A physical quantity is a physical property or quality that can be quantified by measurement. A physical quantity is defined by the product of a numerical value and a unit of measurement. In this section we present a structured approach in order to obtain the dimensionless numbers of any dimensional relation. The approach is based on matrix computations, so it is very convenient for computer implementation.

Chapter Contents:

• 2.1 Physical quantities, units, and dimensions
• 2.1.1 Physical quantity
• 2.1.2 Units
• 2.1.3 Dimensions: fundamental and derived
• 2.1.4 Arithmetic of dimensions
• 2.2 Systems of units: dependence and independence of dimensions
• 2.2.1 System of units
• 2.2.2 Monomial power law
• 2.2.3 Dependent and independent dimensions
• 2.3 Buckingham pi theorem
• 2.4 Matrix approach for finding the dimensionless numbers
• 2.4.1 The dimensional matrix
• 2.4.2 The dimensional set
• 2.5 Dimensional similarity
• 2.5.1 Scale factors
• 2.5.2 Model law
• 2.6 Exercises
• References

Inspec keywords: matrix algebra

Other keywords: structured approach; physical property; dimensional similarity; physical quantity; numerical value; physical quality; dimensional analysis; dimensionless numbers; computer implementation; unit of measurement; matrix computations

Subjects: Numerical approximation and analysis; Linear algebra (numerical analysis); Linear algebra (numerical analysis); Numerical analysis