Dimensional analysis
Almost every quantity in engineering and the sciences carries units, and that single fact constrains the form any physical law can take. These notes develop that constraint into a working method: how to choose a system of dimensions, how to reduce a relationship to its dimensionless parameters, and what Buckingham’s Pi theorem does and does not tell you. The final chapter puts it to work on experimental data and on scale models.
1. Introduction to dimensional analysis1.1 Motivating examples (online notes)
1.2 Objectives and outline (online notes)
2. Units
2.1 SI units for physical quantities (online notes)
2.2 Scales and systems of units (online notes)
2.3 Conversion of derived units (online notes)
3. Dimensions
3.1 Notation (online notes)
3.2 Base and derived dimensions (online notes)
3.3 System of dimensions (online notes)
3.4 Specification of dimensional quantities (online notes)
3.5 Principle of dimensional consistency (online notes)
3.6 Dimensionless combinations of parameters (online notes)
4. Dimensionless forms of equations
4.1 Physical relations between dimensionless parameters (online notes)
4.2 Non-dimensionalizing equations (online notes)
4.3 Non-dimensionalizing charts (online notes)
4.4 Dimensionless relationships (online notes)
4.5 More examples (online notes)
4.6 Buckingham’s Pi theorem (online notes)
4.7 Alternative ways to form dimensionless relationships (online notes)
5. Applications of dimensional analysis
5.1 Non-dimensional presentation of experimental data (online notes)
5.2 Scale models (online notes)
These notes come out of the group's research and publications, browsable by topic. If you would like to work on this material rather than only read it, see the openings.