Principle of similitude

This transparent and easy example clearly shows how dimensional analysis deals with specific problems and what conclusions it allows. It should now be easier to understand Lord Rayleigh s sarcastic comment with which he began his short essay on The Principle of Similitude (3) ... 

I have often been impressed by the scanty attention paid even by original workers in physics to the great principle of similitude. It happens not infrequently that results in the form of laws are put forward as novelties on the basis of elaborate experiments, which might have been predicted a priori after a few minute s consideration. 

Lord Rayleigh. The principle of similitude. Nature 1915 95(2368) (March 18) 66-68. 

In his famous and extremely short essay entitled The principle of similitude Lord Rayleigh [4] discussed 15 different physical problems which can be condensed to laws by using dimensional analysis without performing any experiments. The last of these examples concerned the Boussinesq problem of the steady-state heat transfer from a fixed body to a ideal liquid flowing with the velocity of v. 

Four months after this publication a Letter to the Editor of D. Riabouchinsky [46] appeared in Nature. He pointed out that Lord Rayleigh considered heat, temperature, length and time as four independent units. If we suppose that only three of these quantities are really independent, we obtain a different result. For example, if the temperature is defined as the mean kinetic energy of molecules, the principle of similitude allows us only to affirm that... 

For maximum applicability (extrapolation) be consistent with physical laws - including the principle of similitude. 

Anonymous (1959). Chick, Alton Charles. Who s who in engineering 8 415. Lewis New York. Chick, A.C. (1929). Dimensional analysis and the principle of similitude as applied to hydraulic experiments with models. Hydraulic laboratory practice. 775-827, J.R. Freeman, ed. ASME New York. 

H.H. Bache, Principles of similitude in design of reinforced brittle matrix composites, Paper 3 , in H.W. Reinhardt and A.E. Naaman (eds) High Performance Fiber Reinforced Cement Composites, Proc. RILEM Symp., E FN SPON, London and New York, 1992, pp. 39-56. 

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