Qualitative physics using dimensional analysis

Abstract

In this paper we use dimensional analysis as a method for solving problems in qualitative physics. We pose and solve some of the qualitative reasoning problems discussed in the literature, in the context of devices such as the pressure regulator and the heat exchanger. Using dimensional analysis, such devices or systems can be reasoned about without explicit knowledge of the physical laws that govern the operation of such devices. Instead, the method requires knowledge of the relevant physical variables and their dimensional representation. Our main thesis can be stated as follows: the dimensional representations of physical variables encode a significant amount of physical knowledge; dimensionless numbers provide a representation of the physical processes, and they can be obtained without direct, explicit knowledge of the underlying laws of physics. Then, a variety of partial derivatives can be computed and used to characterize the behavior of the system. These partials, along with some simple heuristics, can be used to reason qualitatively about the behavior of devices and systems. Here we present the techniques for dimensional analysis and develop the representation and reasoning machinery. © 1990.