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