dimensionløs

Dimensionløs, Norwegian for dimensionless, describes a quantity that has no physical dimensions. A dimensionless quantity is a pure number, often arising from ratios of quantities with the same dimension or from nondimensionalization of equations. The concept is central in physics, engineering and mathematics because such quantities are invariant under changes of units.

Formation and analysis: Using dimensional analysis, many expressions can be made dimensionless by dividing by characteristic scales or combining variables to cancel units. The Buckingham Pi theorem formalizes this by expressing relationships as dimensionless products (Pi groups).

Common dimensionless numbers: Reynolds number Re, Mach number Ma, Prandtl number Pr, Nusselt Nu, Strouhal number St, and the fine-structure constant α as a truly fundamental dimensionless constant in physics. In mathematics, angles, trigonometric functions and probability ratios are dimensionless as they do not carry units.

Applications and significance: Dimensionless quantities enable meaningful comparison across systems of different scales, facilitate modeling and simulation through similarity, and allow universal constants to be defined independent of units. They also help identify regimes, such as laminar versus turbulent flow, using Re.

Notes: The designation dimensionless reflects a choice of reference units; any quantity can be made dimensionless by selecting appropriate scales, but the physical interpretation depends on the normalization. In Norwegian and Danish usage, dimensionløs is commonly used across science fields to describe such quantities.