Dimensionless Quantity - List of Dimensionless Quantities

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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