The fundamental nature of measurement is examined by considering the intuitive measurement process of physical entities such as length, time, mass and temperature. From this study four general axioms that are necessary and sufficient for the definition and measurement of an entity are formulated. The theorems and corollaries, which are derived from these four axioms define and establish the intuitive procedure or process used in the measurement of an entity. The concept of derived entities and the fundamental entities is formally defined and their relationship is explained. These axioms and the theorems derived from them have been logically used to establish the type of mathematical relationship that is possible between the measured values of the derived and fundamental entities . It is shown, that the measured value of a derived entity may only be expressed as a product of the powers of the measured values of chosen set of elements of fundamental entities required in the definition of the derived entity. A logical definition for the dimensions of a derived entity follows from this relationship. The relationship of measured values of entities which are inter-dependent is examined and the 'empirical relations' and 'dimensional relations' are defined. Buckingham's Pi-Theorem which states that a functional relationship amongst measured values of the entities which are inter-dependent may always be expressed as a mathematical relationship of non-dimensional products formed from the measured values of elements in the relationship, is established as a logical consequence of the definition of 'dimensional relation' of inter-dependent physical entities.
About the Author
Professor Vasu H Rao is a retired professor at School of Engineering, University of Huddersfield, UK. He obtained his B.E. (Hons) degree in Mechanical Engineering (1960), from Andhra University, India. and subsequently obtained M.Tech. (1963) and PhD (1978) degrees from I.I.T., Kharagpur, India. Before joining University of Huddersfield ( 1979) he was a professor at I.I.T., Kharagpur, and was also Commonwealth Scholar (1970-73) at Melbourne University, Australia. He has taught Mechanical Engineering Science and Thermo-fluids at graduate and post-graduate level for over forty years at the above places during his career. He has also supervised several Masters and PhD programs and has wide experience as a consultant for several industrial projects in the Thermo-fluids area.