Nondimensionalization

Entdimensionalisierung is the partial or complete removal of units from a physical equation by appropriate substitution of variables. This technique can simplify problems involving units of measurement, as the new variables do not depend on the choice of unit. It is closely related to dimensional analysis. In some physical systems, the term scaling is used as a synonym for Entdimensionalisierung to suggest that some variables are better measured relative to a given unit. These units refer to the system intrinsic property, not on other units such as SI units. Entdimensionalisierung must be distinguished from the conversion of extensive variables in an equation in intensive, since the latter method results are still afflicted unit variables.

For each dimension Entdimensionalisierung prone variable is represented by the product of a reference variable and a dimensionless size.

This results in the equation dimensionless numbers, for example, in Fluid Mechanics, the Reynolds number and the Prandtl number. The reference variables are usually chosen so that the new non-dimensional variables of the order of unity is.

The Entdimensionalisierung can also reveal characteristic properties of a system. For example, can be intrinsic constants of a system such as resonance frequencies, lengths or times find. The technique is especially useful for systems which are described by differential equations. An important application is the analysis of control systems.

Meters are an important example of Entdimensionalisierung in everyday life: Most instruments are initially calibrated relative to a known unit, and subsequent measurements done relative to this default value. The measured value is then obtained by scaling with the default value.

• Physics