An Elementary Introduction

Dimensional analysis is given a simplified introduction. Its relationship to the design, the ordering, the performance and the data analysis of experiments is shown through simple examples. A start is made on the logic of the analysis commencing with the basic feature of measurement in science which is followed by the introduction of the associated units-conversion factors. The basic dimensional system is presented leading to the fundamental premise on which the whole analysis is founded. As a preliminary introduction to the pi-theorem, specific physical examples are given.

[1]  E. Buckingham On Physically Similar Systems; Illustrations of the Use of Dimensional Equations , 1914 .

[2]  Units and dimensions , 1996 .

[3]  J. Gibbings Some recent developments in the mechanics of fluids , 1969 .

[4]  Marco Ajmone Marsan,et al.  Performance models of multiprocessor systems , 1987, MIT Press series in computer systems.

[5]  Erhan Çinlar,et al.  Introduction to stochastic processes , 1974 .

[6]  On the Proof That All Even Perfect Numbers Are of Euclid's Type , 1975 .

[7]  Oystein Ore,et al.  Number Theory and Its History , 1949 .

[8]  Vincent Hodgson,et al.  The Single Server Queue. , 1972 .

[9]  Where is the next mersenne prime hiding? , 1983 .

[10]  L. Dickson History of the Theory of Numbers , 1924, Nature.

[11]  J Gibbings The Systematic Experiment , 1986 .

[12]  J. Gibbings A logic of dimensional analysis , 1982 .

[13]  Wolfgang Reisig Petri Nets: An Introduction , 1985, EATCS Monographs on Theoretical Computer Science.

[14]  Erol Gelenbe,et al.  Analysis and Synthesis of Computer Systems , 1980 .

[15]  William Thomson,et al.  Popular Lectures and Addresses: ELECTRICAL UNITS OF MEASUREMENT , 2011 .

[16]  James Clerk Maxwell,et al.  The Scientific Papers of James Clerk Maxwell: On the Mathematical Classification of Physical Quantities , 2011 .

[17]  R. L. Francis A Note on Perfect Numbers. , 1975 .

[18]  S. Goldstein Modern developments in fluid dynamics , 1938 .

[19]  Stephen S. Lavenberg,et al.  Computer Performance Modeling Handbook , 1983, Int. CMG Conference.

[20]  Ettore Picutti Pour l'histoire des sept premiers nombres parfaits , 1989 .

[21]  J. Clerk-Maxwell Remarks on the Mathematical Classification of Physical Quantities , 1869 .

[22]  J. Gibbings On dimensional analysis , 1980 .

[23]  Ronald A. Howard,et al.  Dynamic Probabilistic Systems , 1971 .

[24]  Walter Hilton,et al.  The scale of perfection , 1927 .

[25]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

[26]  Robert B. Cooper,et al.  An Introduction To Queueing Theory , 2016 .