Abstract
AbstractDimensional analysis provides procedures of judicious grouping of variables associated with a physical phenomenon to form dimensionless products of these variables, so that the equation describing the physical phenomenon may be more easily determined experimentally. The concepts of units and dimensions are introduced. The notions of primary and secondary dimensions, dimensional formulas, and the absolute, gravitational, and engineering systems of dimensions are discussed.Dimensional analysis is based on the premise that any equation that correctly describes a physical phenomenon must be dimensionally homogeneous. To this end, the dimensional matrix is introduced. It is shown that the number of products in a complete set of dimensionless products called the β‐numbers associated with a physical phenomenon is equal to the number of variables that are involved in the phenomenon minus the rank of the associated dimensional matrix. The latter is equal to the maximum number of these variables that will not form a dimensionless product. It states that an equation is dimensionally homogeneous only if it is reducible to a relationship among a complete set of dimensionless products. Finally, a systematic procedure for computing and optimizing a complete set of dimensionless products is described.
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