Dimensional Analysis CUED 1A Lecture notes Shreyas Mandre Department of Engineering, University of Cambridge sdm63@cam.ac.uk ©2024-2026 Shreyas Mandre CC-BY-NC-ND with examples from the lecture notes of Dr John P Longley (Last updated: 23 August 2026 ) Contents 1 Introduction to dimensional analysis 1.1 Motivating examples 1.2 Objectives and outline 1.3 Conclusion 2 Units 2.1 SI units for physical quantities 2.2 Scales and systems of units 2.2.1 CGS system 2.2.2 MKS mass system 2.2.3 MKS force system 2.2.4 British mass system a.k.a the Imperial system 2.2.5 American Engineering (force) System 2.3 Conversion of derived units 2.4 Conclusion 3 Dimensions 3.1 Notation 3.2 Base and derived dimensions 3.3 System of dimensions 3.4 Specification of dimensional quantities 3.5 Principle of dimensional consistency 3.6 Dimensionless combinations of parameters 3.7 Conclusion 4 Dimensionless forms of equations 4.1 Physical relations between dimensionless parameters 4.2 Non-dimensionalizing equations 4.3 Non-dimensionalizing charts 4.4 Dimensionless relationships 4.4.1 The principle of the isolated dimension 4.4.2 Recombination of parameters 4.4.3 Iterating to eliminate dimensions 4.5 More examples 4.6 Buckingham’s Pi theorem 4.7 Alternative ways to form dimensionless relationships 4.7.1 Indicial method 4.7.2 Inspection 4.8 Conclusion 5 Applications of Dimensional Analysis 5.1 Non-dimensional presentation of experimental data 5.2 Scale models 5.2.1 Geometric similarity 5.2.2 Dynamic similarity 5.2.3 A ship’s propeller 5.3 Conclusion