Dimensional analysis is an important tool for engineers, aiding the design of experiments and concise expression of the results generated by them. The dimensionless groups, which are the output of a successful dimensional analysis, are usually developed via Buckingham's ‘Pi’ theorem. Because this alone is a necessary, but not sufficient, condition for a solution, difficulties are frequently encountered. This paper presents a general, dimensional analysis algorithm which imposes both necessary and sufficient conditions. Illustrative problems are included, together with a Mathematica program which generates all possible sets of admissible dimensionless groups for a specific problem. L'analyse dimensionnelle est un outil important pour les ingenieurs car elle les aide a concevoir des experiences et a exprimer de maniere concise les resultats qui en decoulent. Les groups non denommes, qui sont le resultat d'une analyse dimensionnelle reussie, sont normalement developpes au moyen du theoreme ‘pi’ de Buckingham...
[1]
D J Goodings,et al.
Reinforced earth and adjacent soils: centrifuge modeling study
,
1989
.
[2]
John F. Douglas.
An introduction to dimensional analysis for engineers
,
1969
.
[3]
R. Butterfield.
Scale modelling of fluid flow in geotechnical centrifuges
,
2000
.
[4]
Hon-Yim Ko,et al.
Centrifugal Modeling of Transient Water Flow
,
1983
.
[5]
Edward S. Taylor,et al.
Dimensional analysis for engineers
,
1974
.
[6]
J. R. Radbill,et al.
Similitude and Approximation Theory
,
1986
.
[7]
E. de St Q. Isaacson,et al.
Dimensional methods in engineering and physics : reference sets and the possibilities of their extension
,
1975
.
[8]
Kanthasamy K. Muraleetharan,et al.
CENTRIFUGE MODELING OF TRANSPORT PROCESSES FOR POLLUTANTS IN SOILS
,
1988
.
[9]
H. Langhaar.
Dimensional analysis and theory of models
,
1951
.