Euler Analysis of a Machine for Raising Waters Proposed by Mr. de Mour

Abstract

We examine a publication by Euler, Sur une nouvelle manière d’élever de l’eau propose par M. de Mour (On a new method to raise water proposed by Mr. de Mour), published in 1753, addressing a type of water sprinkler, consisting of an inclined tube with its lower end immersed into water, and discharging at its top by turning a vertical axis to which the inclined tube is attached. In this publication, Euler uses pioneering approaches by applying the concept of mechanical power to estimate the power needed to drive the machine by the human force, and by measuring time by the length of a pendulum necessary to achieve one oscillation. Several design formulas were derived for the determination of the output of the machine, giving also measures for its construction, and supported at the end by a numerical example to show the feasibility of the proposition. This is, perhaps, one of the earliest attempts to design a rotating machine to raise waters.