CHAPTER II - Similarity, Modelling and Various Examples of the Application of Dimensional Analysis

Abstract

This chapter focuses on similarity, modeling, and various examples of the application of dimensional analysis. The value of dimensional analysis and similarity theory was first demonstrated with special clarity in hydraulics during the study of fluid motion in pipes. Empirical formulas have long been used in hydraulics. These formulas contained a number of dimensional constants, the values of which were determined by special experiments and by fluid properties. The reasoning of dimensional analysis, besides giving a clearer and more general formulation of the problem, led to empirical laws governing the motion of fluids in pipes with different temperatures, diameters, and speeds. Experiment shows that fluid motion in pipes is of two very different types, namely laminar motion and turbulent motion. The fluid particles in laminar motion in a cylindrical pipe move in lines parallel to the generators of the pipe; in turbulent motion, there is disordered mixing of the fluid in a direction perpendicular to the generators.