First Theoretical Constructions to the Fluid Mechanics Problem of the Discharge
Author(s)
Sylvio R. Bistafa
ABSTRACT
After the publication of Hydrodynamics by Daniel Bernoulli in 1738, there was a fierce competition for priority with his father, Johann Bernoulli, and controversies with Jean le Rond D’Alembert, in which Leonard Euler seemed to have tacitly accepted the role of presiding over the disputes. These disputes were aroused by the almost simultaneous publications of Hydraulics by J. Bernoulli in 1743 and of Traité de l’équilibre et du mouvement des fluides by D’Alembert in 1744. It would be shown that despite the fact that the Bernoullis and D’Alembert used their own principles and approaches to the fluid mechanics problem of discharge, they essentially reached the same end. Nonetheless, it was Euler who brought the fluid mechanics problem of discharge to a new and definitive level with two publications. In these publications, for the first time, the pressure force and the friction force appeared explicitly in the formulations. However, the friction force was built under the wrong assumption that, as for the case of solid friction, the fluid friction force was proportional to the pressure. Finally, Lagrange’s memoir on the theory of fluid motion of 1781 is presented as a sequel to these first theoretical constructions.
After the publication of Hydrodynamics by Daniel Bernoulli in 1738, there was a fierce competition for priority with his father, Johann Bernoulli, and controversies with Jean le Rond D’Alembert, in which Leonard Euler seemed to have tacitly accepted the role of presiding over the disputes. These disputes were aroused by the almost simultaneous publications of Hydraulics by J. Bernoulli in 1743 and of Traité de l’équilibre et du mouvement des fluides by D’Alembert in 1744. It would be shown that despite the fact that the Bernoullis and D’Alembert used their own principles and approaches to the fluid mechanics problem of discharge, they essentially reached the same end. Nonetheless, it was Euler who brought the fluid mechanics problem of discharge to a new and definitive level with two publications. In these publications, for the first time, the pressure force and the friction force appeared explicitly in the formulations. However, the friction force was built under the wrong assumption that, as for the case of solid friction, the fluid friction force was proportional to the pressure. Finally, Lagrange’s memoir on the theory of fluid motion of 1781 is presented as a sequel to these first theoretical constructions.
KEYWORDS
History of Fluid Mechanics, First Theories Applied to Fluid Flow, Torricelli’s Law, Bernoulli’s Law
History of Fluid Mechanics, First Theories Applied to Fluid Flow, Torricelli’s Law, Bernoulli’s Law
Cite this paper
Bistafa, S. (2015) First Theoretical Constructions to the Fluid Mechanics Problem of the Discharge. Advances in Historical Studies, 4, 172-199. doi: 10.4236/ahs.2015.43015.
Bistafa, S. (2015) First Theoretical Constructions to the Fluid Mechanics Problem of the Discharge. Advances in Historical Studies, 4, 172-199. doi: 10.4236/ahs.2015.43015.
References
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[1] Bernoulli, D. (1968a). Hydrodynamics. Jointly Translated with Bernoulli, J. Hydraulics from the Latin by T. Carmody and H. Kobus. Dover Pub. Co. [2] Bernoulli, J. (1714). Meditatio de natura centri oscillationis. Opera omnia.
https://books.google.com.br/books?id=10EiPJr29RUC&pg=PA168-IA2&lpg=PA168-IA2&dq=Bernoulli,+
J.+%281714%29+Meditatio+de+natura+centri+oscillationis,+Opera+omnia&source=bl&ots=jwoGTH4vUT
&sig=Gbvscu9wvgfgZCTymkuTx2KJGGw&hl=pt-BR&sa=X&ei=iKAIVdaNC5OXyATEu4HwAw&ved
=0CCMQ6AEwAQ#v=onepage&q=Bernoulli%2C%20J.%20%281714%29%20Meditatio%20de%20natura
%20centri%20oscillationis%2C%20Opera%20omnia&f=false [3] Bernoulli, J. (1968b). Hydraulics. Jointly Translated with Bernoulli, D. Hydrodynamics from the Latin by T. Carmody and H. Kobus. Dover Pub. Co. [4] Blay, M. (2007). La sience du mouvement des eaux—De Torricelli à Lagrange. Paris: éditions Belin. [5] Calero, J. S. (2008). The Genesis of Fluid Mechanics 1640-1780. Series: Studies in History and Philosophy of Science (Vol. 22). Berlin: Springer. [6] D’Alembert, J. R. (1743). Traité de Dynamique.
https://ia902607.us.archive.org/16/items/traitdedynamiqu00dalgoog/traitdedynamiqu00dalgoog.pdf [7] D’Alembert, J. R. (1744). Traité de l’ équilibre et du mouvement des fluides: pour servir de suite au traité de Dynamique.
http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?mode=imagepath&url=/permanent/library/XHFB58ED/pageimg [8] D’Alembert, J. R. (1752). Essai d’une nouvelle théorie de la résistance des fluides.
http://books.google.com.br/books?id=Goc_AAAAcAAJ&printsec=frontcover&hl=pt-BR&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false [9] Darrigol, O. (2005). Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl. Oxford: Oxford University Press. [10] Eckert, M. (2002). Euler and the Fountains of Sanssouci. Archive for History of Exact Sciences, 56, 451-468. http://dx.doi.org/10.1007/s004070200054 [11] Euler, L. (1754). Sur Le mouvement de l’eau par dês tuyaux de conduite. [Eneström index] E 206.
http://eulerarchive.maa.org/ [12] Euler, L. (1757). Principes generaux du mouvement des fluides. [Eneström index] E 226.
http://eulerarchive.maa.org/ [13] Euler, L. (1761). Tentamen theoriae de frictione fluidorum. [Eneström index] E 260.
http://eulerarchive.maa.org/ [14] Hankins, T. L. (1970). Jean d’Alembert Science and the Enlightenment. Oxford: Clarendon Press. [15] Huygens, C. (1669). Regles du mouvement dans la rencontre des corps. Journal de Sçavans.
http://gallica.bnf.fr/ark:/12148/bpt6k581246/f23.image.langPT [16] Huygens, C. (1673). Horologium oscillatorium, sive de motu pendulorum ad horologia aptato demonstrationes geometricae.
http://books.google.com.br/books?id=YgY8AAAAMAAJ&printsec=frontcover&dq=inauthor:%22Christiaan+Huygens%22&hl=pt-BR&sa=X&ei=-JjqU-_rC6K-sQTOuoGgDg&ved=0CCkQ6wEwAQ#v=onepage&q&f=false [17] Huygens, C. (1929). De Motu Corporum Ex Percussione. In Ouvres, La Haye.
http://visualiseur.bnf.fr/CadresFenetre?O=NUMM-77865&I=7&M=pagination [18] Iltis, C. (1971). Leibniz and the Vis Viva Controversy. Isis, 62, 21-35. http://dx.doi.org/10.1086/350705 [19] Lagrange, J. L. (1869). Mémoire Sur la Théorie du Mouvement des Fluides. Ouvres, 4, 695-750. Paris: Gauthier-Villars. [20] Mach, E. (1919). The Science of Mechanics. Chicago & London: The Open Court Publishing Co. [21] Torricelli, E. (1644). Opera Geometrica.
http://archive.org/stream/operageometrica00torrgoog#page/n212/mode/2up [22] Truesdell, C. A. (1955). Rational Fluid Mechanics, 1687-1765. In C. A. Truesdell (Ed.), Opera Omnia (Series II, Vol. 12). Lausanne: Orell Füssli.