Name |
Standard symbol |
Definition |
Field of application |
Abbe number | V | ![V = \frac{ n_d - 1 }{ n_F - n_C }](../I/m/924a73f8660972554f4ec17376b57a0b9da54877.svg) | optics (dispersion in optical materials) |
Activity coefficient | | ![\gamma= \frac {{a}}{{x}}](../I/m/2d49c86dcf47d656c4ec1ce1ed64d223278ec738.svg) | chemistry (Proportion of "active" molecules or atoms) |
Albedo | | ![\alpha= (1-D) \bar \alpha(\theta_i) + D \bar{ \bar \alpha}](../I/m/c2fad17b657cabd5c9e829510a830a2fa8867d17.svg) | climatology, astronomy (reflectivity of surfaces or bodies) |
Archimedes number | Ar | ![\mathrm{Ar} = \frac{g L^3 \rho_\ell (\rho - \rho_\ell)}{\mu^2}](../I/m/d8ce0359a7e01ef5462564f8356a2923460d6f5d.svg) | fluid mechanics (motion of fluids due to density differences) |
Arrhenius number | | | chemistry (ratio of activation energy to thermal energy)[1] |
Atomic weight | M | | chemistry (mass of atom over one atomic mass unit, u, where carbon-12 is exactly 12 u) |
Atwood number | A | | fluid mechanics (onset of instabilities in fluid mixtures due to density differences) |
Bagnold number | Ba | ![\mathrm{Ba} = \frac{\rho d^2 \lambda^{1/2} \gamma}{\mu}](../I/m/b4ee59e514eb8a0a4747f9d3f8315658fdc976c3.svg) | fluid mechanics, geology (ratio of grain collision stresses to viscous fluid stresses in flow of a granular material such as grain and sand)[2] |
Bejan number (fluid mechanics) | Be | | fluid mechanics (dimensionless pressure drop along a channel)[3] |
Bejan number (thermodynamics) | Be | | thermodynamics (ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction)[4] |
Bingham number | Bm | ![\mathrm{Bm} = \frac{ \tau_y L }{ \mu V }](../I/m/521881f326d5d86835534e6609540a86112f25ae.svg) | fluid mechanics, rheology (ratio of yield stress to viscous stress)[1] |
Biot number | Bi | ![\mathrm{Bi} = \frac{h L_C}{k_b}](../I/m/b333caa5e65d495ed5b8c507a5ca6905898a9ea8.svg) | heat transfer (surface vs. volume conductivity of solids) |
Blake number | Bl or B | | geology, fluid mechanics, porous media (inertial over viscous forces in fluid flow through porous media) |
Bodenstein number | Bo or Bd | | chemistry (residence-time distribution; similar to the axial mass transfer Peclet number)[5] |
Bond number | Bo | ![\mathrm{Bo} = \frac{\rho a L^2}{\gamma}](../I/m/76d542a70c5a2d893840268226c798f1f5a52c62.svg) | geology, fluid mechanics, porous media (buoyant versus capillary forces, similar to the Eötvös number) [6] |
Brinkman number | Br | ![\mathrm{Br} = \frac {\mu U^2}{\kappa (T_w - T_0)}](../I/m/d93721d4c1633ef5df77985a651f7a7f46f1b59c.svg) | heat transfer, fluid mechanics (conduction from a wall to a viscous fluid) |
Brownell–Katz number | NBK | | fluid mechanics (combination of capillary number and Bond number) [7] |
Capillary number | Ca | | porous media, fluid mechanics (viscous forces versus surface tension) |
Chandrasekhar number | Q | | magnetohydrodynamics (ratio of the Lorentz force to the viscosity in magnetic convection) |
Colburn J factors | JM, JH, JD | | turbulence; heat, mass, and momentum transfer (dimensionless transfer coefficients) |
Coefficient of kinetic friction | | | mechanics (friction of solid bodies in translational motion) |
Coefficient of static friction | | | mechanics (friction of solid bodies at rest) |
Coefficient of determination | | | statistics (proportion of variance explained by a statistical model) |
Coefficient of variation | | | statistics (ratio of standard deviation to expectation) |
Correlation | ρ or r | | statistics (measure of linear dependence) |
Cost of transport | COT | | energy efficiency, economics (ratio of energy input to kinetic motion) |
Courant–Friedrich–Levy number | C or 𝜈 | | mathematics (numerical solutions of hyperbolic PDEs)[8] |
Damkohler number | Da | ![\mathrm{Da} = k \tau](../I/m/b9720287339fa283b7a5a34a4a4eb0cc8200fc48.svg) | chemistry (reaction time scales vs. residence time) |
Damping ratio | | ![\zeta = \frac{c}{2 \sqrt{km}}](../I/m/d8f17b775df1d28640a5afa39e21c040f18f088a.svg) | mechanics (the level of damping in a system) |
Darcy friction factor | Cf or fD | | fluid mechanics (fraction of pressure losses due to friction in a pipe; four times the Fanning friction factor) |
Darcy number | Da | ![\mathrm{Da} = \frac{K}{d^2}](../I/m/4936968246f15ddd79c462211ae0b2a1427caa30.svg) | porous media (ratio of permeability to cross-sectional area) |
Dean number | D | | turbulent flow (vortices in curved ducts) |
Deborah number | De | | rheology (viscoelastic fluids) |
Decibel | dB | | acoustics, electronics, control theory (ratio of two intensities or powers of a wave) |
Drag coefficient | cd | | aeronautics, fluid dynamics (resistance to fluid motion) |
Dukhin number | Du | | colloid science (ratio of electric surface conductivity to the electric bulk conductivity in heterogeneous systems) |
Eckert number | Ec | | convective heat transfer (characterizes dissipation of energy; ratio of kinetic energy to enthalpy) |
Ekman number | Ek | | geophysics (viscous versus Coriolis forces) |
Elasticity (economics) | E | | economics (response of demand or supply to price changes) |
Eötvös number | Eo | | fluid mechanics (shape of bubbles or drops) |
Ericksen number | Er | | fluid dynamics (liquid crystal flow behavior; viscous over elastic forces) |
Euler number | Eu | | hydrodynamics (stream pressure versus inertia forces) |
Euler's number | e | | mathematics (base of the natural logarithm) |
Excess temperature coefficient | | ![\Theta_r = \frac{c_p (T-T_e)}{U_e^2/2}](../I/m/485154205ef7d4f8ebd13e5e4de5d97f22b62c95.svg) | heat transfer, fluid dynamics (change in internal energy versus kinetic energy)[9] |
Fanning friction factor | f | | fluid mechanics (fraction of pressure losses due to friction in a pipe; 1/4th the Darcy friction factor)[10] |
Feigenbaum constants | , | ![\alpha \approx 2.50290,](../I/m/50caaed719ec4a6a1720c71ef4de9627d39a2781.svg)
| chaos theory (period doubling)[11] |
Fine structure constant | | ![{\displaystyle \alpha ={\frac {e^{2}}{4\pi \varepsilon _{0}hc}}}](../I/m/bc67347d257ae866971c2a4adbca96428c215f27.svg) | quantum electrodynamics (QED) (coupling constant characterizing the strength of the electromagnetic interaction) |
f-number | f | | optics, photography (ratio of focal length to diameter of aperture) |
Föppl–von Kármán number | | | virology, solid mechanics (thin-shell buckling) |
Fourier number | Fo | | heat transfer, mass transfer (ratio of diffusive rate versus storage rate) |
Fresnel number | F | | optics (slit diffraction)[12] |
Froude number | Fr | | fluid mechanics (wave and surface behaviour; ratio of a body's inertia to gravitational forces) |
Gain | – | | electronics (signal output to signal input) |
Gain ratio | – | | bicycling (system of representing gearing; length traveled over length pedaled)[13] |
Galilei number | Ga | | fluid mechanics (gravitational over viscous forces) |
Golden ratio | | | mathematics, aesthetics (long side length of self-similar rectangle) |
Görtler number | G | | fluid dynamics (boundary layer flow along a concave wall) |
Graetz number | Gz | | heat transfer, fluid mechanics (laminar flow through a conduit; also used in mass transfer) |
Grashof number | Gr | | heat transfer, natural convection (ratio of the buoyancy to viscous force) |
Gravitational coupling constant | | ![\alpha_G=\frac{Gm_e^2}{\hbar c}](../I/m/99dca6acf33a6d29c9dd3cbd3e09bf0a947d2abb.svg) | gravitation (attraction between two massy elementary particles; analogous to the Fine structure constant) |
Hatta number | Ha | | chemical engineering (adsorption enhancement due to chemical reaction) |
Hagen number | Hg | | heat transfer (ratio of the buoyancy to viscous force in forced convection) |
Hydraulic gradient | i | | fluid mechanics, groundwater flow (pressure head over distance) |
Iribarren number | Ir | | wave mechanics (breaking surface gravity waves on a slope) |
Jakob number | Ja | ![\mathrm{Ja} = \frac{c_p (T_\mathrm{s} - T_\mathrm{sat}) }{\Delta H_{\mathrm{f}} }](../I/m/945adc71d43dd0901b41670e5cd14d595721542d.svg) | chemistry (ratio of sensible to latent energy absorbed during liquid-vapor phase change)[14] |
Karlovitz number | Ka | | turbulent combustion (characteristic flow time times flame stretch rate) |
Keulegan–Carpenter number | KC | | fluid dynamics (ratio of drag force to inertia for a bluff object in oscillatory fluid flow) |
Knudsen number | Kn | | 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 | | fluid mechanics (counter-current two-phase flow)[15] |
Laplace number | La | | fluid dynamics (free convection within immiscible fluids; ratio of surface tension to momentum-transport) |
Lewis number | Le | | heat and mass transfer (ratio of thermal to mass diffusivity) |
Lift coefficient | CL | | aerodynamics (lift available from an airfoil at a given angle of attack) |
Lockhart–Martinelli parameter | | | two-phase flow (flow of wet gases; liquid fraction)[16] |
Love numbers | h, k, l | | geophysics (solidity of earth and other planets) |
Lundquist number | S | | plasma physics (ratio of a resistive time to an Alfvén wave crossing time in a plasma) |
Mach number | M or Ma | | gas dynamics (compressible flow; dimensionless velocity) |
Magnetic Reynolds number | Rm | | magnetohydrodynamics (ratio of magnetic advection to magnetic diffusion) |
Manning roughness coefficient | n | | open channel flow (flow driven by gravity)[17] |
Marangoni number | Mg | | fluid mechanics (Marangoni flow; thermal surface tension forces over viscous forces) |
Morton number | Mo | | fluid dynamics (determination of bubble/drop shape) |
Nusselt number | Nu | | heat transfer (forced convection; ratio of convective to conductive heat transfer) |
Ohnesorge number | Oh | | fluid dynamics (atomization of liquids, Marangoni flow) |
Péclet number | Pe | ![\mathrm{Pe} = \frac{du\rho c_p}{k} = \mathrm{Re}\, \mathrm{Pr}](../I/m/7176382f7a5d4db8a5be9910fd112f3821118eef.svg) | heat transfer (advection–diffusion problems; total momentum transfer to molecular heat transfer) |
Peel number | NP | | coating (adhesion of microstructures with substrate)[18] |
Perveance | K | | charged particle transport (measure of the strength of space charge in a charged particle beam) |
pH | | | chemistry (the measure of the acidity or basicity of an aqueous solution) |
Pi | | | mathematics (ratio of a circle's circumference to its diameter) |
Pierce parameter | | | Traveling wave tube |
Pixel | px | | digital imaging (smallest addressable unit) |
Poisson's ratio | | | elasticity (load in transverse and longitudinal direction) |
Porosity | | | geology, porous media (void fraction of the medium) |
Power factor | P/S | | electronics (real power to apparent power) |
Power number | Np | | electronics (power consumption by agitators; resistance force versus inertia force) |
Prandtl number | Pr | ![\mathrm{Pr} = \frac{\nu}{\alpha} = \frac{c_p \mu}{k}](../I/m/c789ae3617f8f489280fc2e6c0ac4b551324efd4.svg) | heat transfer (ratio of viscous diffusion rate over thermal diffusion rate) |
Prater number | β | | reaction engineering (ratio of heat evolution to heat conduction within a catalyst pellet)[19] |
Pressure coefficient | CP | | aerodynamics, hydrodynamics (pressure experienced at a point on an airfoil; dimensionless pressure variable) |
Q factor | Q | | physics, engineering (damping of oscillator or resonator; energy stored versus energy lost) |
Radian measure | rad | | mathematics (measurement of planar angles, 1 radian = 180/π degrees) |
Rayleigh number | Ra | | heat transfer (buoyancy versus viscous forces in free convection) |
Refractive index | n | | electromagnetism, optics (speed of light in a vacuum over speed of light in a material) |
Relative density | RD | | hydrometers, material comparisons (ratio of density of a material to a reference material—usually water) |
Relative permeability | | | magnetostatics (ratio of the permeability of a specific medium to free space) |
Relative permittivity | | | electrostatics (ratio of capacitance of test capacitor with dielectric material versus vacuum) |
Reynolds number | Re | | fluid mechanics (ratio of fluid inertial and viscous forces)[1] |
Richardson number | Ri | | fluid dynamics (effect of buoyancy on flow stability; ratio of potential over kinetic energy)[20] |
Rockwell scale | – | | mechanical hardness (indentation hardness of a material) |
Rolling resistance coefficient | Crr | ![C_{rr} = \frac{F}{N_f}](../I/m/a1139e8c4bc9bc5b130ad3c9fa83600a8ca35c2d.svg) | vehicle dynamics (ratio of force needed for motion of a wheel over the normal force) |
Roshko number | Ro | | fluid dynamics (oscillating flow, vortex shedding) |
Rossby number | Ro | | geophysics (ratio of inertial to Coriolis force) |
Rouse number | P or Z | | sediment transport (ratio of the sediment fall velocity and the upwards velocity of grain) |
Schmidt number | Sc | | mass transfer (viscous over molecular diffusion rate)[21] |
Shape factor | H | | boundary layer flow (ratio of displacement thickness to momentum thickness) |
Sherwood number | Sh | | mass transfer (forced convection; ratio of convective to diffusive mass transport) |
Shields parameter | or | | sediment transport (threshold of sediment movement due to fluid motion; dimensionless shear stress) |
Sommerfeld number | S | | hydrodynamic lubrication (boundary lubrication)[22] |
Specific gravity | SG | | (same as Relative density) |
Stanton number | St | | heat transfer and fluid dynamics (forced convection) |
Stefan number | Ste | ![\mathrm{Ste} = \frac{c_p \Delta T}{L}](../I/m/01f5e94ef7974a674d45de8edb888b7330b30032.svg) | phase change, thermodynamics (ratio of sensible heat to latent heat) |
Stokes number | Stk or Sk | ![\mathrm{Stk} = \frac{\tau U_o}{d_c}](../I/m/083df09cde8dfe1eeb4652e8c490624849296cb3.svg) | particles suspensions (ratio of characteristic time of particle to time of flow) |
Strain | | ![\epsilon = \cfrac{\partial{F}}{\partial{X}} - 1](../I/m/7b728d1a5f08ae0ecf6e30fc69f275e3dcc4b0e2.svg) | materials science, elasticity (displacement between particles in the body relative to a reference length) |
Strouhal number | St or Sr | ![\mathrm{St} = {\omega L\over v}](../I/m/32b6a366f8610d53bd8d1ff7f94c6476f9e0e84b.svg) | fluid dynamics (continuous and pulsating flow; nondimensional frequency)[23] |
Stuart number | N | | magnetohydrodynamics (ratio of electromagnetic to inertial forces) |
Taylor number | Ta | ![\mathrm{Ta} = \frac{4\Omega^2 R^4}{\nu^2}](../I/m/0f097fff0636027e240b5963985a77c5fdbfeb0a.svg) | fluid dynamics (rotating fluid flows; inertial forces due to rotation of a fluid versus viscous forces) |
Transmittance | T | ![T={\frac {I}{I_{0}}}](../I/m/f04a619c8518e69512d6b716710f65529be0b39f.svg) | optics, spectroscopy (the ratio of the intensities of radiation exiting through and incident on a sample) |
Ursell number | U | ![\mathrm{U} = \frac{H\, \lambda^2}{h^3}](../I/m/747b64f6dcf9bb35f837f0d67542d430f4c988d5.svg) | wave mechanics (nonlinearity of surface gravity waves on a shallow fluid layer) |
Vadasz number | Va | ![\mathrm{Va} = \frac{\phi\, \mathrm{Pr}}{\mathrm{Da}}](../I/m/1aab10de3591c4196db3380538e0360fd77cf7f3.svg) | porous media (governs the effects of porosity , the Prandtl number and the Darcy number on flow in a porous medium) [24] |
van 't Hoff factor | i | ![i = 1 + \alpha (n - 1)](../I/m/6727544fcf66acc52fb8c0d7a05379f9c75656c4.svg) | quantitative analysis (Kf and Kb) |
Wallis parameter | j* | ![j^* = R \left( \frac{\omega \rho}{\mu} \right)^\frac{1}{2}](../I/m/e2dc1efa4377898e665e821afc8a6bc0758789ca.svg) | multiphase flows (nondimensional superficial velocity)[25] |
Weaver flame speed number | Wea | | combustion (laminar burning velocity relative to hydrogen gas)[26] |
Weber number | We | ![\mathrm{We} = \frac{\rho v^2 l}{\sigma}](../I/m/af88baa80544c927dfa26c08f471599a0fbd8e11.svg) | multiphase flow (strongly curved surfaces; ratio of inertia to surface tension) |
Weissenberg number | Wi | ![\mathrm{Wi} = \dot{\gamma} \lambda](../I/m/305734fece08e48422d34c81a0c723e0c681f026.svg) | viscoelastic flows (shear rate times the relaxation time)[27] |
Womersley number | | ![\alpha = R \left( \frac{\omega \rho}{\mu} \right)^\frac{1}{2}](../I/m/2c707dfd9e4ceacf3d3e64f36dcbd77bab5923c4.svg) | biofluid mechanics (continuous and pulsating flows; ratio of pulsatile flow frequency to viscous effects)[28] |