Name
|
Standard symbol
|
Definition
|
Field of application
|
Archimedes number |
Ar |
|
fluid mechanics (motion of
fluids due to
density differences)
|
Asakuma number |
As |
|
heat transfer (ratio of heat generation of
microwave
dielectric heating to thermal diffusion
[6]
|
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)
[7]
|
Bejan number (
fluid mechanics) |
Be |
|
fluid mechanics (dimensionless
pressure drop along a
channel)
[8]
|
Bejan number (
thermodynamics) |
Be |
|
thermodynamics (ratio of
heat transfer
irreversibility to total irreversibility due to heat transfer and
fluid friction)
[9]
|
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)
|
Bond number |
Bo |
|
geology,
fluid mechanics,
porous media (
buoyant versus
capillary forces, similar to the
Eötvös number)
[10]
|
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)
[11]
|
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)
|
Darcy friction factor |
Cf or fD |
|
fluid mechanics (fraction of
pressure losses due to
friction in a
pipe; four times the
Fanning friction factor)
|
Dean number |
D |
|
turbulent flow (
vortices in curved ducts)
|
Deborah number |
De |
|
rheology (
viscoelastic fluids)
|
Drag coefficient |
cd |
|
aeronautics,
fluid dynamics (resistance to fluid motion)
|
Eckert number |
Ec |
|
convective heat transfer (characterizes
dissipation of
energy; ratio of
kinetic energy to
enthalpy)
|
Ekman number |
Ek |
|
geophysics (
viscous versus
Coriolis forces)
|
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)
|
Excess temperature coefficient |
|
|
heat transfer,
fluid dynamics (change in
internal energy versus
kinetic energy)
[12]
|
Fanning friction factor |
f |
|
fluid mechanics (fraction of
pressure losses due to
friction in a
pipe; 1/4th the
Darcy friction factor)
[13]
|
Fourier number |
Fo |
|
heat transfer,
mass transfer (ratio of diffusive rate versus storage rate)
|
Froude number |
Fr |
|
fluid mechanics (
wave and
surface behaviour; ratio of a body's
inertia to
gravitational forces)
|
Galilei number |
Ga |
|
fluid mechanics (
gravitational over
viscous forces)
|
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)
|
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)
|
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)
|
Kutateladze number |
Ku |
|
fluid mechanics (counter-current
two-phase flow)
[14]
|
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)
[15]
|
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)
[16]
|
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)
|
Péclet number |
Pe |
|
mass transfer (
advection–
diffusion problems; total
momentum transfer to diffusive mass transfer)
|
Prandtl number |
Pr |
|
heat transfer (ratio of
viscous diffusion rate over
thermal diffusion rate)
|
Pressure coefficient |
CP |
|
aerodynamics,
hydrodynamics (
pressure experienced at a point on an
airfoil; dimensionless pressure variable)
|
Rayleigh number |
Ra |
|
heat transfer (
buoyancy versus
viscous forces in
free convection)
|
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)
[17]
|
Roshko number |
Ro |
|
fluid dynamics (oscillating flow,
vortex
shedding)
|
Schmidt number |
Sc |
|
mass transfer (
viscous over molecular
diffusion rate)
[18]
|
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)
|
Sommerfeld number |
S |
|
hydrodynamic lubrication (boundary
lubrication)
[19]
|
Stanton number |
St |
|
heat transfer and
fluid dynamics (forced
convection)
|
Stokes number |
Stk or Sk |
|
particles suspensions (ratio of characteristic
time of particle to time of flow)
|
Strouhal number |
St or Sr |
|
fluid dynamics (continuous and pulsating flow; nondimensional
frequency)
[20]
|
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)
|
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)
[21]
|
Wallis parameter |
j* |
|
multiphase flows (nondimensional
superficial velocity)
[22]
|
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)
[23]
|
Womersley number |
|
|
biofluid mechanics (continuous and pulsating flows; ratio of
pulsatile flow
frequency to
viscous effects)
[24]
|
Zel'dovich number |
|
|
fluid dynamics,
Combustion (Measure of
activation energy)
|