E226 -- Principes generaux du mouvement des fluides

(General principles concerning the motion of fluids)

(based on Clifford A. Truesdell's introduction to Opera Omnia Series II, Volume 12)
Here Euler treats the motion of fluids on the same footing as in E225, dealing with the principles of the equilibrium of fluids; in fact, he uses many of the ideas, especially that of pressure, of E225 in this work. This paper contains some of the earliest remarks indicating the role of boundary conditions in determining the appropriate integral for a partial differential equation. He also assumes that the state of the fluid is known at a certain time, and he reduces all of the theory of the motion of fluids to a solution of certain analytic formulae. Euler proves that solutions of the equations of motion can exist even when the forces are such that equilibrium is impossible. He shows that the existence of a velocity-potential is a special circumstance by exhibiting counterexamples of simple vortex flows (the first appearance of such flows) and motions that we now know as generalized Poiseuille flows (this marks the first appearance of these flows in this generality).

According to C. G. J. Jacobi, a treatise with this title was presented to the Berlin Academy on September 4, 1755.

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