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Advanced dimensional analysis and self-similarity

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Prof. Sandro Longo

Parma, 14-15 July 2022

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General info
The course is organised in presence and in streaming. Final examination, oral or written, only for students attending in presence.

Link to the registration form
The Registration is free of charge. Meals are not included.
Participation is limited to a total of 30 students, either in presence or in remote.
Language: English
The green pass is mandatory and the current legislation on Covid-19 will be respected.


The lessons in presence will take place at the Campus of the University of Parma, in the S. Elisabetta Conference Center on Thursday 14, Friday 15 July 2022.
Address: Parco Area delle Scienze, 43124, Parma, PR


This short course aims at introducing the basic and theoretical concepts of Dimensional Analysis and Similarity, with applications in several fields of Engineering.

Detailed Program

1 Dimensional Analysis 2h
1.1 The classification of physical quantities
1.2 Systems of units of measurement
1.3 The dimension of a physical quantity and the transformation of the units of measurement
1.4 The principle of dimensional homogeneity
1.5 The structure of the typical equation on the basis of the Dimensional Analysis
1.6 The Buckingham method (Theorem of Π)
1.7 A corollary of Buckingham's theorem: the Theorem of Sonin
2  Handling Dimensionless Groups in Dimensional Analysis 1h
2.1 The Dimensional and Physical Relevance of Variables
2.2 Reducing the Number of Dimensionless Groups
2.3 Formalisation of Matrix Methods
2.4 A Recipe for Dimensionless Groups
3 Symmetry and affine transformations 1.5 h
3.1 The structure of the functions of dimensionless groups
3.2 The Use of Symmetry to Specify the Expression of the Function
3.3 Group Theory and Affine Transformations for Self-similar Solutions
4 The Theory of Similarity and Applications to Models 1 h
4.1 Similarities
4.2 The Condition of Similarity on the Basis of Dimensional  
4.3 The Condition of Similarity on the Basis of Direct Analysis
5 Applications of Dimensional Analysis to problems of forces and deformations 2 h
5.1 Classification of structural models
5.2 The similarity in structural models
5.3 Statically stressed structures
5.5 The phenomena of instability
5.6 Dynamically stressed structures
5.7 Shock forces
5.8 Aero-elastic models
5.9 Models of explosive loads outside the structure
5.10 Dynamic models with earthquake action
5.11 Scale effects in structural models
6 Applications in Geotechnics 2 h
6.1 The vibrating table
6.2 The similarity conditions for a model on a vibrating table
6.3 The similarity conditions for centrifugal models
6.4 Scale in centrifugal models
6.5 Scaling effects and anomalies in centrifuges
6.6 Transport models for contaminants in centrifuges
6.7 Similarity for dynamical models in centrifuges
6.8 Similarities in tectonic processes
6.9 Some applications for solving classic problems
6.10 Dimensional Analysis of debris flow
6.11 Physical process in scouring of Phalesie
7 Applications in Fluid Mechanics and Hydraulics 2.5 h
7.1 The dimensionless groups in Fluid Mechanics
7.2 Similarity conditions in hydraulic models
7.3 The similarity of Reynolds
7.4 The similarity of Froude
7.5 The similarity of Mach
7.6 Similarities in filtration processes
7.7 Geometrically distorted hydraulic models
                7.7.1 Scaling effects in hydraulic models
                7.7.2 Analogue models


Recommended texts:

Dimensional Analysis
analisi dimensionale
Pubblicato Friday, 18 March, 2022 - 19:42 | ultima modifica Sunday, 20 March, 2022 - 17:02