## ABSTRACT

The impetus for the development of the equations of ﬂuid mechanics originated with the prize competition of 1750 of the Berlin Academy (Académie Royale des Sciences et Belles-Lettres de Prusse) for a theory explaining the resistance of ﬂuids. As it turns out, the Academy was not happy with the quality of the submitted manuscripts.y The Academy decided that no contestant had earned the prize, and urged the contestants to compare their results with experiments. Sometime after this, on August 31, 1752, Euler read to the Academy his memoir onDe motu ﬂuidorum in genere.z This memoir is Euler’s ﬁrst attempt to develop a theory of ﬂuid motion. It is of great historical value because in it Euler derived the incompressible equation of continuity, see Figure 3.1. A few years later Euler derived the inviscid compressible equations (mass and momentum conservation, not energy) from Newton’s laws of mechanics. The original work was presented to the Berlin Academy on September 4, 1755. The work was published in 1757 as three separate, but consecutive, articles in the journal of the Academy. The equations appeared on the second article under the title General Principles Concerning the Motion of Fluids [69]. These were among the ﬁrst nonlinear ﬁeld equations ever formulated. For a brief history of ﬂuid mechanics covering the period from 1687 to 1845, see [222]; for an in-depth account, see [52] and [223].