Any fundamental parameter (made up of a dimensionless assembly of observable factors) which usefully quantifies a physically similar model.

A dimensionless number can be used in the analysis of prototype models, to predict behavior in similar full-scale systems. A well known dimensionless number is the Mach number.

A dimensionless number is most often a ratio of two physical, geometrical, mechanical, thermal, or chemical quantities. In the example of the mach number it is the ratio of an object's speed in a fluid to the speed of sound in that fluid.

Many dimensionless numbers exist; often named after famous researchers in a particular field (e.g. Ernst Mach). Following is a list of (some, but definitely not all) dimensionless numbers:

  • Archimedes Number
    • Gravitational force / Viscous force
  • Arrhenius Number (Mass transfer, reaction rates)
    • Activation Energy / Potential energy
  • Bingham Number (Bingham plastic flow)
    • Yield stress / viscous stress
  • Biot Number (Heat transfer, unsteady state)
    • Thermal internal resistance / Surface film resistance
  • Blake Number (Momentum transfer)
    • Inertial force / Viscous force
  • Bond Number (Atomization, bubble and droplet calculations)
    • Gravitational force / Surface tension force
  • Capillary Number (Atomization)
    • Viscous force / Surface tension force
  • Cauchy Number (Momentum transfer, compressible flow)
    • Inertial force / Compressibility force
  • Cavitation Number (Cavitation)
    • Excess of local static head / vapor pressure head
  • Drag Coefficient (Flow calculations)
    • Gravitational Force / Inertial Force
  • Elasticity Number (Viscoelastic flow)
    • Elastic Force / Inertial Force
  • Euler Number (Compressible flow)
    • Pressure Force / Inertial Force
  • Feigenbaum number (Chaos theory, Physics)
  • Fine-Structure Constant (Physics)
  • Froude Number (Wave and surface behavior)
    • Inertial Force / Gravitational force
  • Galileo Number (Heat transfer, viscous flow)
    • Re.gravity force / Viscous force
  • Grashof Number (Heat transfer, convection)
    • Buoyancy force / Viscous force
  • Knudsen Number (Momentum transfer, gas flow calculations)
    • Length of mean free path / Characteristic dimension
  • Lewis Number (Heat transfer, Mass transfer)
  • Lift Coefficient (flow calculations)
  • Mach Number (general and (near)ultrasonic flow)
    • Velocity / Velocity of sound in fluid
  • Nusselt Number (Heat transfer)
    • Total heat transfer / Conductive heat transfer
  • Peclet Number (Heat transfer, convection)
    • Bulk Heat Transfer / Conductive Heat Transfer
  • Power Number (Momentum transfer, power consumption in agitators/pumps)
    • Drag force / Inertial force
  • Prandtl Number (Heat transfer, forced convection)
    • Momentum diffusivity / Thermal diffusivity Transfer
  • Rayleigh Number (Heat transfer, free convection)
  • Reynolds Number (Dynamic similarity)
    • Inertial force / Viscous force
  • Schmidt Number (Mass transfer)
    • Kinetic viscosity / Molecular diffusivity
  • Stanton Number (Heat transfer, forced convection)
    • Heat transfered / Thermal capacity of fluid
  • Weber Number (Bubble formation)
    • Inertial force / Surface tension force

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