Dimensional Analysis and Similarity in Fluid Mechanics

2Dimensional Analysis: Rayleigh Method and Vaschy-Buckingham Method

2.1 Introduction

Dimensional analysis is a practical method that is used to verify the homogeneity of a physical formula through its dimensional equations and to determine the form of an equation on the basis of the hypotheses of the physical quantities on which they are based.

This method is based on the fact that only quantities of the same size can be compared or added. It provides a basis for modeling using models and for studying the effects of scale.

Dimensional analysis is applied to many problems:

• – determination of non-dimensional numbers involved in physical phenomena;
• – modeling of phenomena using models;
• – determination of scale effects.

There are many different fields where dimensional analysis can be applied, including:

• – a loss of load (or drop in pressure) in load flow;
• – flows on open surfaces;
• – aerodynamics, flow resistance;
• – the forming and propagation of waves;
• – the resistance of materials.

Dimensional analysis can be a very powerful way to obtain formulas, the literal expressions of given physical quantities, from simple intuitive reasoning.

Dimensional analysis is only an intuitive and approximate method: the accuracy of its reasoning and the results or formulas are only guaranteed to one constant.

2.2 Definition of dimensional analysis

Dimensional analysis involves applying the concept that the conditions established by the fact that the numerical value of a physical quantity ...