The analytical results obtained by means of this so-called “classical hydrodynamics” usually do not agree at all with the practical phenomena … Hydrodynamics thus has little significance for the engineer because of the great mathematical knowledge required for it and the negligible possibility of applying its results. Therefore the engineers—such as Bernoulli, Hagen, Wiessbach, Darcy, Bazin, and Boussinesq—put their trust in a mass of empirical data collectively known as the “science of hydraulics”, a branch of knowledge which grew more and more unlike hydrodynamics. While the methods of classical hydrodynamics were of a specifically analytical character, those of hydraulics were mostly synthetic … In classical hydrodynamics everything was sacrificed to logical construction; hydraulics on the other hand treated each problem as a separate case and lacked an underlying theory by which the various problems could be correlated. Theoretical hydrodynamics seemed to lose all contact with reality; simplifying assumptions were made which were not permissible even as approximations. Hydraulics disintegrated into a collection of unrelated problems; each individual problem was solved by assuming a formula containing some undetermined coefficients and then determining those so as to fit the facts as well as possible. Hydraulics seemed to become more and more a science of coefficients.

At an early stage in the development of the theory of turbulence the idea arose that turbulent motion consists of eddies of more or less definite range of sizes. […]