Euler’s Power Calculations of "natural Forces" to Raise Waters with Piston Pumps

Introduction: In a 1754 publication, Discussion plus particulière de diverses manières d’elever de l’eau par le moyen des pompes avec le plus grand avantage (Very detailed explanation of the different methods of raising water through pumps with the greatest effectiveness), Leonhard Euler (1707–1783) made extensive use of the concept of mechanical power in estimates of the power needed to raise waters with piston pumps, by means of natural forces such as human and horse force, running waters, and windmills. Purpose of the study: We aimed to revisit this publication to show to the modern reader Euler’s pioneering approach in providing rational calculations of the power of natural forces needed to drive different machines to raise waters with piston pumps. Methods: After a brief historical review on the use of natural forces to drive machines and the evolution of the concept of mechanical power, the method employed was the examination and an annotated reproduction of the main formulation using Euler’s original notation and ways of scientific writing of the time. Discussion: We address the evolution of hydropower and wind power, particularly for the generation of electricity, and also show that despite of its much lower attractiveness, there have been some attempts in the use of human and animal power in developing countries, particularly in applications that do not require large and constant amounts of power inputs.