E206 -- Sur le mouvement de l'eau par des tuyaux de conduite

(On the motion of water in conduits)

(based on Clifford A. Truesdell's introduction to Opera Omnia Series II, Volume 12)
This is the first of Euler's papers on hydraulics. It starts with a critical survey of the existing results on hydraulics, though he concludes that "it is also clear that these reproaches are not proper to the true theory, but only the superficial knowledge inappropriately honored with this title." The goal of this paper is to discuss the following problem: Given a circular tube with diameter z centered around the plane curve x = x(s), y = y(s), where y is vertical, find the pressure on the walls of the cylinder when water is driven through it by a pump with vertical cylinder, bore a, and with piston having a speed equivalent to a hight v after having traveled a distance r downward. This paper marks the first appearance of the use of pressure p as we now know it. Euler manages to obtain a complete theory of a one-cylinder pump with numerical results that he presents in a table. This may also contain the first solution of a theoretical design problem in engineering.


According to C. G. J. Jacobi, a treatise with this title was presented to the Berlin Academy on October 23, 1749.

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