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)
|