Dimensional Analysis and Similitude

Abstract

Dimensional analysis is a powerful tool in designing, ordering, and analyzing the experiment results and also synthesizing them. One of the important theorems in dimensional analysis is known as the Buckingham Π theorem, so called since it involves non-dimensional groups of the products of the quantities. In this chapter, Buckingham Π theorem and its uses are thoroughly discussed. Physical models for hydraulic structures or river courses are usually built to carry out experimental studies under controlled laboratory conditions. The main purposes of physical models are to replicate a small-scale hydraulic structure or flow phenomenon in a river and to investigate the model performance under different flow and sediment conditions. The concept of similitude is commonly used so that the measurements made in a laboratory model study can be used to describe the characteristics of similar systems in the practical field situations. This chapter describes hydraulic similitude in terms of geometric, kinematic, and dynamic similitude. Two categories of hydraulic models are discussed: Immobile bed models and mobile bed models. The analysis leads to the definition of model-scale ratios. A number of illustrative examples are presented.