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Dimensionless quantity
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In dimensional analysis, a dimensionless quantity (or more precisely, a quantity with the dimensions of 1) is a quantity without any physical units and thus a pure number. Such a number is typically defined as a product or ratio of quantities which do have units, in such a way that all the units cancel out.
Example
"out of every 10 apples I gather, 1 is rotten."  the rottentogathered ratio is (1 apple) / (10 apples) = 0.1 = 10%, which is a dimensionless quantity.
List of dimensionless quantities
There are infinitely many dimensionless quantities and they are often called numbers. Some of those that are used most often have been given names, as in the following list of examples (alphabetical order):
Name  Field of application 

Abbe number  optics (dispersion in optical materials) 
Albedo  climatology, astronomy (reflectivity of surfaces or bodies) 
Archimedes number  motion of fluids due to density differences 
Bagnold number  flow of grain, sand, etc. [1] 
Biot number  surface vs. volume conductivity of solids 
Bodenstein number  residencetime distribution 
Bond number  capillary action driven by buoyancy [2] 
Brinkman number  heat transfer by conduction from the wall to a viscous fluid 
Brownell Katz number  combination of capillary number and Bond number 
Capillary number  fluid flow influenced by surface tension 
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 
CourantFriedrichLevy number  numerical solutions of hyperbolic PDEs[3] 
Damköhler numbers  reaction time scales vs. transport phenomena 
Darcy friction factor  fluid flow 
Dean number  vortices in curved ducts 
Deborah number  rheology of viscoelastic fluids 
Decibel  ratio of two intensities of sound 
Drag coefficient  flow resistance 
e  mathematics 
Eckert number  convective heat transfer 
Ekman number  geophysics (frictional (viscous) forces) 
Elasticity (economics)  widely used to measure how demand or supply responds to price changes 
Eötvös number  determination of bubble/drop shape 
Euler number  hydrodynamics (pressure forces vs. inertia forces) 
Fanning friction factor  fluid flow in pipes [4] 
Feigenbaum constants  chaos theory (period doubling) [5] 
Fine structure constant  quantum electrodynamics (QED) 
Foppl–von Karman number  thinshell buckling 
Fourier number  heat transfer 
Fresnel number  slit diffraction [6] 
Froude number  wave and surface behaviour 
Gain  electronics (signal output to signal input) 
Galilei number  gravitydriven viscous flow 
Graetz number  heat flow 
Grashof number  free convection 
Hatta number  adsorption enhancement due to chemical reaction 
Hagen number  forced convection 
Karlovitz number  turbulent combustion 
Knudsen number  continuum approximation in fluids 
Kt/V  medicine 
Laplace number  free convection within immiscible fluids 
Lewis number  ratio of mass diffusivity and thermal diffusivity 
LockhartMartinelli parameter  flow of wet gases [7] 
Lift coefficient  lift available from an airfoil at a given angle of attack 
Mach number  gas dynamics 
Magnetic Reynolds number  magnetohydrodynamics 
Manning roughness coefficient  open channel flow (flow driven by gravity) [8]PDF (109 KiB) 
Marangoni number  Marangoni flow due to thermal surface tension deviations 
Morton number  determination of bubble/drop shape 
Nusselt number  heat transfer with forced convection 
Ohnesorge number  atomization of liquids, Marangoni flow 
Péclet number  advection–diffusion problems 
Peel number  adhesion of microstructures with substrate [9] 
Pi  mathematics (ratio of a circle's circumference to its diameter) 
Poisson's ratio  elasticity (load in transverse and longitudinal direction) 
Power factor  electronics (real power to apparent power) 
Power number  power consumption by agitators 
Prandtl number  forced and free convection 
Pressure coefficient  pressure experienced at a point on an airfoil 
Radian  measurement of angles 
Rayleigh number  buoyancy and viscous forces in free convection 
Refractive index  electromagnetism, optics 
Reynolds number  flow behavior (inertia vs. viscosity) 
Richardson number  effect of buoyancy on flow stability [10] 
Rockwell scale  mechanical hardness 
Rossby number  inertial forces in geophysics 
Schmidt number  fluid dynamics (mass transfer and diffusion) [11] 
Sherwood number  mass transfer with forced convection 
Sommerfeld number  boundary lubrication [12] 
Stanton number  heat transfer in forced convection 
Stefan number  heat transfer during phase change 
Stokes number  particle dynamics 
Strain  materials science, elasticity 
Strouhal number  continuous and pulsating flow [13] 
Taylor number  rotating fluid flows 
van 't Hoff factor  quantitative analysis (K_{f} and K_{b}) 
Weaver flame speed number  laminar burning velocity relative to hydrogen gas [14] 
Weber number  multiphase flow with strongly curved surfaces 
Weissenberg number  viscoelastic flows [15] 
Womersley number  continuous and pulsating flows [16] 
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