Units of measurement, dimensions, and dimensional analysis

Abstract

Abstract In this chapter the crucial role of units and dimensions in the analysis of any problem involving physical quantities is explained. The International System of Units (SI) is introduced. The major advantage of collecting the physical quantities, which are included in either a theoretical analysis or an experiment, into non-dimensional groups is shown to be a reduction in the number of quantities which need to be considered separately. This process, known as dimensional analysis, is based upon the principle of dimensional homogeneity. Buckingham’s Π theorem is introduced as a method for determining the number of non-dimensional groups (the Π’s) corresponding with a set of dimensional quantities and their dimensions. A systematic and simple procedure for identifying these groups is the sequential elimination of dimensions. The scale-up from a model to a geometrically similar full-size version is shown to require dynamic similarity. The definitions and names of the non-dimensional groups most frequently encountered in fluid mechanics have been introduced and their physical significance explained.