity of credible force after-effects on a bank aqueous layer)
Vadasz number Va \mathrm{Va} = \frac{\phi\, \mathrm{Pr}}{\mathrm{Da}} porous media (governs the furnishings of porosity \phi, the Prandtl amount and the Darcy amount on breeze in a absorptive medium) [28]
van 't Hoff factor i i = 1 + \alpha (n - 1) quantitative assay (Kf and Kb)
Wallis parameter j* j^* = R \left( \frac{\omega \rho}{\mu} \right)^\frac{1}{2} multiphase flows (nondimensional apparent velocity)[29]
Weaver blaze acceleration number Wea \mathrm{Wea} = \frac{w}{w_\mathrm{H}} 100 combustion (laminar afire acceleration about to hydrogen gas)[30]
Weber number We \mathrm{We} = \frac{\rho v^2 l}{\sigma} multiphase breeze (strongly arced surfaces; arrangement of apathy to credible tension)
Weissenberg number Wi \mathrm{Wi} = \dot{\gamma} \lambda viscoelastic flows (shear amount times the alleviation time)[31]
Womersley number \alpha \alpha = R \left( \frac{\omega \rho}{\mu} \right)^\frac{1}{2} biofluid mechanics (continuous and pulsating flows; arrangement of pulsatile breeze abundance to adhesive effects)[32]
Name Standard symbol Definition Field of application
Abbe number V V = \frac{ n_d - 1 }{ n_F - n_C } optics (dispersion in optical materials)
Activity coefficient \gamma \gamma= \frac {{a}}{{x}} chemistry (Proportion of "active" molecules or atoms)
Albedo \alpha \alpha= (1-D) \bar \alpha(\theta_i) + D \bar{ \bar \alpha} climatology, astrochemistry (reflectivity of surfaces or bodies)
Archimedes number Ar \mathrm{Ar} = \frac{g L^3 \rho_\ell (\rho - \rho_\ell)}{\mu^2} fluid mechanics (motion of fluids due to physique differences)
Arrhenius number \alpha \alpha = \frac{E_a}{RT} chemistry (ratio of activation activity to thermal energy)[5]
Atomic weight M chemistry (mass of atom over one diminutive accumulation unit, u, breadth carbon-12 is absolutely 12 u)
Atwood number A \mathrm{A} = \frac{\rho_1 - \rho_2} {\rho_1 + \rho_2} fluid mechanics (onset of instabilities in aqueous mixtures due to physique differences)
Bagnold number Ba \mathrm{Ba} = \frac{\rho d^2 \lambda^{1/2} \gamma}{\mu} fluid mechanics, cartography (ratio of atom blow stresses to adhesive aqueous stresses in breeze of a diminutive actual such as atom and sand)[6]
Bejan number
(fluid mechanics) Be \mathrm{Be} = \frac{\Delta P L^2} {\mu \alpha} fluid mechanics (dimensionless burden bead forth a channel)[7]
Bejan number
(thermodynamics) Be \mathrm{Be} = \frac{\dot S'_{\mathrm{gen},\, \Delta T}}{\dot S'_{\mathrm{gen},\, \Delta T}+ \dot S'_{\mathrm{gen},\, \Delta p}} thermodynamics (ratio of calefaction alteration irreversibility to absolute irreversibility due to calefaction alteration and aqueous friction)[8]
Bingham number Bm \mathrm{Bm} = \frac{ \tau_y L }{ \mu V } fluid mechanics, rheology (ratio of crop accent to adhesive stress)[5]
Biot number Bi \mathrm{Bi} = \frac{h L_C}{k_b} heat alteration (surface vs. aggregate application of solids)
Blake number Bl or B \mathrm{B} = \frac{u \rho}{\mu (1 - \epsilon) D} geology, aqueous mechanics, absorptive media (inertial over adhesive armament in aqueous breeze through absorptive media)
Bodenstein number Bo or Bd \mathrm{Bo} = vL/\mathcal{D} = \mathrm{Re}\, \mathrm{Sc} chemistry (residence-time distribution; agnate to the axial accumulation alteration Peclet number)[9]
Bond number Bo \mathrm{Bo} = \frac{\rho a L^2}{\gamma} geology, aqueous mechanics, absorptive media (buoyant against capilary forces, agnate to the Eötvös number) [10]
Brinkman number Br \mathrm{Br} = \frac {\mu U^2}{\kappa (T_w - T_0)} heat transfer, aqueous mechanics (conduction from a bank to a adhesive fluid)
Brownell–Katz number NBK \mathrm{N}_\mathrm{BK} = \frac{u \mu}{k_\mathrm{rw}\sigma} fluid mechanics (combination of capillary amount and Bond number) [11]
Capillary number Ca \mathrm{Ca} = \frac{\mu V}{\gamma} porous media, aqueous mechanics (viscous armament against credible tension)
Chandrasekhar number Q \mathrm{Q} = \frac{{B_0}^2 d^2}{\mu_0 \rho \nu \lambda} magnetohydrodynamics (ratio of the Lorentz force to the bendability in alluring convection)
Colburn J factors JM, JH, JD turbulence; heat, mass, and drive alteration (dimensionless alteration coefficients)
Coefficient of active friction \mu_k mechanics (friction of solid bodies in translational motion)
Coefficient of changeless friction \mu_s mechanics (friction of solid bodies at rest)
Coefficient of determination R^2 statistics (proportion of about-face explained by a statistical model)
Coefficient of variation \frac{\sigma}{\mu} \frac{\sigma}{\mu} statistics (ratio of accepted aberration to expectation)
Correlation ПЃ or r \frac{{\mathbb E}[(X-\mu_X)(Y-\mu_Y)]}{\sigma_X \sigma_Y} or \frac{\sum_{k=1}^n (x_k-\bar x)(y_k-\bar y)}{\sqrt{\sum_{k=1}^n (x_k-\bar x)^2 \sum_{k=1}^n (y_k-\bar y)^2}} breadth \bar x = \sum_{k=1}^n x_k/n and analogously for \bar y statistics (measure of beeline dependence)
Courant–Friedrich–Levy number C or 𝜈 C = \frac {u\,\Delta t} {\Delta x} mathematics (numerical solutions of abstract PDEs)[12]
Damkohler number Da \mathrm{Da} = k \tau chemistry (reaction time scales vs. abode time)
Damping ratio \zeta \zeta = \frac{c}{2 \sqrt{km}} mechanics (the akin of damping in a system)
Darcy abrasion factor Cf or fD fluid mechanics (fraction of burden losses due to abrasion in a pipe; four times the Fanning abrasion factor)
Darcy number Da \mathrm{Da} = \frac{K}{d^2} porous media (ratio of permeability to cross-sectional area)
Dean number D \mathrm{D} = \frac{\rho V d}{\mu} \left( \frac{d}{2 R} \right)^{1/2} turbulent breeze (vortices in arced ducts)
Deborah number De \mathrm{De} = \frac{t_\mathrm{c}}{t_\mathrm{p}} rheology (viscoelastic fluids)
Decibel dB acoustics, electronics, ascendancy approach (ratio of two intensities or admiral of a wave)
Drag coefficient cd c_\mathrm{d} = \dfrac{2 F_\mathrm{d}}{\rho v^2 A}\, , aeronautics, aqueous dynamics (resistance to aqueous motion)
Dukhin number Du \mathrm{Du} = \frac{\kappa^{\sigma}}{{\Kappa_m} a} colloid science (ratio of electric credible application to the electric aggregate application in amalgamate systems)
Eckert number Ec \mathrm{Ec} = \frac{V^2}{c_p\Delta T} convective calefaction alteration (characterizes amusement of energy; arrangement of active activity to enthalpy)
Ekman number Ek \mathrm{Ek} = \frac{\nu}{2D^2\Omega\sin\varphi} geophysics (viscous against Coriolis forces)
Elasticity
(economics) E E_{x,y} = \frac{\partial ln(x)}{\partial ln(y)} = \frac{\partial x}{\partial y}\frac{y}{x} economics (response of appeal or accumulation to amount changes)
Eötvös number Eo \mathrm{Eo}=\frac{\Delta\rho \,g \,L^2}{\sigma} fluid mechanics (shape of bubbles or drops)
Ericksen number Er \mathrm{Er}=\frac{\mu v L}{K} fluid dynamics (liquid clear breeze behavior; adhesive over adaptable forces)
Euler number Eu \mathrm{Eu}=\frac{\Delta{}p}{\rho V^2} hydrodynamics (stream burden against apathy forces)
Euler's number e e = \displaystyle\sum\limits_{n = 0}^{ \infty} \dfrac{1}{n!} = \approx 2.71828 mathematics (base of the accustomed logarithm)
Excess temperature coefficient \Theta_r \Theta_r = \frac{c_p (T-T_e)}{U_e^2/2} heat transfer, aqueous dynamics (change in centralized activity against active energy)[13]
Fanning abrasion factor f fluid mechanics (fraction of burden losses due to abrasion in a pipe; 1/4th the Darcy abrasion factor)[14]
Feigenbaum constants \alpha, \delta \alpha \approx 2.50290,
\ \delta \approx 4.66920 chaos approach (period doubling)[15]
Fine anatomy constant \alpha \alpha = \frac{e^2}{2\varepsilon_0 hc} quantum electrodynamics (QED) (coupling connected anecdotic the backbone of the electromagnetic interaction)
f-number f f = \frac {{\ell}}{{D}} optics, photography (ratio of focal breadth to bore of aperture)
Föppl–von Kármán number \gamma \gamma = \frac{Y r^2}{\kappa} virology, solid mechanics (thin-shell buckling)
Fourier number Fo \mathrm{Fo} = \frac{\alpha t}{L^2} heat transfer, accumulation alteration (ratio of deviating amount against accumulator rate)
Fresnel number F \mathit{F} = \frac{a^{2}}{L \lambda} optics (slit diffraction)[16]
Froude number Fr \mathrm{Fr} = \frac{v}{\sqrt{g\ell}} fluid mechanics (wave and credible behaviour; arrangement of a body's apathy to gravitational forces)
Gain – electronics (signal achievement to arresting input)
Gain ratio – bicycling (system of apery gearing; breadth catholic over breadth pedaled)[17]
Galilei number Ga \mathrm{Ga} = \frac{g\, L^3}{\nu^2} fluid mechanics (gravitational over adhesive forces)
Golden ratio \varphi \varphi = \frac{1+\sqrt{5}}{2} \approx 1.61803 mathematics, aesthetics (long ancillary breadth of self-similar rectangle)
Görtler number G \mathrm{G} = \frac{U_e \theta}{\nu} \left( \frac{\theta}{R} \right)^{1/2} fluid dynamics (boundary band breeze forth a biconcave wall)
Graetz number Gz \mathrm{Gz} = {D_H \over L} \mathrm{Re}\, \mathrm{Pr} heat transfer, aqueous mechanics (laminar breeze through a conduit; aswell acclimated in accumulation transfer)
Grashof number Gr \mathrm{Gr}_L = \frac{g \beta (T_s - T_\infty ) L^3}{\nu ^2} heat transfer, accustomed alteration (ratio of the airiness to adhesive force)
Gravitational coupling constant \alpha_G \alpha_G=\frac{Gm_e^2}{\hbar c} gravitation (attraction amid two massy elementary particles; akin to the Fine anatomy constant)
Hatta number Ha \mathrm{Ha} = \frac{N_{\mathrm{A}0}}{N_{\mathrm{A}0}^{\mathrm{phys}}} chemical engineering (adsorption accessory due to actinic reaction)
Hagen number Hg \mathrm{Hg} = -\frac{1}{\rho}\frac{\mathrm{d} p}{\mathrm{d} x}\frac{L^3}{\nu^2} heat alteration (ratio of the airiness to adhesive force in affected convection)
Hydraulic gradient i i = \frac{\mathrm{d}h}{\mathrm{d}l} = \frac{h_2 - h_1}{\mathrm{length}} fluid mechanics, groundwater breeze (pressure arch over distance)
Iribarren number Ir \mathrm{Ir} = \frac{\tan \alpha}{\sqrt{H/L_0}} wave mechanics (breaking credible force after-effects on a slope)
Jakob number Ja \mathrm{Ja} = \frac{c_p (T_\mathrm{s} - T_\mathrm{sat}) }{\Delta H_{\mathrm{f}} } chemistry (ratio of alive to abeyant activity captivated during liquid-vapor appearance change)[18]
Karlovitz number Ka \mathrm{Ka} = k t_c turbulent agitation (characteristic breeze time times blaze amplitude rate)
Keulegan–Carpenter number KC \mathrm{K_C} = \frac{V\,T}{L} fluid dynamics (ratio of annoyance force to apathy for a barefaced article in oscillatory aqueous flow)
Knudsen number Kn \mathrm{Kn} = \frac {\lambda}{L} gas dynamics (ratio of the atomic beggarly chargeless aisle breadth to a adumbrative concrete breadth scale)
Kt/V Kt/V medicine (hemodialysis and peritoneal dialysis treatment; dimensionless time)
Kutateladze number Ku \mathrm{Ku} = \frac{U_h \rho_g^{1/2}}{\left({\sigma g (\rho_l - \rho_g)}\right)^{1/4}} fluid mechanics (counter-current two-phase flow)[19]
Laplace number La \mathrm{La} = \frac{\sigma \rho L}{\mu^2} fluid dynamics (free alteration aural immiscible fluids; arrangement of credible astriction to momentum-transport)
Lewis number Le \mathrm{Le} = \frac{\alpha}{D} = \frac{\mathrm{Sc}}{\mathrm{Pr}} heat and accumulation alteration (ratio of thermal to accumulation diffusivity)
Lift coefficient CL C_\mathrm{L} = \frac{L}{q\,S} aerodynamics (lift accessible from an airfoil at a accustomed bend of attack)
Lockhart–Martinelli parameter \chi \chi = \frac{m_\ell}{m_g} \sqrt{\frac{\rho_g}{\rho_\ell}} two-phase breeze (flow of wet gases; aqueous fraction)[20]
Love numbers h, k, l geophysics (solidity of apple and added planets)
Lundquist number S S = \frac{\mu_0LV_A}{\eta} plasma physics (ratio of a arresting time to an AlfvГ©n beachcomber bridge time in a plasma)
Mach number M or Ma \mathrm{M} = \frac{{v}}{{v_\mathrm{sound}}} gas dynamics (compressible flow; dimensionless velocity)
Magnetic Reynolds number Rm \mathrm{R}_\mathrm{m} = \frac{U L}{\eta} magnetohydrodynamics (ratio of alluring advection to alluring diffusion)
Manning acerbity coefficient n open approach breeze (flow apprenticed by gravity)[21]
Marangoni number Mg \mathrm{Mg} = - {\frac{\mathrm{d}\sigma}{\mathrm{d}T}}\frac{L \Delta T}{\eta \alpha} fluid mechanics (Marangoni flow; thermal credible astriction armament over adhesive forces)
Morton number Mo \mathrm{Mo} = \frac{g \mu_c^4 \, \Delta \rho}{\rho_c^2 \sigma^3} fluid dynamics (determination of bubble/drop shape)
Nusselt number Nu \mathrm{Nu} =\frac{hd}{k} heat alteration (forced convection; arrangement of convective to conductive calefaction transfer)
Ohnesorge number Oh \mathrm{Oh} = \frac{ \mu}{ \sqrt{\rho \sigma L }} = \frac{\sqrt{\mathrm{We}}}{\mathrm{Re}} fluid dynamics (atomization of liquids, Marangoni flow)
Péclet number Pe \mathrm{Pe} = \frac{du\rho c_p}{k} = \mathrm{Re}\, \mathrm{Pr} heat alteration (advection–diffusion problems; absolute drive alteration to atomic calefaction transfer)
Peel number NP N_\mathrm{P} = \frac{\text{Restoring force}}{\text{Adhesive force}} coating (adhesion of microstructures with substrate)[22]
Perveance K {K} = \frac{{I}}{{I_0}}\,\frac{{2}}{{\beta}^3{\gamma}^3} (1-\gamma^2f_e) charged atom carriage (measure of the backbone of amplitude allegation in a answerable atom beam)
pH \mathrm{pH} \mathrm{pH} = - \log_{10}(a_{\textrm{H}^+}) = \log_{10}\left(\frac{1}{a_{\textrm{H}^+}}\right) the admeasurement of the acidity or basicity of an aqueous solution
Pi \pi \pi = \frac{C}{d} \approx 3.14159 mathematics (ratio of a circle's ambit to its diameter)
Pixel px digital imaging (smallest addressable unit)
Poisson's ratio \nu \nu = -\frac{\mathrm{d}\varepsilon_\mathrm{trans}}{\mathrm{d}\varepsilon_\mathrm{axial}} elasticity (load in axle and longitudinal direction)
Porosity \phi \phi = \frac{V_\mathrm{V}}{V_\mathrm{T}} geology, absorptive media (void atom of the medium)
Power factor P/S electronics (real ability to credible power)
Power number Np N_p = {P\over \rho n^3 d^5} electronics (power afire by agitators; attrition force against apathy force)
Prandtl number Pr \mathrm{Pr} = \frac{\nu}{\alpha} = \frac{c_p \mu}{k} heat alteration (ratio of adhesive circulation amount over thermal circulation rate)
Prater number ОІ \beta = \frac{-\Delta H_r D_{TA}^e C_{AS}}{\lambda^e T_s} reaction engineering (ratio of calefaction change to calefaction advice aural a agitator pellet)[23]
Pressure coefficient CP C_p = {p - p_\infty \over \frac{1}{2} \rho_\infty V_\infty^2} aerodynamics, hydrodynamics (pressure accomplished at a point on an airfoil; dimensionless burden variable)
Q factor Q physics, engineering (damping of oscillator or resonator; activity stored against activity lost)
Radian measure rad \text{arc length}/\text{radius} mathematics (measurement of collapsed angles, 1 radian = 180/ПЂ degrees)
Rayleigh number Ra \mathrm{Ra}_{x} = \frac{g \beta} {\nu \alpha} (T_s - T_\infin) x^3 heat alteration (buoyancy against adhesive armament in chargeless convection)
Refractive index n n=\frac{c}{v} electromagnetism, eyes (speed of ablaze in a exhaustion over acceleration of ablaze in a material)
Relative density RD RD = \frac{\rho_\mathrm{substance}}{\rho_\mathrm{reference}} hydrometers, actual comparisons (ratio of physique of a actual to a advertence material—usually water)
Relative permeability \mu_r \mu_r = \frac{\mu}{\mu_0} magnetostatics (ratio of the permeability of a specific average to chargeless space)
Relative permittivity \varepsilon_r \varepsilon_{r} = \frac{C_{x}} {C_{0}} electrostatics (ratio of capacitance of assay capacitor with dielectric actual against vacuum)
Reynolds number Re \mathrm{Re} = \frac{vL\rho}{\mu} fluid mechanics (ratio of aqueous inertial and adhesive forces)[5]
Richardson number Ri \mathrm{Ri} = \frac{gh}{u^2} = \frac{1}{\mathrm{Fr}^2} fluid dynamics (effect of airiness on breeze stability; arrangement of abeyant over active energy)[24]
Rockwell scale – mechanical acerbity (indentation acerbity of a material)
Rolling attrition coefficient Crr C_{rr} = \frac{F}{N_f} vehicle dynamics (ratio of force bare for motion of a caster over the accustomed force)
Roshko number Ro \mathrm{Ro} = {f L^{2}\over \nu} =\mathrm{St}\,\mathrm{Re} fluid dynamics (oscillating flow, amphitheater shedding)
Rossby number Ro \mathrm{Ro}=\frac{U}{Lf} geophysics (ratio of inertial to Coriolis force)
Rouse number P or Z \mathrm{P} = \frac{w_s}{\kappa u_*} sediment carriage (ratio of the debris abatement acceleration and the upwards acceleration of grain)
Schmidt number Sc \mathrm{Sc} = \frac{\nu}{D} mass alteration (viscous over atomic circulation rate)[25]
Shape factor H H = \frac {\delta^*}{\theta} boundary band breeze (ratio of displacement array to drive thickness)
Sherwood number Sh \mathrm{Sh} = \frac{K L}{D} mass alteration (forced convection; arrangement of convective to deviating accumulation transport)
Shields parameter \tau_* or \theta \tau_{\ast} = \frac{\tau}{(\rho_s - \rho) g D} sediment carriage (threshold of debris movement due to aqueous motion; dimensionless microburst stress)
Sommerfeld number S \mathrm{S} = \left( \frac{r}{c} \right)^2 \frac {\mu N}{P} hydrodynamic lubrication (boundary lubrication)[26]
Specific gravity SG (same as About density)
Stanton number St \mathrm{St} = \frac{h}{c_p \rho V} = \frac{\mathrm{Nu}}{\mathrm{Re}\,\mathrm{Pr}} heat alteration and aqueous dynamics (forced convection)
Stefan number Ste \mathrm{Ste} = \frac{c_p \Delta T}{L} phase change, thermodynamics (ratio of alive calefaction to abeyant heat)
Stokes number Stk or Sk \mathrm{Stk} = \frac{\tau U_o}{d_c} particles suspensions (ratio of appropriate time of atom to time of flow)
Strain \epsilon \epsilon = \cfrac{\partial{F}}{\partial{X}} - 1 materials science, animation (displacement amid particles in the physique about to a advertence length)
Strouhal number St or Sr \mathrm{St} = {\omega L\over v} fluid dynamics (continuous and pulsating flow; nondimensional frequency)[27]
Stuart number N \mathrm{N} = \frac {B^2 L_{c} \sigma}{\rho U} = \frac{\mathrm{Ha}^2}{\mathrm{Re}} magnetohydrodynamics (ratio of electromagnetic to inertial forces)
Taylor number Ta \mathrm{Ta} = \frac{4\Omega^2 R^4}{\nu^2} fluid dynamics (rotating aqueous flows; inertial armament due to circling of a aqueous against adhesive forces)
Ursell number U \mathrm{U} = \frac{H\, \lambda^2}{h^3} wave mechanics (nonlinearity of credible force after-effects on a bank aqueous layer)
Vadasz number Va \mathrm{Va} = \frac{\phi\, \mathrm{Pr}}{\mathrm{Da}} porous media (governs the furnishings of porosity \phi, the Prandtl amount and the Darcy amount on breeze in a absorptive medium) [28]
van 't Hoff factor i i = 1 + \alpha (n - 1) quantitative assay (Kf and Kb)
Wallis parameter j* j^* = R \left( \frac{\omega \rho}{\mu} \right)^\frac{1}{2} multiphase flows (nondimensional apparent velocity)[29]
Weaver blaze acceleration number Wea \mathrm{Wea} = \frac{w}{w_\mathrm{H}} 100 combustion (laminar afire acceleration about to hydrogen gas)[30]
Weber number We \mathrm{We} = \frac{\rho v^2 l}{\sigma} multiphase breeze (strongly arced surfaces; arrangement of apathy to credible tension)
Weissenberg number Wi \mathrm{Wi} = \dot{\gamma} \lambda viscoelastic flows (shear amount times the alleviation time)[31]
Womersley number \alpha \alpha = R \left( \frac{\omega \rho}{\mu} \right)^\frac{1}{2} biofluid mechanics (continuous and pulsating flows; arrangement of pulsatile breeze abundance to adhesive effects)[32]
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