Characteristic quantities and dimensional analysis

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 68)

Abstract

Phenomena in the physical sciences are described with quantities that have a numerical value and a dimension, i.e., a physical unit. Dimensional analysis is a powerful aspect of modeling and simulation. Characteristic quantities formed by a combination of model parameters can give new insights without detailed analytic or numerical calculations. Dimensional requirements lead to Buckingham’s Π theorem—a general mathematical structure of all models in physics. These aspects are illustrated with many examples of modeling, e.g., an elastic beam on supports, wave propagation on a liquid surface, the Lennard-Jones potential for the interaction between atoms, the Lindemann melting rule, and saturation phenomena in electrical and thermal conduction.

Keywords

Dimensional analysis Characteristic quantity Scaling Buckingham’s theorem Lennard-Jones interaction 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Theoretical Physics, Royal Institute of TechnologyAlbaNova University CenterStockholmSweden

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