Similarity Theory

Abstract

The knowledge gained from similarity theory is applied in many fields of natural and engineering science, among others in fluid mechanics. In this field, similarity considerations are often used for providing insight into the flow phenomenon and for generalization of results. The importance of similarity theory rests on the recognition that it is possible to gain important new insights into flows from the similarity of conditions and processes without having to seek direct solutions for posed problems. This will be known to most readers of this book from geometry, where geometrically similar figures and bodies, e.g. similar triangles, are introduced and employed extend considerations. In this way, the height of a tower or the width of a river can, for example, be found by means of similarity considerations, without directly determining the height or the width. From similarity considerations in the field of geometry, it is known that a sufficient condition for the presence of geometrically similar triangles, quadrangles, etc., is the equality of corresponding angles or equality of the ratios of the corresponding sides, i.e. it holds for similar triangles: $${L_1 \over l_1} = {L_2 \over l_2} = {L_3 \over l_3} = {\rm constant}$$ (7.1). For a channel with a step: $${L_1 \over l_1} = {L_2 \over l_2} = {D \over d} = {H \over h} = {\rm constant}$$ (7.2). ensures geometrical similarity. The geometric similarity of fluid flow boundaries is always an important assumption for extended similarity considerations in fluid mechanics, i.e. the geometric similarity, is an inherent part of the subject of this chapter.