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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