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.
Originally published in Mémoires de l'académie des sciences de Berlin 11, 1757, pp. 274-315
Opera Omnia: Series 2, Volume 12, pp. 54 - 91
- Original publication: E226
- E226 can be viewed or downloaded from Digitalisierte Akademieschriften und Schriften zur Geschichte der Königlich Preußischen Akademie der Wissenschaften, which includes serial publications of the Prussian Academy of Science in the 18th and 19th Centuries.
- The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E226 include:
- Watson JV., “The early fluidic and optical physics of cytometry.” Cytometry, 38 (1), pp. 2-14 (Feb 15 1999).
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