Degree GrantorUniversity of Canterbury
The Π-theorem was proved and dimensional analysis was used to derive basic formulae for various physical phenomena. Dimensional analysis was used to non-dimensionalize equations leading to the appearance of key dimensionless groups and the sometimes powerful extension due to Huntley was explored. The theory of modeling was explained and self-similar solutions were sought to problems. Types of similarity were classified, and it was shown that dimensional analysis can decrease the number of variables in a problem when formulating a solution under the assumption of complete or incomplete similarity and when dimensional analysis is used in conjunction with a transformation group. To illustrate the ideas we used real-world examples from a range of disciplines.
SubjectsField of Research::01 - Mathematical Sciences
- Engineering: Reports