Name |
Standard symbol |
Definition |
Named after |
Field of application |
Archimedes number | Ar |  |
Archimedes | fluid mechanics (motion of fluids due to density differences) |
Atwood number | A |  |
George Atwood[citation needed] | fluid mechanics (onset of instabilities in fluid mixtures due to density differences) |
Bagnold number |
Ba |
 |
Ralph Bagnold |
Granular flow (grain collision stresses to viscous fluid stresses) |
Bejan number | Be |  |
Adrian Bejan | fluid mechanics (dimensionless pressure drop along a channel)[4] |
Bingham number | Bm |  |
Eugene C. Bingham | fluid mechanics, rheology (ratio of yield stress to viscous stress)[5] |
Biot number | Bi |  |
Jean-Baptiste Biot | heat transfer (surface vs. volume conductivity of solids) |
Blake number | Bl or B |  |
Frank C. Blake (1892–1926) | geology, fluid mechanics, porous media (inertial over viscous forces in fluid flow through porous media) |
Bond number | Bo |  |
Wilfrid Noel Bond | geology, fluid mechanics, porous media (buoyant versus capillary forces, similar to the Eötvös number)[6] |
Brinkman number | Br |  |
Henri Brinkman | heat transfer, fluid mechanics (conduction from a wall to a viscous fluid) |
Burger number |
Bu |
 |
Alewyn P. Burger (1927–2003) |
meteorology, oceanography (density stratification versus Earth's rotation) |
Brownell–Katz number | NBK |  |
Lloyd E. Brownell and Donald L. Katz | fluid mechanics (combination of capillary number and Bond number)[7] |
Capillary number | Ca |  |
| porous media, fluid mechanics (viscous forces versus surface tension) |
Cauchy number | Ca |  |
Augustin-Louis Cauchy | compressible flows (inertia forces versus compressibility force) |
Cavitation number | Ca |  |
| multiphase flow (hydrodynamic cavitation, pressure over dynamic pressure) |
Chandrasekhar number | C |  |
Subrahmanyan Chandrasekhar | hydromagnetics (Lorentz force versus viscosity) |
Colburn J factors | JM, JH, JD | |
Allan Philip Colburn (1904–1955) | turbulence; heat, mass, and momentum transfer (dimensionless transfer coefficients) |
Damkohler number | Da |  |
Gerhard Damköhler | chemistry (reaction time scales vs. residence time) |
Darcy friction factor | Cf or fD | |
Henry Darcy | fluid mechanics (fraction of pressure losses due to friction in a pipe; four times the Fanning friction factor) |
Darcy number |
Da |
 |
Henry Darcy |
Fluid dynamics (permeability of the medium versus its cross-sectional area in porous media) |
Dean number | D |  |
William Reginald Dean | turbulent flow (vortices in curved ducts) |
Deborah number | De |  |
Deborah | rheology (viscoelastic fluids) |
Drag coefficient | cd |  |
| aeronautics, fluid dynamics (resistance to fluid motion) |
Dukhin number |
Du |
 |
Stanislav and Andrei Dukhin |
Fluid heterogeneous systems (surface conductivity to various electrokinetic and electroacoustic effects) |
Eckert number | Ec |  |
Ernst R. G. Eckert | convective heat transfer (characterizes dissipation of energy; ratio of kinetic energy to enthalpy) |
Ekman number |
Ek |
 |
Vagn Walfrid Ekman |
Geophysics (viscosity to Coriolis force ratio) |
Eötvös number | Eo |  |
Loránd Eötvös | fluid mechanics (shape of bubbles or drops) |
Ericksen number | Er |  |
Jerald Ericksen | fluid dynamics (liquid crystal flow behavior; viscous over elastic forces) |
Euler number | Eu |  |
Leonhard Euler | hydrodynamics (stream pressure versus inertia forces) |
Excess temperature coefficient |  |  |
| heat transfer, fluid dynamics (change in internal energy versus kinetic energy)[8] |
Fanning friction factor | f | |
John T. Fanning | fluid mechanics (fraction of pressure losses due to friction in a pipe; 1/4th the Darcy friction factor)[9] |
Froude number | Fr |  |
William Froude | fluid mechanics (wave and surface behaviour; ratio of a body's inertia to gravitational forces) |
Galilei number | Ga |  |
Galileo Galilei | fluid mechanics (gravitational over viscous forces) |
Görtler number | G |  |
Henry Görtler [de] | fluid dynamics (boundary layer flow along a concave wall) |
Goucher number [fr] |
Go |
 |
Frederick Shand Goucher (1888–1973) |
fluid dynamics (wire coating problems) |
Garcia-Atance number | GA |  |
Gonzalo Garcia-Atance Fatjo | phase change (ultrasonic cavitation onset, ratio of pressures over pressure due to acceleration) |
Graetz number | Gz |  |
Leo Graetz | heat transfer, fluid mechanics (laminar flow through a conduit; also used in mass transfer) |
Grashof number | Gr |  |
Franz Grashof | heat transfer, natural convection (ratio of the buoyancy to viscous force) |
Hartmann number | Ha |  |
Julius Hartmann (1881–1951) | magnetohydrodynamics (ratio of Lorentz to viscous forces) |
Hagen number | Hg |  |
Gotthilf Hagen | heat transfer (ratio of the buoyancy to viscous force in forced convection) |
Iribarren number | Ir |  |
Ramón Iribarren | wave mechanics (breaking surface gravity waves on a slope) |
Jakob number | Ja |  |
Max Jakob | heat transfer (ratio of sensible heat to latent heat during phase changes) |
Jesus number |
Je |
 |
Jesus |
Surface tension (ratio of surface tension and weight) |
Karlovitz number | Ka |  |
Béla Karlovitz | turbulent combustion (characteristic flow time times flame stretch rate) |
Kapitza number | Ka |  |
Pyotr Kapitsa | fluid mechanics (thin film of liquid flows down inclined surfaces) |
Keulegan–Carpenter number | KC |  |
Garbis H. Keulegan (1890–1989) and Lloyd H. Carpenter | fluid dynamics (ratio of drag force to inertia for a bluff object in oscillatory fluid flow) |
Knudsen number | Kn |  |
Martin Knudsen | gas dynamics (ratio of the molecular mean free path length to a representative physical length scale) |
Kutateladze number | Ku |  |
Samson Kutateladze | fluid mechanics (counter-current two-phase flow)[10] |
Laplace number | La |  |
Pierre-Simon Laplace | fluid dynamics (free convection within immiscible fluids; ratio of surface tension to momentum-transport) |
Lewis number | Le |  |
Warren K. Lewis | 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 |  |  |
R. W. Lockhart and Raymond C. Martinelli | two-phase flow (flow of wet gases; liquid fraction)[11] |
Mach number | M or Ma |  |
Ernst Mach | gas dynamics (compressible flow; dimensionless velocity) |
Marangoni number | Mg |  |
Carlo Marangoni | fluid mechanics (Marangoni flow; thermal surface tension forces over viscous forces) |
Markstein number | Ma |  |
George H. Markstein | turbulence, combustion (Markstein length to laminar flame thickness) |
Morton number | Mo |  |
Rose Morton | fluid dynamics (determination of bubble/drop shape) |
Nusselt number | Nu |  |
Wilhelm Nusselt | heat transfer (forced convection; ratio of convective to conductive heat transfer) |
Ohnesorge number | Oh |  |
Wolfgang von Ohnesorge | fluid dynamics (atomization of liquids, Marangoni flow) |
Péclet number | Pe | or  |
Jean Claude Eugène Péclet | fluid mechanics (ratio of advective transport rate over molecular diffusive transport rate), heat transfer (ratio of advective transport rate over thermal diffusive transport rate) |
Prandtl number | Pr |  |
Ludwig Prandtl | 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 |  |
John William Strutt, 3rd Baron Rayleigh | heat transfer (buoyancy versus viscous forces in free convection) |
Reynolds number | Re |  |
Osborne Reynolds | fluid mechanics (ratio of fluid inertial and viscous forces)[5] |
Richardson number | Ri |  |
Lewis Fry Richardson | fluid dynamics (effect of buoyancy on flow stability; ratio of potential over kinetic energy)[12] |
Roshko number | Ro |  |
Anatol Roshko | fluid dynamics (oscillating flow, vortex shedding) |
Rossby number | Ro |  |
Carl-Gustaf Rossby | fluid flow (geophysics, ratio of inertial force to Coriolis force) |
Rouse number |
P |
 |
Hunter Rouse |
Fluid dynamics (concentration profile of suspended sediment) |
Schmidt number | Sc |  |
Ernst Heinrich Wilhelm Schmidt (1892–1975) | mass transfer (viscous over molecular diffusion rate)[13] |
Scruton number |
Sc |
 |
Christopher 'Kit' Scruton |
Fluid dynamics (vortex resonance) |
Shape factor | H |  |
| boundary layer flow (ratio of displacement thickness to momentum thickness) |
Sherwood number | Sh |  |
Thomas Kilgore Sherwood | mass transfer (forced convection; ratio of convective to diffusive mass transport) |
Shields parameter |
θ |
 |
Albert F. Shields |
Fluid dynamics (motion of sediment) |
Sommerfeld number | S |  |
Arnold Sommerfeld | hydrodynamic lubrication (boundary lubrication)[14] |
Stanton number | St |  |
Thomas Ernest Stanton | heat transfer and fluid dynamics (forced convection) |
Stokes number | Stk or Sk |  |
Sir George Stokes, 1st Baronet | particles suspensions (ratio of characteristic time of particle to time of flow) |
Strouhal number | St |  |
Vincenc Strouhal | Vortex shedding (ratio of characteristic oscillatory velocity to ambient flow velocity) |
Stuart number | N |  |
John Trevor Stuart | magnetohydrodynamics (ratio of electromagnetic to inertial forces) |
Taylor number | Ta |  |
G. I. Taylor | fluid dynamics (rotating fluid flows; inertial forces due to rotation of a fluid versus viscous forces) |
Thoma number |
σ |
 |
Dieter Thoma (1881–1942) |
multiphase flow (hydrodynamic cavitation, pressure over dynamic pressure) |
Ursell number | U |  |
Fritz Ursell | wave mechanics (nonlinearity of surface gravity waves on a shallow fluid layer) |
Wallis parameter | j∗ |  |
Graham B. Wallis | multiphase flows (nondimensional superficial velocity)[15] |
Weber number | We |  |
Moritz Weber | multiphase flow (strongly curved surfaces; ratio of inertia to surface tension) |
Weissenberg number | Wi |  |
Karl Weissenberg | viscoelastic flows (shear rate times the relaxation time)[16] |
Womersley number |  |  |
John R. Womersley | biofluid mechanics (continuous and pulsating flows; ratio of pulsatile flow frequency to viscous effects)[17] |
Zeldovich number |  |  |
Yakov Zeldovich | fluid dynamics, Combustion (Measure of activation energy) |