Name Definition Field of application

Abbe No. V

optics (dispersion in optical materials)

Activity

coefficient

chemistry (Proportion of "active" molecules or

atoms)

Albedo

climatology, astronomy (reflectivity of surfaces or

bodies)

Archimedes No. Ar

fluid mechanics (motion of fluids due

to density differences)

Arrhenius No.

chemistry (ratio of activation energy to thermal

energy)[5]

Atomic weight M

chemistry (mass of atom over one atomic mass

unit, u, where carbon-12 is exactly 12 u)

Atwood No. A

fluid mechanics (onset of instabilities

in fluid mixtures due to density differences)

Bagnold No. Ba

fluid mechanics, geology (ratio of grain collision

stresses to viscous fluid stresses in flow of

agranular material such as grain and sand)[6]

Bejan No.

(fluid mechanics) Be

fluid mechanics (dimensionless pressure drop

along a channel)[7]

Bejan No.

(thermodynamics) Be

thermodynamics (ratio of heat

transfer irreversibility to total irreversibility due to

heat transfer andfluid friction)[8]

Name Definition Field of application

Bingham No. Bm

fluid mechanics, rheology (ratio of yield stress to

viscous stress)[5]

Biot No. Bi

heat transfer (surface vs. volume conductivity of

solids)

Blake No. Bl or B

geology, fluid mechanics, porous media (inertial

over viscous forces in fluid flow through porous

media)

Bodenstein No. Bo or Bd

chemistry (residence-time distribution; similar to

the axial mass transfer Peclet No.)[9]

Bond No. Bo

geology, fluid mechanics, porous

media (buoyant versus capilary forces, similar to

the Eötvös No.) [10]

Brinkman No. Br

heat transfer, fluid mechanics (conduction from a

wall to a viscous fluid)

Brownell–Katz

No.

NBK

fluid mechanics (combination of capillary

No. and Bond No.) [11]

Capillary No. Ca

porous media, fluid mechanics (viscous

forces versus surface tension)

Chandrasekhar

No.

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)

Name Definition Field of application

Coefficient of

kinetic friction

mechanics (friction of solid bodies in translational

motion)

Coefficient of

static friction

mechanics (friction of solid bodies at rest)

Courant–

Friedrich–Levy

No.

C or 𝜈

mathematics (numerical solutions of hyperbolic

PDEs)[12]

Damkohler No. 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 No. Da

porous media (ratio of permeability to cross-

sectional area)

Dean No. D

turbulent flow (vortices in curved ducts)

Deborah No. De

rheology (viscoelastic fluids)

Decibel dB

acoustics, electronics, control theory (ratio of

two intensities or powers of a wave)

Name Definition Field of application

Drag coefficient cd

aeronautics, fluid dynamics (resistance to fluid

motion)

Dukhin No. Du

colloid science (ratio of electric surface

conductivity to the electric bulk conductivity

inheterogeneous systems)

Eckert No. Ec

convective heat

transfer (characterizes dissipation of energy; ratio

of kinetic energy to enthalpy)

Ekman No. Ek

geophysics (viscous versus Coriolis forces)

Elasticity

(economics) E

economics (response

of demand or supply to price changes)

Eötvös No. Eo

fluid mechanics (shape of bubbles or drops)

Ericksen No. Er

fluid dynamics (liquid crystal flow

behavior; viscous over elastic forces)

Euler No. Eu

hydrodynamics (stream pressure versus inertia for

ces)

Euler's No. e

mathematics (base of the natural logarithm)

Name Definition Field of application

Excess

temperature

coefficient

heat transfer, fluid dynamics (change in internal

energy versus kinetic energy)[13]

Fanning friction

factor

f

fluid mechanics (fraction of pressure losses due

to friction in a pipe; 1/4th the Darcy friction

factor)[14]

Feigenbaum

constants

,

chaos theory (period doubling)[15]

Fine structure

constant

quantum electrodynamics (QED) (coupling

constant characterizing the strength of

theelectromagnetic interaction)

f-No. f

optics, photography (ratio of focal

length to diameter of aperture)

Föppl–von

Kármán No.

virology, solid mechanics (thin-shell buckling)

Fourier No. Fo

heat transfer, mass transfer (ratio of diffusive rate

versus storage rate)

Fresnel No. F

optics (slit diffraction)[16]

Froude No. Fr

fluid mechanics (wave and surface behaviour;

ratio of a body's inertia to gravitational forces)

Gain –

electronics (signal output to signal input)

Name Definition Field of application

Gain ratio –

bicycling (system of representing gearing; length

traveled over length pedaled)[17]

Galilei No. Ga

fluid mechanics (gravitational over viscous forces)

Golden ratio

mathematics, aesthetics (long side length of self-

similar rectangle)

Görtler No. G

fluid dynamics (boundary layer flow along a

concave wall)

Graetz No. Gz

heat transfer, fluid mechanics (laminar

flow through a conduit; also used in mass

transfer)

Grashof No. 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 No. Ha

chemical engineering (adsorption enhancement

due to chemical reaction)

Hagen No. Hg

heat transfer (ratio of

the buoyancy to viscous force in forced

convection)

Name Definition Field of application

Hydraulic

gradient

i

fluid mechanics, groundwater flow (pressure

head over distance)

Iribarren No. Ir

wave mechanics (breaking surface gravity

waves on a slope)

Jakob No. Ja

chemistry (ratio of sensible to latent

energy absorbed during liquid-vapor phase

change)[18]

Karlovitz No. Ka

turbulent combustion (characteristic flow time

times flame stretch rate)

Keulegan–

Carpenter No.

KC

fluid dynamics (ratio of drag force to inertia for a

bluff object in oscillatory fluid flow)

Knudsen No. 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 No. Ku

fluid mechanics (counter-current two-phase

flow)[19]

Laplace No. La

fluid dynamics (free

convection within immiscible fluids; ratio

of surface tension to momentum-transport)

Name Definition Field of application

Lewis No. 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)[20]

Love No.s h, k, l

geophysics (solidity of earth and other planets)

Lundquist No. S

plasma physics (ratio of a resistive time to

an Alfvén wave crossing time in a plasma)

Mach No. M or Ma

gas dynamics (compressible flow;

dimensionless velocity)

Magnetic

Reynolds No.

Rm

magnetohydrodynamics (ratio of

magnetic advection to magnetic diffusion)

Manning

roughness

coefficient

n

open channel flow (flow driven by gravity)[21]

Marangoni No. Mg

fluid mechanics (Marangoni flow; thermal surface

tension forces over viscous forces)

Morton No. Mo

fluid dynamics (determination

of bubble/drop shape)

Name Definition Field of application

Nusselt No. Nu

heat transfer (forced convection; ratio

of convective to conductive heat transfer)

Ohnesorge No. Oh

fluid dynamics (atomization of liquids, Marangoni

flow)

Péclet No. Pe

heat transfer (advection–diffusion problems;

total momentum transfer to molecular heat

transfer)

Peel No. NP

coating (adhesion of microstructures with substrat

e)[22]

Perveance K

charged particle transport (measure of the

strength of space charge in a charged particle

beam)

Pi

mathematics (ratio of a circle's circumference to

its diameter)

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 No. Np

electronics (power consumption by

agitators; resistance force versus inertia force)

Name Definition Field of application

Prandtl No. Pr

heat transfer (ratio of viscous diffusion rate

over thermal diffusion rate)

Prater No. β

reaction engineering (ratio of heat evolution

to heat conduction within a catalyst pellet)[23]

Pressure

coefficient

CP

aerodynamics, hydrodynamics (pressure experien

ced at a point on an airfoil; dimensionless

pressure variable)

Q factor Q

physics, engineering (damping of oscillator or res

onator; energy stored versus energy lost)

Radian measure rad

mathematics (measurement of planar angles, 1

radian = 180/π degrees)

Rayleigh No. 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—

usuallywater)

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 v. vacuum)

Name Definition Field of application

Reynolds No. Re

fluid mechanics (ratio of

fluid inertial and viscous forces)[5]

Richardson No. Ri

fluid dynamics (effect of buoyancy on flow

stability; ratio of potential over kinetic energy)[24]

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 No. Ro

fluid dynamics (oscillating flow, vortex shedding)

Rossby No. Ro

geophysics (ratio of inertial to Coriolis force)

Rouse No. P or Z

sediment transport (ratio of the sediment fall

velocity and the upwards velocity of grain)

Schmidt No. Sc

mass transfer (viscous over

molecular diffusion rate)[25]

Shape factor H

boundary layer flow (ratio of displacement

thickness to momentum thickness)

Sherwood No. Sh

mass transfer (forced convection; ratio

of convective to diffusive mass transport)

Name Definition Field of application

Shields

parameter

or

sediment transport (threshold of sediment

movement due to fluid motion;

dimensionless shear stress)

Sommerfeld No. S

hydrodynamic lubrication (boundary lubrication)[26]

Specific gravity SG

(same as Relative density)

Stanton No. St

heat transfer and fluid

dynamics (forced convection)

Stefan No. Ste

phase change, thermodynamics (ratio of sensible

heat to latent heat)

Stokes No. 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 No. St or Sr

fluid dynamics (continuous and pulsating flow;

nondimensional frequency)[27]

Stuart No. N

magnetohydrodynamics (ratio

of electromagnetic to inertial forces)

Taylor No. Ta

fluid dynamics (rotating fluid flows; inertial forces

due to rotation of a fluid versus viscous forces)

Name Definition Field of application

Ursell No. U

wave mechanics (nonlinearity of surface gravity

waves on a shallow fluid layer)

Vadasz No. Va

porous media (governs the effects of porosity ,

the Prandtl No. and the Darcy No. on flow in

a porous medium) [28]

van 't Hoff factor i

quantitative analysis (Kf and Kb)

Wallis

parameter

j*

multiphase flows (nondimensional superficial

velocity)[29]

Weaver flame

speed No.

Wea

combustion (laminar burning velocity relative

to hydrogen gas)[30]

Weber No. We

multiphase flow (strongly curved surfaces; ratio

of inertia to surface tension)

Weissenberg

No.

Wi

viscoelastic flows (shear rate times the relaxation

time)[31]

Womersley No.

biofluid mechanics (continuous and pulsating

flows; ratio of pulsatile flow frequency to viscous

effects)[32]