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]