adimensjonal

Adimensjonal, or dimensionless, describes a quantity that has no physical units. Adimensjonal quantities are obtained as ratios of quantities with the same dimensions or by nondimensionalizing governing equations. Because they do not carry units, their numerical value does not depend on the chosen system of measurement, making them especially useful for comparing different physical scales.

Common examples include mathematical constants such as pi, and physical ratios such as the refractive index, Mach number, Reynolds number, Strouhal number, and Prandtl number. These numbers are pure scalars; their values convey information about systems independent of unit choices or size.

In practice, adimensjonalization is a standard step in modeling. Dimensional analysis checks the consistency of equations, and nondimensionalization reduces the number of parameters by grouping them into dimensionless groups via the Buckingham Pi theorem or by introducing characteristic scales.

Adimensjonal quantities play a crucial role in scaling laws, similarity analysis, and experimental design. They enable the comparison of phenomena across materials, geometries, and conditions, and help identify dominant processes and regimes where certain effects prevail.

Notes: Some contexts use "dimensionless" and "adimensjonal" interchangeably. The concept requires careful definition to ensure the quantity is indeed unit-free; otherwise, an apparent dimensionless form might hide a remaining scale.