Eur. Phys. J. H 40, 375–384 (2015)
https://doi.org/10.1140/epjh/e2015-60031-2

Euler’s friction of fluids theory and the estimation of fountain jet heights

Polytechnic School, University of São Paulo, 05508-900 São Paulo, Brazil

^a e-mail: sbistafa@usp.br

Received: 17 June 2015
Received in final form: 7 August 2015
Published online: 15 September 2015

Abstract

In 1761, Leonhard Euler (1707–1783) published a treatise with the title “Attempt at a Theory of the Friction of Fluids”, in which he assumed that, as is the case for solid friction, fluid friction is proportional to pressure. Several experiments were proposed by Euler to derive a friction factor, which were intended to experimentally confirm his equations. Detailed developments of five different problems of discharge were presented in his treatise, taking into account the loss of head in the conduits. In the Appendix, an example is given of the calculation of the jet heights of a particular fountain, fed with conduits of different cross-sectional areas. Application of the current method for the calculation of head losses in pipes reveals that Euler grossly overestimated the fountain jet heights.