Principles of the motion of fluids
This work is important in the history of rational mechanics. In it, Euler treats the theory of the motion of fluids in general: "given a mass of fluid, either free or confined in vessels, when an arbitrary motion shall have been impressed upon it, and meanwhile it is acted upon by arbitrary forces, the motion in which its several particles are to travel shall be determined, and at the same time the pressure with which the several parts act, as well mutually upon each other as also upon the sides of a vessel, shall be ascertained." Assuming the continuity and incompressibility of the fluid, Euler derives the continuity equation ∂u/∂x + ∂v/∂y + ∂w/∂z = 0 and the dynamical equations for ideal incompressible fluids, thus separating for the first time the kinematical from the dynamical aspects of the theory of continua. In addition, he proves that a necessary condition for the potential flow in a homogeneous incompressible fluid is the completeness of the differential Q dx + q dy + j dz. He also generalizes the earlier theory of friction in tubes and gives a rule for finding the most general homogeneous harmonic nth-degree polynomial. Euler proves that the only rigid potential motion is a state of uniform translation. This is the first part of a three-part treatise on fluid mechanics. For the rest of Euler's "De motu Flouidorum" see "Sectio secunda de principiis motus fluidorum" (E396) and "Sectio tertia de motu fluidorum" (E409). (Based on Clifford Truesdell's introduction to Opera Omnia Series II, Volume 12.)
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 6, pp. 271-311.
Opera Omnia Citation
Series 2, Volume 12, pp.133-168.