Dimensional Analysis and Model Similitude

Abstract

Dimensional analysis is one of the most important mathematical tools in the study of fluid motion. It is a mathematical technique which makes use of dimensions of physical quantities as an aid to the solutions to many engineering problems. The main advantage of a dimensional analysis of a problem is that it reduces the number of variables by combining dimensional variables to form dimensionless products. Dimensional analysis has been found useful in both analytical and experimental work in the study of fluid mechanics and is closely related to the model similitude which is required for conducting experiments in laboratory. To explore the idea of dimensional analysis and model similitude, the discussion on dimensions and units of physical variables is introduced, followed by the Buckingham theorem and a suggested procedure in conducting dimensional analysis. The mathematical foundations of dimensional analysis and the theory of physical model, specifically the modeling law, are outlined, and the differential equations of fluid motion in dimensional forms are brought to dimensionless forms to illustrate the significant dimensionless products. The physical interpretations of obtained dimensionless products are given to show their influence in achieving a complete model similarity of a physical process.