List of dimensionless quantities

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This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers, dimensionless ratios, or dimensionless physical constants; these topics are discussed in the article.

Contents

Biology and medicine

NameStandard symbolDefinitionField of application
Basic reproduction number number of infections caused on average by an infectious individual over entire infectious period epidemiology
Body fat percentage total mass of fat divided by total body mass, multiplied by 100biology
Kt/V Kt/V medicine (hemodialysis and peritoneal dialysis treatment; dimensionless time)
Waist–hip ratio waist circumference divided by hip circumferencebiology
Waist-to-chest ratio waist circumference divided by chest circumferencebiology
Waist-to-height ratio waist circumference divided by heightbiology

Chemistry

NameStandard symbolDefinitionNamed afterField of application
Activity coefficient chemistry (Proportion of "active" molecules or atoms)
Arrhenius number Svante Arrhenius chemistry (ratio of activation energy to thermal energy) [1]
Atomic weight M chemistry (mass of one atom divided by the atomic mass constant, 1  Da )
Bodenstein number Bo or Bd Max Bodenstein chemistry (residence-time distribution; similar to the axial mass transfer Peclet number) [2]
Damköhler numbers Da Gerhard Damköhler chemistry (reaction time scales vs. residence time)
Hatta number HaShirôji Hatta (1895–1973) chemical engineering (adsorption enhancement due to chemical reaction)
Jakob number Ja chemistry (ratio of sensible to latent energy absorbed during liquid-vapor phase change) [3]
pH chemistry (the measure of the acidity or basicity of an aqueous solution)
van 't Hoff factor i Jacobus Henricus van 't Hoff quantitative analysis (Kf and Kb)
Wagner number Wa electrochemistry (ratio of kinetic polarization resistance to solution ohmic resistance in an electrochemical cell) [4]
Weaver flame speed number Wea combustion (laminar burning velocity relative to hydrogen gas) [5]

Physics

Physical constants

Fluids and heat transfer

Solids

NameStandard symbolDefinitionNamed afterField of application
Coefficient of kinetic friction mechanics (friction of solid bodies in translational motion)
Coefficient of static friction mechanics (friction of solid bodies at rest)
Föppl–von Kármán number August Föppl and Theodore von Kármán virology, solid mechanics (thin-shell buckling)
Rockwell scale Hugh M. (1890–1957) and Stanley P. (1886–1940) Rockwell mechanical hardness (indentation hardness of a material)
Rolling resistance coefficient Crr vehicle dynamics (ratio of force needed for motion of a wheel over the normal force)

Optics

NameStandard symbolDefinitionNamed afterField of application
Abbe number V Ernst Abbe optics (dispersion in optical materials)
f-number N optics, photography (ratio of focal length to diameter of aperture)
Fresnel number F Augustin-Jean Fresnel optics (slit diffraction) [6]
Refractive index n electromagnetism, optics (speed of light in vacuum over speed of light in a material)
Transmittance T optics, spectroscopy (the ratio of the intensities of radiation exiting through and incident on a sample)

Other

NameStandard symbolDefinitionNamed afterField of application
Fine-structure constant quantum electrodynamics (QED) (coupling constant characterizing the strength of the electromagnetic interaction)
Havnes parameter O. HavnesIn dusty plasma physics, ratio of the total charge carried by the dust particles to the charge carried by the ions , with the number density of particles
Helmholtz number Hermann von Helmholtz The most important parameter in duct acoustics. If is the dimensional frequency, then is the corresponding free field wavenumber and is the corresponding dimensionless frequency [7]
Lundquist number SStig Lundqvist plasma physics (ratio of a resistive time to an Alfvén wave crossing time in a plasma)
Perveance K charged particle transport (measure of the strength of space charge in a charged particle beam)
Pierce parameter Traveling wave tube
Beta Plasma and fusion power. Ratio of plasma thermal pressure to magnetic pressure, controlling the level of turbulence in a magnetised plasma.
Poisson's ratio elasticity (strain in transverse and longitudinal direction)
Q factor Q physics, engineering (Damping ratio of oscillator or resonator; energy stored versus energy lost)
Relative density RD hydrometers, material comparisons (ratio of density of a material to a reference material—usually water)
Relative permeability magnetostatics (ratio of the permeability of a specific medium to free space)
Relative permittivity electrostatics (ratio of capacitance of test capacitor with dielectric material versus vacuum)
Specific gravity SG(same as Relative density)
Stefan number Ste Josef Stefan phase change, thermodynamics (ratio of sensible heat to latent heat)
Strain materials science, elasticity (displacement between particles in the body relative to a reference length)
Erlang Agner Krarup Erlang telephony (a measure of offered load on a telephone circuit)

Mathematics and statistics

Geography, geology and geophysics

NameStandard symbolDefinitionNamed afterField of application
Albedo climatology, astronomy (reflectivity of surfaces or bodies)
Dieterich–Ruina–Rice number James H. Dieterich, Andy Ruina, and James R. Rice mechanics, friction, rheology, geophysics (stiffness ratio for frictional contacts) [8]
Love numbers h, k, l Augustus Edward Hough Love geophysics (solidity of earth and other planets)
Porosity geology, porous media (void fraction of the medium)
Rossby number Ro Carl-Gustav Arvid Rossby geophysics (ratio of inertial to Coriolis force)

Sport

NameStandard symbolDefinitionField of application
Blondeau number sport science, team sports [9]
Gain ratio bicycling (system of representing gearing; length traveled over length pedaled) [10]
Runs Per Wicket Ratio RpW ratio cricket [11]
Winning percentage Various, e.g. or Various sports

Other fields

NameStandard symbolDefinitionField of application
Capacity factor energy
Cohesion number CohChemical engineering, material science, mechanics (A scale to show the energy needed for detaching two solid particles) [12] [13]
Cost of transport COT energy efficiency, economics (ratio of energy input to kinetic motion)
Damping ratio mechanics, electrical engineering (the level of damping in a system)
Decibel dB acoustics, electronics, control theory (ratio of two intensities or powers of a wave)
Elasticity
(economics)
E economics (response of demand or supply to price changes)
Gain electronics (signal output to signal input)
Load factor energy
Peel number NP coating (adhesion of microstructures with substrate) [14]
Pixel px digital imaging (smallest addressable unit)
Power factor pf electrical (real power to apparent power)
Power number Npfluid mechanics, power consumption by rotary agitators; resistance force versus inertia force)
Prater number β reaction engineering (ratio of heat evolution to heat conduction within a catalyst pellet) [15]
Relative density RD hydrometers, material comparisons (ratio of density of a material to a reference material—usually water)

References

  1. "Table of Dimensionless Numbers" (PDF). Retrieved 2009-11-05.
  2. Becker, A.; Hüttinger, K. J. (1998). "Chemistry and kinetics of chemical vapor deposition of pyrocarbon—II pyrocarbon deposition from ethylene, acetylene and 1,3-butadiene in the low temperature regime". Carbon. 36 (3): 177. doi:10.1016/S0008-6223(97)00175-9.
  3. Incropera, Frank P. (2007). Fundamentals of heat and mass transfer . John Wiley & Sons, Inc. p.  376. ISBN   9780470055540.
  4. Popov, Konstantin I.; Djokić, Stojan S.; Grgur, Branimir N. (2002). Fundamental Aspects of Electrometallurgy. Boston, MA: Springer. pp. 101–102. ISBN   978-0-306-47564-1.
  5. Kuneš, J. (2012). "Technology and Mechanical Engineering". Dimensionless Physical Quantities in Science and Engineering. pp. 353–390. doi:10.1016/B978-0-12-416013-2.00008-7. ISBN   978-0-12-416013-2.
  6. Fresnel number Archived 2011-10-01 at the Wayback Machine
  7. S.W. RIENSTRA, 2015, Fundamentals of Duct Acoustics, Von Karman Institute Lecture Notes
  8. Barbot, S. (2019). "Slow-slip, slow earthquakes, period-two cycles, full and partial ruptures, and deterministic chaos in a single asperity fault". Tectonophysics. 768: 228171. Bibcode:2019Tectp.76828171B. doi: 10.1016/j.tecto.2019.228171 .
  9. Blondeau, J. (2021). "The influence of field size, goal size and number of players on the average number of goals scored per game in variants of football and hockey: the Pi-theorem applied to team sports". Journal of Quantitative Analysis in Sports. 17 (2): 145–154. doi:10.1515/jqas-2020-0009. S2CID   224929098.
  10. Gain Ratio – Sheldon Brown
  11. "World Test Championship Playing Conditions: What's different?" (PDF). International Cricket Council. Retrieved 11 August 2021.
  12. Behjani, Mohammadreza Alizadeh; Rahmanian, Nejat; Ghani, Nur Fardina bt Abdul; Hassanpour, Ali (2017). "An investigation on process of seeded granulation in a continuous drum granulator using DEM" (PDF). Advanced Powder Technology. 28 (10): 2456–2464. doi:10.1016/j.apt.2017.02.011.
  13. Alizadeh Behjani, Mohammadreza; Hassanpour, Ali; Ghadiri, Mojtaba; Bayly, Andrew (2017). "Numerical Analysis of the Effect of Particle Shape and Adhesion on the Segregation of Powder Mixtures". EPJ Web of Conferences. 140: 06024. Bibcode:2017EPJWC.14006024A. doi: 10.1051/epjconf/201714006024 . ISSN   2100-014X.
  14. Van Spengen, W. M.; Puers, R.; De Wolf, I. (2003). "The prediction of stiction failures in MEMS". IEEE Transactions on Device and Materials Reliability. 3 (4): 167. doi:10.1109/TDMR.2003.820295.
  15. Davis, Mark E.; Davis, Robert J. (2012). Fundamentals of Chemical Reaction Engineering. Dover. p. 215. ISBN   978-0-486-48855-4.

Bibliography