Dimensional analysis

one of the seven units of measurement that define the International System of Units

measure of probability that a specific process will take place in a collision of two particles

analysis of the relationships between different physical quantities by identifying their base quantities and units of measure

abstract space whose coordinates are the dynamic variables of the studied system

uniformity of a material or system at every point

dimensional analysis theorem

estimation problem designed to teach dimensional analysis or approximation

unit of measurement adopted by convention for a base quantity

thumb|right|280px|A full scale NASA X-43|X-43 [[wind tunnel test. The test is designed to have dynamic similitude with the real application to ensure valid results.]]

Nondimensionalization is the partial or full removal of physical dimensions from an equation involving physical quantities by a suitable substitution of variables. This technique can simplify and parameterize problems where measured units are involved. It is closely related to dimensional analysis. In some physical systems, the term scaling is used interchangeably with nondimensionalization, in order to suggest that certain quantities are better measured relative to some appropriate unit. These units refer to quantities intrinsic to the system, rather than units such as SI units. Nondimensiona