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What does "dimensionless" mean?

transition from laminar to turbulent flow in a plume of smoke

A dimensionless quantity has no physical unit of measurement. It can either be a pure number (e.g. a number of items) or it might be a ratio between two properties that have the same dimensions (e.g. kg/kg or 8 out of 10 cats), or it may be a measurement composed of other properties where all the dimensions cancel.

Dimensionless properties have been derived in many fields of science and engineering, and the fact that they have no dimensions is no accident. They usually represent the relative importance of different physical effects. For example the Reynolds number has great importance in fluid mechanics, and indicates the relative magnitude of the inertial and viscous forces in a moving fluid. It can be used to predict the point at which a fluid flow makes the transition from laminar flow to turbulence, based on the fluid velocity, the length scale and the properties of the fluid.

Because the dimensions cancel, in theory the value of a dimensionless property should be independent of the units system chosen. This is true for simple ratios, e.g. the value of kg/kg will be the same as the value expressed in lb/lb. However for more complex dimensionless quantities it may still be necessary to specify the units used because of inconsistencies within different units systems.

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