Dimensional Analysis and Similarity in Fluid Mechanics

Introduction

The analytical methods (or models) that are used in solving the problems of fluid mechanics are not always satisfactory (as they do not give good results) in practice. This is because it is necessary to use simplifications or detailed and onerous analyses.

The alternative to this is to call upon past experience and deduce correlations applicable to all cases of the same type of problem. In many cases, the experimental conditions in the laboratory are not the same as those in real life (for example, the dimensions of the centrifugal pump model and its prototype, or the different fluids), and in these cases, dimensional analysis is used. This analysis allows for dimensionless correlations of dimensionless numbers to be obtained, which are generally applicable to all practical cases. In other words, these dimensionless correlations can be applied under dynamic conditions, similar to those in which they were established by using, for instance, a different fluid.

Dimensional analysis is a practical method for verifying homogeneity (the method devised by John William Strutt Rayleigh) of a physical formula through its dimensional equations. This is achieved by subdividing the physical quantities included in the formula into a product of fundamental or basic values: length, duration, mass, electrical intensity, etc., each of which are irreducible with respect to all others.

Dimensional analysis is based on the principle that only the values of the same dimension can be ...