Dimensional analysis

Dimensional analysis is a mathematical tool often applied by engineering sciences to reduce the complexity of a problem. Therefore, the number of variables involved in the description of a problem reduced by the number of their dimensions. This can save considerable time in doing experiments.

but how is it done?

Dimensional analysis provides solutions to differential equations, without integration. People that are good at this evidently do not know "how" they do it, they just "know" the important variables and how they interact. Probably the best practioners are engineers and mathematicians with deep or intuitive understanding of physics (as in French and Russians :).

References

Barenblatt?, G. I., "Scaling, Self-Similarity, and Intermediate Asymptotics", Cambridge University Press, 1996

Bridgman, P. W., "Dimensional Analysis", Yale University Press, 1937

Langhaar, H. L., "Dimensional Analysis and Theory of Models", Wiley, 1951

Murphy, N. F., Dimensional Analysis, Bull. V.P.I., 1949, 42(6)

Porter, "The Method of Dimensions", Methuen, 1933

Boucher and Alves, Dimensionless Numbers, Chem. Eng. Progress, 1960, 55, pp.55-64

Buckingham, E., On Physically Similar Systems: Illustrations of the Use of Dimensional Analysis, Phys. Rev, 1914, 4, p.345

Klinkenberg A. Chem. Eng. Science, 1955, 4, pp. 130-140, 167-177

Rayleigh, Lord, The Principle of Similitude, Nature 1915, 95, pp. 66-68

Silberberg, I. H. and McKetta? J. J., Jr., Learning How to Use Dimensional Analysis, Petrol. Refiner, 1953, 32(4), p179; (5), p.147; (6), p.101; (7), p. 129

Van Driest, E. R., On Dimensional Analysis and the Presentation of Data in Fluid Flow Problems, J. App. Mech, 1946, 68, A-34, March

Perry, J. H. et al., "Standard System of Nomenclature for Chemical Engineering Unit Operations", Trans. Am. Inst. Chem. Engrs., 1944, 40, 251

Moody, L. F., "Friction Factors for Pipe Flow", Trans. Am. Soc. Mech. Engrs., 1944, 66, 671