Análise Dimensional: materiais para um livro aberto

Abstract

This work has as a first objective facilitate the understanding of Mechanics, and in fact all Physics for Middle and High School students, and to serve as reference material for teachers. But our main goal is to show that Dimensional Analysis is much more than a simple tool to remember formulas for exams. It represents in reality a deep understanding of scale invariances and similitudes found in the phenomena of Nature. We present several historical notes, highlighting the legacy of Prof. Fernando Lobo Carneiro to the Brazilian Engineering. Using Brigdman’s and Vaschy-Buckingham theorems, we present a good number of examples, some playful, others historical, others already at university level, as well as many suggestions for future studies - put as “to learn more’. The first Theorem is here taken pragmatically as a definition of a derived quantity from the seven fundamental quantities of the recently revised International System of Metrology. We present a demonstration of Vaschy-Buckingham’s Pi-theorem using ideas from the theory of transformation groups. This monograph is written as a proposal for an open book, emphasizing the importance of Dimensional Analysis as a guide for the development of mathematical theories, and as an indispensable tool in the planning of experiments.