Name |
Standard symbol |
Definition |
Field of application |
Abbe number | V |
| optics (dispersion in optical materials) |
Activity coefficient |
|
| chemistry (Proportion of "active" molecules or atoms) |
Albedo |
|
| climatology, astronomy (reflectivity of surfaces or bodies) |
Archimedes number | Ar |
| 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 |
| 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 |
| fluid mechanics, rheology (ratio of yield stress to viscous stress)[1] |
Biot number | Bi |
| 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 |
| geology, fluid mechanics, porous media (buoyant versus capillary forces, similar to the Eötvös number) [6] |
Brinkman number | Br |
| 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) |
Cohesion number |
Coh |
|
Chemical engineering, material science, mechanics (A scale to show the energy needed for detaching two solid particles)[8][9] |
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)[10] |
Damkohler number | Da |
| chemistry (reaction time scales vs. residence time) |
Damping ratio |
|
| 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 |
| 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 |
|
| heat transfer, fluid dynamics (change in internal energy versus kinetic energy)[11] |
Fanning friction factor | f | | fluid mechanics (fraction of pressure losses due to friction in a pipe; 1/4th the Darcy friction factor)[12] |
Feigenbaum constants |
,
|
| chaos theory (period doubling)[13] |
Fine-structure constant |
|
| 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)[14] |
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)[15] |
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 |
|
| 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) |
Havnes parameter |
|
| In Dusty plasma physics, ratio of the total charge
carried by the dust particles
to the charge carried by the ions
, with
the number density of particles |
Helmholtz number |
|
| The most important parameter in duct acoustics. If
is the dimensional frequency, then
is the corresponding free field wavenumber and
is the corresponding dimensionless frequency [16] |
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 |
| chemistry (ratio of sensible to latent energy absorbed during liquid-vapor phase change)[17] |
Karlovitz number | Ka |
| turbulent combustion (characteristic chemical time scale to Kolmogorov time scale) |
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)[18] |
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)[19] |
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)[20] |
Marangoni number | Mg |
| fluid mechanics (Marangoni flow; thermal surface tension forces over viscous forces) |
Markstein number |
|
| fluid dynamics, combustion (turbulent combustion flames) |
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 |
| heat transfer (advection–diffusion problems; total momentum transfer to molecular heat transfer) |
Peel number | NP |
| coating (adhesion of microstructures with substrate)[21] |
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) |
Beta (plasma physics) |
|
| Plasma (physics) and Fusion power. Ratio of plasma thermal pressure to magnetic pressure, controlling the level of turbulence in a magnetised plasma. |
Poisson's ratio |
|
| elasticity (strain in transverse and longitudinal direction) |
Porosity |
|
| geology, porous media (void fraction of the medium) |
Power factor | pf |
|
electrical (real power to apparent power) |
Power number | Np |
| electronics (power consumption by agitators; resistance force versus inertia force) |
Prandtl number | Pr |
| 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)[22] |
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)[23] |
Rockwell scale | – | | mechanical hardness (indentation hardness of a material) |
Rolling resistance coefficient | Crr |
| 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)[24] |
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)[25] |
Specific gravity | SG | | (same as Relative density) |
Stanton number | St |
| heat transfer and fluid dynamics (forced convection) |
Stefan number | Ste |
| phase change, thermodynamics (ratio of sensible heat to latent heat) |
Stokes number | Stk or Sk |
| particles suspensions (ratio of characteristic time of particle to time of flow) |
Strain |
|
| materials science, elasticity (displacement between particles in the body relative to a reference length) |
Strouhal number | St or Sr |
| fluid dynamics (continuous and pulsating flow; nondimensional frequency)[26] |
Stuart number | N |
| magnetohydrodynamics (ratio of electromagnetic to inertial forces) |
Taylor number | Ta |
| fluid dynamics (rotating fluid flows; inertial forces due to rotation of a fluid versus viscous forces) |
Transmittance | T |
| optics, spectroscopy (the ratio of the intensities of radiation exiting through and incident on a sample) |
Ursell number | U |
| wave mechanics (nonlinearity of surface gravity waves on a shallow fluid layer) |
Vadasz number | Va |
| porous media (governs the effects of porosity
, the Prandtl number and the Darcy number on flow in a porous medium) [27] |
van 't Hoff factor | i |
| quantitative analysis (Kf and Kb) |
Wallis parameter | j* |
| multiphase flows (nondimensional superficial velocity)[28] |
Weaver flame speed number | Wea |
| combustion (laminar burning velocity relative to hydrogen gas)[29] |
Weber number | We |
| multiphase flow (strongly curved surfaces; ratio of inertia to surface tension) |
Weissenberg number | Wi |
| viscoelastic flows (shear rate times the relaxation time)[30] |
Womersley number |
|
| biofluid mechanics (continuous and pulsating flows; ratio of pulsatile flow frequency to viscous effects)[31] |
Zel'dovich number |
|
| fluid dynamics, Combustion (Measure of activation energy) |