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After the publication of Hydrodynamics by Daniel Bernoulli in 1738, there was a fierce competition for priority with his father, Johann Bernoulli, and controversies with Jean le Rond D’Alembert, in which Leonard Euler seemed to have tacitly accepted the role of presiding over the disputes. These disputes were aroused by the almost simultaneous publications of Hydraulics by J. Bernoulli in 1743 and of Traite de l’equilibre et du mouvement des fluides by D’Alembert in 1744. It would be shown that despite the fact that the Bernoullis and D’Alembert used their own principles and approaches to the fluid mechanics problem of discharge, they essentially reached the same end. Nonetheless, it was Euler who brought the fluid mechanics problem of discharge to a new and definitive level with two publications. In these publications, for the first time, the pressure force and the friction force appeared explicitly in the formulations. However, the friction force was built under the wrong assumption that, as for the case of solid friction, the fluid friction force was proportional to the pressure. Finally, Lagrange’s memoir on the theory of fluid motion of 1781 is presented as a sequel to these first theoretical constructions.

First Theoretical Constructions to the Fluid Mechanics Problem of the Discharge