An Alternate Means to Form Non-Dimensional Products in Dimensional Analysis

Abstract

Abstract Dimensional analysis is taught early in an undergraduate curriculum for mechanical engineering, usually during the very first course in fluid mechanics. Such analysis has its roots in the work of Lord Rayleigh, and the mechanics of the process as typically taught to undergraduates follows directly from the classic paper due to Buckingham on what is now known as the Pi Theorem. Students are meant to learn that dimensional analysis is a powerful tool for: developing insight with respect to flow physics, creating new models of physical processes, guiding the performance of experiments and flowfield simulations, aiding the sensible presentation of technical results, and fostering the replication of experiments and simulations. Unfortunately, the usual method for finding non-dimensional products taught to undergraduates requires the selection of scaling variables that can seem arbitrary and the solution of a number of sets of simultaneous equations that is typically tedious and prone to simple errors of arithmetic. As a consequence, students often fail to gain the intended appreciation for the usefulness of dimensional analysis. Fortunately, another technique for forming Π products that does not suffer from these same drawbacks was presented by the late Prof. B. S. Massey of University College London. This paper is intended to disseminate his so-called “step-by-step method” to a wider audience and thus to encourage the adoption of the technique for use in undergraduate curricula.