From Newton’s mechanics to Euler’s equations

The Euler equations of hydrodynamics, which appeared in their present form in the 1750s, did not emerge in the middle of a desert. We shall see in particular how the Bernoullis contributed much to the transmutation of hydrostatics into hydrodynamics, how d’Alembert was the first to describe fluid motion using partial differential equations and a general principle linking statics and dynamics, and how Euler developed the modern concept of internal pressure field which allowed him to apply Newton’s second law to infinitesimal elements of the fluid.