Force, Energy, Entropy, and Energy Dissipation Rate

Abstract

The science of mechanics has been developed along two parallel lines, that is, the vectorial and the variational approaches. The vectorial approach is based on force and momentum while the variational approach is based on entropy, energy, or energy dissipation rate. This paper provides a review and comparison of the basic characteristics, strengths and weaknesses, and interrelationships between the two approaches. Some of the basic difficulties of solving hydraulic problems from the vectorial approach alone are cited to indicate the need for the variational approach. Examples of applications of principles and theories based on variational approach are given to demonstrate the flexibility and applicability of the approach to solve or explain complicated and diversified phenomena from a simple and unified point of view.