Name

Standard symbol

Definition

Field of application

Abbe number 
V 
$V\; =\; \backslash frac\{\; n\_d\; \; 1\; \}\{\; n\_F\; \; n\_C\; \}$ 
optics (dispersion in optical materials)

Activity coefficient 
$\backslash gamma$ 
$\backslash gamma=\; \backslash frac$ 
chemistry (Proportion of "active" molecules or atoms)

Albedo 
$\backslash alpha$ 
$\{\backslash alpha\}=\; (1D)\; \backslash bar\; \backslash alpha(\backslash theta\_i)\; +\; D\; \backslash bar\{\; \backslash bar\; \backslash alpha\}$ 
climatology, astronomy (reflectivity of surfaces or bodies)

Archimedes number 
Ar 
$\backslash mathrm\{Ar\}\; =\; \backslash frac\{g\; L^3\; \backslash rho\_\backslash ell\; (\backslash rho\; \; \backslash rho\_\backslash ell)\}\{\backslash mu^2\}$ 
fluid mechanics (motion of fluids due to density differences)

Arrhenius number 
$\backslash alpha$ 
$\backslash alpha\; =\; \backslash frac\{E\_a\}\{RT\}$ 
chemistry (ratio of activation energy to thermal energy)^{[5]}

Atomic weight 
M 

chemistry (mass of atom over one atomic mass unit, u, where carbon12 is exactly 12 u)

Atwood number 
A 
$\backslash mathrm\{A\}\; =\; \backslash frac\{\backslash rho\_1\; \; \backslash rho\_2\}\; \{\backslash rho\_1\; +\; \backslash rho\_2\}$ 
fluid mechanics (onset of instabilities in fluid mixtures due to density differences)

Bagnold number 
Ba 
$\backslash mathrm\{Ba\}\; =\; \backslash frac\{\backslash rho\; d^2\; \backslash lambda^\{1/2\}\; \backslash gamma\}\{\backslash mu\}$ 
fluid mechanics, geology (ratio of grain collision stresses to viscous fluid stresses in flow of a granular material such as grain and sand)^{[6]}

Bejan number (fluid mechanics) 
Be 
$\backslash mathrm\{Be\}\; =\; \backslash frac\{\backslash Delta\; P\; L^2\}\; \{\backslash mu\; \backslash alpha\}$ 
fluid mechanics (dimensionless pressure drop along a channel)^{[7]}

Bejan number (thermodynamics) 
Be 
$\backslash mathrm\{Be\}\; =\; \backslash frac\{\backslash dot\; S\text{'}\_\{\backslash mathrm\{gen\},\backslash ,\; \backslash Delta\; T\}\}\{\backslash dot\; S\text{'}\_\{\backslash mathrm\{gen\},\backslash ,\; \backslash Delta\; T\}+\; \backslash dot\; S\text{'}\_\{\backslash mathrm\{gen\},\backslash ,\; \backslash Delta\; p\}\}$ 
thermodynamics (ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction)^{[8]}

Bingham number 
Bm 
$\backslash mathrm\{Bm\}\; =\; \backslash frac\{\; \backslash tau\_y\; L\; \}\{\; \backslash mu\; V\; \}$ 
fluid mechanics, rheology (ratio of yield stress to viscous stress)^{[5]}

Biot number 
Bi 
$\backslash mathrm\{Bi\}\; =\; \backslash frac\{h\; L\_C\}\{k\_b\}$ 
heat transfer (surface vs. volume conductivity of solids)

Blake number 
Bl or B 
$\backslash mathrm\{B\}\; =\; \backslash frac\{u\; \backslash rho\}\{\backslash mu\; (1\; \; \backslash epsilon)\; D\}$ 
geology, fluid mechanics, porous media (inertial over viscous forces in fluid flow through porous media)

Bodenstein number 
Bo or Bd 
$\backslash mathrm\{Bo\}\; =\; vL/\backslash mathcal\{D\}\; =\; \backslash mathrm\{Re\}\backslash ,\; \backslash mathrm\{Sc\}$ 
chemistry (residencetime distribution; similar to the axial mass transfer Peclet number)^{[9]}

Bond number 
Bo 
$\backslash mathrm\{Bo\}\; =\; \backslash frac\{\backslash rho\; a\; L^2\}\{\backslash gamma\}$ 
geology, fluid mechanics, porous media (buoyant versus capilary forces, similar to the Eötvös number) ^{[10]}

Brinkman number 
Br 
$\backslash mathrm\{Br\}\; =\; \backslash frac\; \{\backslash mu\; U^2\}\{\backslash kappa\; (T\_w\; \; T\_0)\}$ 
heat transfer, fluid mechanics (conduction from a wall to a viscous fluid)

Brownell–Katz number 
N_{BK} 
$\backslash mathrm\{N\}\_\backslash mathrm\{BK\}\; =\; \backslash frac\{u\; \backslash mu\}\{k\_\backslash mathrm\{rw\}\backslash sigma\}$ 
fluid mechanics (combination of capillary number and Bond number) ^{[11]}

Capillary number 
Ca 
$\backslash mathrm\{Ca\}\; =\; \backslash frac\{\backslash mu\; V\}\{\backslash gamma\}$ 
porous media (viscous forces versus surface tension)

Chandrasekhar number 
Q 
$\backslash mathrm\{Q\}\; =\; \backslash frac$ 
mechanics (the level of damping in a system)

Darcy friction factor 
C_{f} or f_{D} 

fluid mechanics (fraction of pressure losses due to friction in a pipe; four times the Fanning friction factor)

Darcy number 
Da 
$\backslash mathrm\{Da\}\; =\; \backslash frac\{K\}\{d^2\}$ 
porous media (ratio of permeability to crosssectional area)

Dean number 
D 
$\backslash mathrm\{D\}\; =\; \backslash frac\{\backslash rho\; V\; d\}\{\backslash mu\}\; \backslash left(\; \backslash frac\{d\}\{2\; R\}\; \backslash right)^\{1/2\}$ 
turbulent flow (vortices in curved ducts)

Deborah number 
De 
$\backslash mathrm\{De\}\; =\; \backslash frac\{t\_\backslash mathrm\{c\}\}\{t\_\backslash mathrm\{p\}\}$ 
rheology (viscoelastic fluids)

Decibel 
dB 

acoustics, electronics, control theory (ratio of two intensities or powers of a wave)

Drag coefficient 
c_{d} 
$c\_\backslash mathrm\{d\}\; =\; \backslash dfrac\{2\; F\_\backslash mathrm\{d\}\}\{\backslash rho\; v^2\; A\}\backslash ,\; ,$ 
aeronautics, fluid dynamics (resistance to fluid motion)

Dukhin number 
Du 
$\backslash mathrm\{Du\}\; =\; \backslash frac\{\backslash kappa^\{\backslash sigma\}\}\{L\; \backslash lambda\}$ 
optics (slit diffraction)^{[17]}

Froude number 
Fr 
$\backslash mathrm\{Fr\}\; =\; \backslash frac\{v\}\{\backslash sqrt\{g\backslash ell\}\}$ 
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)^{[18]}

Galilei number 
Ga 
$\backslash mathrm\{Ga\}\; =\; \backslash frac\{g\backslash ,\; L^3\}\{\backslash nu^2\}$ 
fluid mechanics (gravitational over viscous forces)

Golden ratio 
$\backslash varphi$ 
$\backslash varphi\; =\; \backslash frac\{1+\backslash sqrt\{5\}\}\{2\}\; \backslash approx\; 1.61803$ 
mathematics, aesthetics (long side length of selfsimilar rectangle)

Görtler number 
G 
$\backslash mathrm\{G\}\; =\; \backslash frac\{U\_e\; \backslash theta\}\{\backslash nu\}\; \backslash left(\; \backslash frac\{\backslash theta\}\{R\}\; \backslash right)^\{1/2\}$ 
fluid dynamics (boundary layer flow along a concave wall)

Graetz number 
Gz 
$\backslash mathrm\{Gz\}\; =\; \{D\_H\; \backslash over\; L\}\; \backslash mathrm\{Re\}\backslash ,\; \backslash mathrm\{Pr\}$ 
heat transfer, fluid mechanics (laminar flow through a conduit; also used in mass transfer)

Grashof number 
Gr 
$\backslash mathrm\{Gr\}\_L\; =\; \backslash frac\{g\; \backslash beta\; (T\_s\; \; T\_\backslash infty\; )\; L^3\}\{\backslash nu\; ^2\}$ 
heat transfer, natural convection (ratio of the buoyancy to viscous force)

Gravitational coupling constant 
$\backslash alpha\_G$ 
$\backslash alpha\_G=\backslash frac\{Gm\_e^2\}\{\backslash hbar\; c\}$ 
gravitation (attraction between two massy elementary particles; analogous to the Fine structure constant)

Hatta number 
Ha 
$\backslash mathrm\{Ha\}\; =\; \backslash frac\{N\_\{\backslash mathrm\{A\}0\}\}\{N\_\{\backslash mathrm\{A\}0\}^\{\backslash mathrm\{phys\}\}\}$ 
chemical engineering (adsorption enhancement due to chemical reaction)

Hagen number 
Hg 
$\backslash mathrm\{Hg\}\; =\; \backslash frac\{1\}\{\backslash rho\}\backslash frac\{\backslash mathrm\{d\}\; p\}\{\backslash mathrm\{d\}\; x\}\backslash frac\{L^3\}\{\backslash nu^2\}$ 
heat transfer (ratio of the buoyancy to viscous force in forced convection)

Hydraulic gradient 
i 
$i\; =\; \backslash frac\{\backslash mathrm\{d\}h\}\{\backslash mathrm\{d\}l\}\; =\; \backslash frac\{h\_2\; \; h\_1\}\{\backslash mathrm\{length\}\}$ 
fluid mechanics, groundwater flow (pressure head over distance)

Iribarren number 
Ir 
$\backslash mathrm\{Ir\}\; =\; \backslash frac\{\backslash tan\; \backslash alpha\}\{\backslash sqrt\{H/L\_0\}\}$ 
wave mechanics (breaking surface gravity waves on a slope)

Jakob Number 
Ja 
$\backslash mathrm\{Ja\}\; =\; \backslash frac\{c\_p\; (T\_\backslash mathrm\{s\}\; \; T\_\backslash mathrm\{sat\})\; \}\{\backslash Delta\; H\_\{\backslash mathrm\{f\}\}\; \}$ 
chemistry (ratio of sensible to latent energy absorbed during liquidvapor phase change)^{[19]}

Karlovitz number 
Ka 
$\backslash mathrm\{Ka\}\; =\; k\; t\_c$ 
turbulent combustion (characteristic flow time times flame stretch rate)

Keulegan–Carpenter number 
K_{C} 
$\backslash mathrm\{K\_C\}\; =\; \backslash frac\{V\backslash ,T\}\{L\}$ 
fluid dynamics (ratio of drag force to inertia for a bluff object in oscillatory fluid flow)

Knudsen number 
Kn 
$\backslash mathrm\{Kn\}\; =\; \backslash frac\; \{\backslash lambda\}\{L\}$ 
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 
$\backslash mathrm\{Ku\}\; =\; \backslash frac\{U\_h\; \backslash rho\_g^\{1/2\}\}\{\backslash left(\{\backslash sigma\; g\; (\backslash rho\_l\; \; \backslash rho\_g)\}\backslash right)^\{1/4\}\}$ 
fluid mechanics (countercurrent twophase flow)^{[20]}

Laplace number 
La 
$\backslash mathrm\{La\}\; =\; \backslash frac\{\backslash sigma\; \backslash rho\; L\}\{\backslash mu^2\}$ 
fluid dynamics (free convection within immiscible fluids; ratio of surface tension to momentumtransport)

Lewis number 
Le 
$\backslash mathrm\{Le\}\; =\; \backslash frac\{\backslash alpha\}\{D\}\; =\; \backslash frac\{\backslash mathrm\{Sc\}\}\{\backslash mathrm\{Pr\}\}$ 
heat and mass transfer (ratio of thermal to mass diffusivity)

Lift coefficient 
C_{L} 
$C\_\backslash mathrm\{L\}\; =\; \backslash frac\{L\}\{q\backslash ,S\}$ 
aerodynamics (lift available from an airfoil at a given angle of attack)

Lockhart–Martinelli parameter 
$\backslash chi$ 
$\backslash chi\; =\; \backslash frac\{m\_\backslash ell\}\{m\_g\}\; \backslash sqrt\{\backslash frac\{\backslash rho\_g\}\{\backslash rho\_\backslash ell\}\}$ 
twophase flow (flow of wet gases; liquid fraction)^{[21]}

Love numbers 
h, k, l 

geophysics (solidity of earth and other planets)

Lundquist number 
S 
$S\; =\; \backslash frac\{\backslash mu\_0LV\_A\}\{\backslash eta\}$ 
plasma physics (ratio of a resistive time to an Alfvén wave crossing time in a plasma)

Mach number 
M or Ma 
$\backslash mathrm\{M\}\; =\; \backslash frac$} 
gas dynamics (compressible flow; dimensionless velocity)

Magnetic Reynolds number 
R_{m} 
$\backslash mathrm\{R\}\_\backslash mathrm\{m\}\; =\; \backslash frac\{U\; L\}\{\backslash eta\}$ 
magnetohydrodynamics (ratio of magnetic advection to magnetic diffusion)

Manning roughness coefficient 
n 

open channel flow (flow driven by gravity)^{[22]}

Marangoni number 
Mg 
$\backslash mathrm\{Mg\}\; =\; \; \{\backslash frac\{\backslash mathrm\{d\}\backslash sigma\}\{\backslash mathrm\{d\}T\}\}\backslash frac\{L\; \backslash Delta\; T\}\{\backslash eta\; \backslash alpha\}$ 
fluid mechanics (Marangoni flow; thermal surface tension forces over viscous forces)

Morton number 
Mo 
$\backslash mathrm\{Mo\}\; =\; \backslash frac\{g\; \backslash mu\_c^4\; \backslash ,\; \backslash Delta\; \backslash rho\}\{\backslash rho\_c^2\; \backslash sigma^3\}$ 
fluid dynamics (determination of bubble/drop shape)

Nusselt number 
Nu 
$\backslash mathrm\{Nu\}\; =\backslash frac\{hd\}\{k\}$ 
heat transfer (forced convection; ratio of convective to conductive heat transfer)

Ohnesorge number 
Oh 
$\backslash mathrm\{Oh\}\; =\; \backslash frac\{\; \backslash mu\}\{\; \backslash sqrt\{\backslash rho\; \backslash sigma\; L\; \}\}\; =\; \backslash frac\{\backslash sqrt\{\backslash mathrm\{We\}\}\}\{\backslash mathrm\{Re\}\}$ 
fluid dynamics (atomization of liquids, Marangoni flow)

Péclet number 
Pe 
$\backslash mathrm\{Pe\}\; =\; \backslash frac\{du\backslash rho\; c\_p\}\{k\}\; =\; \backslash mathrm\{Re\}\backslash ,\; \backslash mathrm\{Pr\}$ 
heat transfer (advection–diffusion problems; total momentum transfer to molecular heat transfer)

Peel number 
N_{P} 
$N\_\backslash mathrm\{P\}\; =\; \backslash frac\{\backslash text\{Restoring\; force\}\}\{\backslash text\{Adhesive\; force\}\}$ 
coating (adhesion of microstructures with substrate)^{[23]}

Perveance 
K 
$\{K\}\; =\; \backslash frac$\,\frac{\mathrm{d}\varepsilon_\mathrm{axial}} 
elasticity (load in transverse and longitudinal direction)

Porosity 
$\backslash phi$ 
$\backslash phi\; =\; \backslash frac\{V\_\backslash mathrm\{V\}\}\{V\_\backslash mathrm\{T\}\}$ 
geology, porous media (void fraction of the medium)

Power factor 
P/S 

electronics (real power to apparent power)

Power number 
N_{p} 
$N\_\{p\}\; =\; \{P\backslash over\; \backslash rho\; n^\{3\}\; d^\{5\}\}$ 
electronics (power consumption by agitators; resistance force versus inertia force)

Prandtl number 
Pr 
$\backslash mathrm\{Pr\}\; =\; \backslash frac\{\backslash nu\}\{\backslash alpha\}\; =\; \backslash frac\{c\_p\; \backslash mu\}\{k\}$ 
heat transfer (ratio of viscous diffusion rate over thermal diffusion rate)

Prater number 
β 
$\backslash beta\; =\; \backslash frac\{\backslash Delta\; H\_r\; D\_\{TA\}^e\; C\_\{AS\}\}\{\backslash lambda^e\; T\_s\}$ 
reaction engineering (ratio of heat evolution to heat conduction within a catalyst pellet)^{[24]}

Pressure coefficient 
C_{P} 
$C\_p\; =\; \{p\; \; p\_\backslash infty\; \backslash over\; \backslash frac\{1\}\{2\}\; \backslash rho\_\backslash infty\; V\_\backslash infty^2\}$ 
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 
$\backslash text\{arc\; length\}/\backslash text\{radius\}$ 
mathematics (measurement of planar angles, 1 radian = 180/π degrees)

Rayleigh number 
Ra 
$\backslash mathrm\{Ra\}\_\{x\}\; =\; \backslash frac\{g\; \backslash beta\}\; \{\backslash nu\; \backslash alpha\}\; (T\_s\; \; T\_\backslash infin)\; x^3$ 
heat transfer (buoyancy versus viscous forces in free convection)

Refractive index 
n 
$n=\backslash frac\{c\}\{v\}$ 
electromagnetism, optics (speed of light in a vacuum over speed of light in a material)

Relative density 
RD 
$RD\; =\; \backslash frac\{\backslash rho\_\backslash mathrm\{substance\}\}\{\backslash rho\_\backslash mathrm\{reference\}\}$ 
hydrometers, material comparisons (ratio of density of a material to a reference material—usually water)

Relative permeability 
$\backslash mu\_r$ 
$\backslash mu\_r\; =\; \backslash frac\{\backslash mu\}\{\backslash mu\_0\}$ 
magnetostatics (ratio of the permeability of a specific medium to free space)

Relative permittivity 
$\backslash varepsilon\_r$ 
$\backslash varepsilon\_\{r\}\; =\; \backslash frac\{C\_\{x\}\}\; \{C\_\{0\}\}$ 
electrostatics (ratio of capacitance of test capacitor with dielectric material versus vacuum)

Reynolds number 
Re 
$\backslash mathrm\{Re\}\; =\; \backslash frac\{vL\backslash rho\}\{\backslash mu\}$ 
fluid mechanics (ratio of fluid inertial and viscous forces)^{[5]}

Richardson number 
Ri 
$\backslash mathrm\{Ri\}\; =\; \backslash frac\{gh\}\{u^2\}\; =\; \backslash frac\{1\}\{\backslash mathrm\{Fr\}^2\}$ 
fluid dynamics (effect of buoyancy on flow stability; ratio of potential over kinetic energy)^{[25]}

Rockwell scale 
– 

mechanical hardness (indentation hardness of a material)

Rolling resistance coefficient 
C_{rr} 
$C\_\{rr\}\; =\; \backslash frac\{F\}\{N\_f\}$ 
vehicle dynamics (ratio of force needed for motion of a wheel over the normal force)

Roshko number 
Ro 
$\backslash mathrm\{Ro\}\; =\; \{f\; L^\{2\}\backslash over\; \backslash nu\}\; =\backslash mathrm\{St\}\backslash ,\backslash mathrm\{Re\}$ 
fluid dynamics (oscillating flow, vortex shedding)

Rossby number 
Ro 
$\backslash mathrm\{Ro\}=\backslash frac\{U\}\{Lf\}$ 
geophysics (ratio of inertial to Coriolis force)

Rouse number 
P or Z 
$\backslash mathrm\{P\}\; =\; \backslash frac\{w\_s\}\{\backslash kappa\; u\_*\}$ 
sediment transport (ratio of the sediment fall velocity and the upwards velocity of grain)

Schmidt number 
Sc 
$\backslash mathrm\{Sc\}\; =\; \backslash frac\{\backslash nu\}\{D\}$ 
mass transfer (viscous over molecular diffusion rate)^{[26]}

Shape factor 
H 
$H\; =\; \backslash frac\; \{\backslash delta^*\}\{\backslash theta\}$ 
boundary layer flow (ratio of displacement thickness to momentum thickness)

Sherwood number 
Sh 
$\backslash mathrm\{Sh\}\; =\; \backslash frac\{K\; L\}\{D\}$ 
mass transfer (forced convection; ratio of convective to diffusive mass transport)

Shields parameter 
$\backslash tau\_*$ or $\backslash theta$ 
$\backslash tau\_\{\backslash ast\}\; =\; \backslash frac\{\backslash tau\}\{(\backslash rho\_s\; \; \backslash rho)\; g\; D\}$ 
sediment transport (threshold of sediment movement due to fluid motion; dimensionless shear stress)

Sommerfeld number 
S 
$\backslash mathrm\{S\}\; =\; \backslash left(\; \backslash frac\{r\}\{c\}\; \backslash right)^2\; \backslash frac\; \{\backslash mu\; N\}\{P\}$ 
hydrodynamic lubrication (boundary lubrication)^{[27]}

Specific gravity 
SG 

(same as Relative density)

Stanton number 
St 
$\backslash mathrm\{St\}\; =\; \backslash frac\{h\}\{c\_p\; \backslash rho\; V\}\; =\; \backslash frac\{\backslash mathrm\{Nu\}\}\{\backslash mathrm\{Re\}\backslash ,\backslash mathrm\{Pr\}\}$ 
heat transfer and fluid dynamics (forced convection)

Stefan number 
Ste 
$\backslash mathrm\{Ste\}\; =\; \backslash frac\{c\_p\; \backslash Delta\; T\}\{L\}$ 
phase change, thermodynamics (ratio of sensible heat to latent heat)

Stokes number 
Stk or S_{k} 
$\backslash mathrm\{Stk\}\; =\; \backslash frac\{\backslash tau\; U\_o\}\{d\_c\}$ 
particles suspensions (ratio of characteristic time of particle to time of flow)

Strain 
$\backslash epsilon$ 
$\backslash epsilon\; =\; \backslash cfrac\{\backslash partial\{F\}\}\{\backslash partial\{X\}\}\; \; 1$ 
materials science, elasticity (displacement between particles in the body relative to a reference length)

Strouhal number 
St or Sr 
$\backslash mathrm\{St\}\; =\; \{\backslash omega\; L\backslash over\; v\}$ 
fluid dynamics (continuous and pulsating flow; nondimensional frequency)^{[28]}

Stuart number 
N 
$\backslash mathrm\{N\}\; =\; \backslash frac\; \{B^2\; L\_\{c\}\; \backslash sigma\}\{\backslash rho\; U\}\; =\; \backslash frac\{\backslash mathrm\{Ha\}^2\}\{\backslash mathrm\{Re\}\}$ 
magnetohydrodynamics (ratio of electromagnetic to inertial forces)

Taylor number 
Ta 
$\backslash mathrm\{Ta\}\; =\; \backslash frac\{4\backslash Omega^2\; R^4\}\{\backslash nu^2\}$ 
fluid dynamics (rotating fluid flows; inertial forces due to rotation of a fluid versus viscous forces)

Ursell number 
U 
$\backslash mathrm\{U\}\; =\; \backslash frac\{H\backslash ,\; \backslash lambda^2\}\{h^3\}$ 
wave mechanics (nonlinearity of surface gravity waves on a shallow fluid layer)

Vadasz number 
Va 
$\backslash mathrm\{Va\}\; =\; \backslash frac\{\backslash phi\backslash ,\; \backslash mathrm\{Pr\}\}\{\backslash mathrm\{Da\}\}$ 
porous media (governs the effects of porosity $\backslash phi$, the Prandtl number and the Darcy number on flow in a porous medium) ^{[29]}

van 't Hoff factor 
i 
$i\; =\; 1\; +\; \backslash alpha\; (n\; \; 1)$ 
quantitative analysis (K_{f} and K_{b})

Wallis parameter 
j^{*} 
$j^*\; =\; R\; \backslash left(\; \backslash frac\{\backslash omega\; \backslash rho\}\{\backslash mu\}\; \backslash right)^\backslash frac\{1\}\{2\}$ 
multiphase flows (nondimensional superficial velocity)^{[30]}

Weaver flame speed number 
Wea 
$\backslash mathrm\{Wea\}\; =\; \backslash frac\{w\}\{w\_\backslash mathrm\{H\}\}\; 100$ 
combustion (laminar burning velocity relative to hydrogen gas)^{[31]}

Weber number 
We 
$\backslash mathrm\{We\}\; =\; \backslash frac\{\backslash rho\; v^2\; l\}\{\backslash sigma\}$ 
multiphase flow (strongly curved surfaces; ratio of inertia to surface tension)

Weissenberg number 
Wi 
$\backslash mathrm\{Wi\}\; =\; \backslash dot\{\backslash gamma\}\; \backslash lambda$ 
viscoelastic flows (shear rate times the relaxation time)^{[32]}

Womersley number 
$\backslash alpha$ 
$\backslash alpha\; =\; R\; \backslash left(\; \backslash frac\{\backslash omega\; \backslash rho\}\{\backslash mu\}\; \backslash right)^\backslash frac\{1\}\{2\}$ 
biofluid mechanics (continuous and pulsating flows; ratio of pulsatile flow frequency to viscous effects)^{[33]}
