List of Dimensionless Quantities
All numbers are dimensionless quantities. Certain dimensionless quantities of some importance are given below:
| Name | Standard symbol | Definition | Field of application |
|---|---|---|---|
| Abbe number | V | optics (dispersion in optical materials) | |
| Activity coefficient | γ | chemistry (Proportion of "active" molecules or atoms) | |
| Albedo | climatology, astronomy (reflectivity of surfaces or bodies) | ||
| Archimedes number | Ar | motion of fluids due to density differences | |
| Arrhenius number | Ratio of activation energy to thermal energy | ||
| Atomic weight | M | chemistry | |
| Bagnold number | Ba | flow of bulk solids such as grain and sand. | |
| Blowdown circulation number | BC | deviation from isothermal flow in blowdown (rapid depressurization) of a pressure vessel | |
| Bejan number |
Be | the ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction | |
| Bejan number |
Be | dimensionless pressure drop along a channel | |
| Bingham number | Bm | Ratio of yield stress to viscous stress | |
| Bingham capillary number | Bm.Ca | Ratio of yield stress to capillary pressure | |
| Biot number | Bi | surface vs. volume conductivity of solids | |
| Blake number | Bl or B | relative importance of inertia compared to viscous forces in fluid flow through porous media | |
| Bodenstein number | Bo | residence-time distribution | |
| Bond number | Bo | capillary action driven by buoyancy | |
| Brinkman number | Br | heat transfer by conduction from the wall to a viscous fluid | |
| Brownell–Katz number | combination of capillary number and Bond number | ||
| Capillary number | Ca | fluid flow influenced by surface tension | |
| Chandrasekhar number | magnetic convection to represent ratio of the Lorentz force to the viscosity | ||
| Coefficient of static friction | friction of solid bodies at rest | ||
| Coefficient of kinetic friction | friction of solid bodies in translational motion | ||
| Colburn j factor | dimensionless heat transfer coefficient | ||
| Courant–Friedrich–Levy number | numerical solutions of hyperbolic PDEs | ||
| Damkohler number | Da | reaction time scales vs. resonance time | |
| Damping ratio | the level of damping in a system | ||
| Darcy friction factor | or | fluid flow | |
| Dean number | D | vortices in curved ducts | |
| Deborah number | De | rheology of viscoelastic fluids | |
| Decibel | dB | ratio of two intensities, often sound | |
| Drag coefficient | flow resistance | ||
| Dukhin number | Du | ratio of electric surface conductivity to the electric bulk conductivity in heterogeneous systems | |
| Euler's number | e | mathematics | |
| Eckert number | Ec | convective heat transfer | |
| Ekman number | Ek | geophysics (frictional (viscous) forces) | |
| Elasticity (economics) | E | widely used to measure how demand or supply responds to price changes | |
| Eötvös number | Eo | determination of bubble/drop shape | |
| Ericksen number | Er | liquid crystal flow behavior | |
| Euler number | Eu | hydrodynamics (pressure forces vs. inertia forces) | |
| Excess temperature coefficient | Θr | thermal and fluid dynamics | |
| Fanning friction factor | f | fluid flow in pipes | |
| Feigenbaum constants | chaos theory (period doubling) | ||
| Fine structure constant | quantum electrodynamics (QED) | ||
| f-number | optics, photography | ||
| Foppl–von Karman number | thin-shell buckling | ||
| Fourier number | Fo | heat transfer | |
| Fresnel number | F | slit diffraction | |
| Froude number | Fr | wave and surface behaviour | |
| Gain | electronics (signal output to signal input) | ||
| Gain Ratio | system of representing bicycle gearing | ||
| Galilei number | Ga | gravity-driven viscous flow | |
| Golden ratio | mathematics and aesthetics | ||
| Graetz number | Gz | heat flow | |
| Grashof number | Gr | free convection | |
| Gravitational coupling constant | Gravitation | ||
| Hatta number | Ha | adsorption enhancement due to chemical reaction | |
| Hagen number | Hg | forced convection | |
| Hydraulic gradient | i | groundwater flow | |
| Jakob Number | Ja | Ratio of sensible to latent energy absorbed during liquid-vapor phase change | |
| Karlovitz number | turbulent combustion turbulent combustion | ||
| Keulegan–Carpenter number | ratio of drag force to inertia for a bluff object in oscillatory fluid flow | ||
| Knudsen number | Kn | ratio of the molecular mean free path length to a representative physical length scale | |
| Kt/V | medicine | ||
| Kutateladze number | K | counter-current two-phase flow | |
| Laplace number | La | free convection within immiscible fluids | |
| Lewis number | Le | ratio of mass diffusivity and thermal diffusivity | |
| Lift coefficient | lift available from an airfoil at a given angle of attack | ||
| Lockhart–Martinelli parameter | flow of wet gases | ||
| Love number | measuring the solidity of the earth | ||
| Lundquist number | ratio of a resistive time to an Alfvén wave crossing time in a plasma | ||
| Mach number | M | gas dynamics | |
| Magnetic Reynolds number | magnetohydrodynamics | ||
| Manning roughness coefficient | n | open channel flow (flow driven by gravity) | |
| Marangoni number | Mg | Marangoni flow due to thermal surface tension deviations | |
| Morton number | Mo | determination of bubble/drop shape | |
| Mpemba number | thermal conduction and diffusion in freezing of a solution | ||
| Nusselt number | Nu | heat transfer with forced convection | |
| Ohnesorge number | Oh | atomization of liquids, Marangoni flow | |
| Péclet number | Pe | advection–diffusion problems; relates total momentun transfer to molecular heat transfer. | |
| Peel number | adhesion of microstructures with substrate | ||
| Perveance | K | 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 | ||
| Power factor | electronics (real power to apparent power) | ||
| Power number | power consumption by agitators | ||
| Prandtl number | Pr | ratio of viscous diffusion rate over thermal diffusion rate | |
| Pressure coefficient | pressure experienced at a point on an airfoil | ||
| Q factor | describes how under-damped an oscillator or resonator is | ||
| Angle | rad | measurement of angles | |
| Rayleigh number | Ra | buoyancy and viscous forces in free convection | |
| Refractive index | n | electromagnetism, optics | |
| Reynolds number | Re | Ratio of fluid inertial and viscous forces | |
| Relative density | RD | hydrometers, material comparisons | |
| Richardson number | Ri | effect of buoyancy on flow stability | |
| Rockwell scale | mechanical hardness | ||
| Rolling resistance coefficient | Crr | vehicle dynamics | |
| Rossby number | inertial forces in geophysics | ||
| Rouse number | Z or P | sediment transport | |
| Schmidt number | Sc | fluid dynamics (mass transfer and diffusion) | |
| Shape factor | H | ratio of displacement thickness to momentum thickness in boundary layer flow | |
| Sherwood number | Sh | mass transfer with forced convection | |
| Shields parameter | τ∗ or θ | threshold of sediment movement due to fluid motion | |
| Sommerfeld number | boundary lubrication | ||
| Stanton number | St | heat transfer in forced convection | |
| Stefan number | Ste | heat transfer during phase change | |
| Stokes number | Stk or | particle dynamics in a fluid stream | |
| Strain | materials science, elasticity | ||
| Strouhal number | St or Sr | nondimensional frequency, continuous and pulsating flow | |
| Taylor number | Ta | rotating fluid flows | |
| Ursell number | U | nonlinearity of surface gravity waves on a shallow fluid layer | |
| Vadasz number | Va | governs the effects of porosity, the Prandtl number and the Darcy number on flow in a porous medium | |
| van 't Hoff factor | i | quantitative analysis (Kf and Kb) | |
| Wallis parameter | J* | nondimensional superficial velocity in multiphase flows | |
| Weaver flame speed number | laminar burning velocity relative to hydrogen gas | ||
| Weber number | We | multiphase flow with strongly curved surfaces | |
| Weissenberg number | Wi | viscoelastic flows | |
| Womersley number | continuous and pulsating flows |
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