In dimensional analysis, a dimensionless quantity is a quantity without a physical unit and is thus a pure number. Such a number is typically defined as a product or ratio of quantities that might have units individually, but these cancel out in the combination. Dimensionless quantities are widely used in the fields of mathematics, physics, engineering, and economics, but also in everyday life.
According to the Buckingham π theorem of dimensional analysis, the functional dependence between a certain number of variables can be reduced by the number of independent dimensions occurring in those variables to give a set of p = n − k independent, dimensionless quantities. For the purposes of the experimenter, different systems which share the same description by dimensionless quantity are equivalent.
The Ruark number (RU) is a dimensionless number seen in fluid mechanics.