What are the examples of dimensionless quantities in physics?

Answer 1

NameStandard symbolDefinitionField of applicationAbbe numberVoptics (dispersion in optical materials)Activity coefficientγchemistry (Proportion of "active" molecules or atoms)Albedoclimatology, astronomy (reflectivity of surfaces or bodies)Archimedes numberArmotion of fluids due to density differencesArrhenius numberRatio of activation energy to thermal energy[5]Atomic weightMchemistryBagnold numberBaflow of bulk solids such as grain and sand.[6]Blowdown circulation numberBCdeviation from isothermal flow in blowdown (rapid depressurization) of a pressure vessel[7]Bejan number

(thermodynamics)Bethe ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction[8]Bejan number

(fluid mechanics)Bedimensionless pressure drop along a channel[9]Bingham numberBmRatio of yield stress to viscous stress[5]Bingham capillary numberBm.CaRatio of yield stress to capillary pressure[10]Biot numberBisurface vs. volume conductivity of solidsBlake numberBl or Brelative importance of inertia compared to viscous forces in fluid flow through porous mediaBodenstein numberBoresidence-time distributionBond numberBocapillary action driven by buoyancy [11]Brinkman numberBrheat transfer by conduction from the wall to a viscous fluidBrownell-Katz numbercombination of capillary number and Bond numberCapillary numberCafluid flow influenced by surface tensionChandrasekhar numbermagnetic convection to represent ratio of the Lorentz forceto the viscosityCoefficient of static frictionfriction of solid bodies at restCoefficient of kinetic frictionfriction of solid bodies in translational motionColburn j factordimensionless heat transfer coefficientCourant-Friedrich-Levy numbernumerical solutions of hyperbolic PDEs [12]Damkohler numberDareaction time scales vs. resonance timeDamping ratiothe level of damping in a systemDarcy friction factor or fluid flowDean numberDvortices in curved ductsDeborah numberDerheology of viscoelastic fluidsDecibeldBratio of two intensities, often soundDrag coefficientflow resistanceDukhin numberDuratio of electric surface conductivity to the electric bulk conductivity in heterogeneous systemsEuler's numberemathematicsEckert numberEcconvective heat transferEkman numberEkgeophysics (frictional (viscous) forces)Elasticity (economics)Ewidely used to measure how demand or supply responds to price changesEötvös numberEodetermination of bubble/drop shapeEricksen numberErliquid crystal flow behaviorEuler numberEuhydrodynamics (pressure forces vs. inertia forces)Excess temperature coefficientΘrthermal and fluid dynamics[13]Fanning friction factorffluid flow in pipes [14]Feigenbaum constantschaos theory (period doubling) [15]Fine structure constantquantum electrodynamics (QED)f-numberoptics, photographyFoppl-von Karman numberthin-shell bucklingFourier numberFoheat transferFresnel numberFslit diffraction [16]Froude numberFrwave and surface behaviourGainelectronics (signal output to signal input)Gain Ratiosystem of representing bicycle gearing [17]Galilei numberGagravity-driven viscous flowGolden ratiomathematics and aestheticsGraetz numberGzheat flowGrashof numberGrfree convectionGravitational coupling constantGravitationHatta numberHaadsorption enhancement due to chemical reactionHagen numberHgforced convectionHydraulic gradientigroundwater flowJakob NumberJaRatio of sensible to latent energy absorbed during liquid-vapor phase change[18]Karlovitz numberturbulent combustion turbulent combustionKeulegan-Carpenter numberratio of drag force to inertia for a bluff object in oscillatoryfluid flowKnudsen numberKnratio of the molecular mean free path length to a representative physical length scaleKt/VmedicineKutateladze numberKcounter-current two-phase flowLaplace numberLafree convection within immiscible fluidsLewis numberLeratio of mass diffusivity and thermal diffusivityLift coefficientlift available from an airfoil at a given angle of attackLockhart-Martinelli parameterflow of wet gases [19]Love numbermeasuring the solidity of the earthLundquist numberratio of a resistive time to an Alfvén wave crossing time in a plasmaMach numberMRatio of current speed to the speed of sound, i.e. Mach 1 is the speed of sound, Mach 0.5 is half the speed of sound, Mach 2 is twice the speed of sound.gas dynamicsMagnetic Reynolds numbermagnetohydrodynamicsManning roughness coefficientnopen channel flow (flow driven by gravity) [20]Marangoni numberMgMarangoni flow due to thermal surface tension deviationsMorton numberModetermination of bubble/drop shapeMpemba numberthermal conduction and diffusion in freezing of a solution[21]Nusselt numberNuheat transfer with forced convectionOhnesorge numberOhatomization of liquids, Marangoni flowPéclet numberPeadvection-diffusion problems; relates total momentun transfer to molecular heat transfer.Peel numberadhesion of microstructures with substrate [22]PerveanceKmeasure of the strength of space charge in a charged particle beamPimathematics (ratio of a circle's circumference to its diameter)Poisson's ratioelasticity (load in transverse and longitudinal direction)PorositygeologyPower factorelectronics (real power to apparent power)Power numberpower consumption by agitatorsPrandtl numberPrratio of viscous diffusion rate over thermal diffusion ratePressure coefficientpressure experienced at a point on an airfoilQ factordescribes how under-damped an oscillator or resonator isRadianradmeasurement of anglesRayleigh numberRabuoyancy and viscous forces in free convectionRefractive indexnelectromagnetism, opticsReynolds numberReRatio of fluid inertial and viscous forces[5]Relative densityRDhydrometers, material comparisonsRichardson numberRieffect of buoyancy on flow stability [23]Rockwell scalemechanical hardnessRolling resistance coefficientCrrvehicle dynamicsRossby numberinertial forces in geophysicsRouse numberZ or Psediment transportSchmidt numberScfluid dynamics (mass transfer and diffusion) [24]Shape factorHratio of displacement thickness to momentum thickness inboundary layer flowSherwood numberShmass transfer with forced convectionShields parameterτ∗ or θthreshold of sediment movement due to fluid motionSommerfeld numberboundary lubrication [25]Stanton numberStheat transfer in forced convectionStefan numberSteheat transfer during phase changeStokes numberStk or particle dynamics in a fluid streamStrainmaterials science, elasticityStrouhal numberStor Srnondimensional frequency, continuous and pulsating flow[26]Taylor numberTarotating fluid flowsUrsell numberUnonlinearity of surface gravity waves on a shallow fluid layerVadasz numberVagoverns the effects of porosity , the Prandtl number and the Darcy number on flow in a porous mediumvan 't Hoff factoriquantitative analysis (Kf and Kb)Wallis parameterJ*nondimensional superficial velocity in multiphase flowsWeaver flame speed numberlaminar burning velocity relative to hydrogen gas [27]Weber numberWemultiphase flow with strongly curved surfacesWeissenberg numberWiviscoelastic flows [28]Womersley number

Answer 2

Some examples of dimensionless quantities in physics include the fine structure constant, which characterizes the strength of the electromagnetic interaction, and the Euler number, which arises in fluid dynamics to describe the ratio of inertial forces to viscous forces. Another example is the Reynolds number, which characterizes the behavior of fluid flow in relation to turbulence.