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Jean Le Rond D'Alembert: A New Theory of the Resistance of FluidsApplication of the Same Principles to Some Research on Streams in Rivers

Jean Le Rond D'Alembert: A New Theory of the Resistance of Fluids: Application of the Same... [156. Let be Bm (Fig. 9.1) the bottom of the river, CM its upper surface, and let it be assumed that the river flows from C to M, and that its riverbed is of equal width everywhere. Drawing at will the horizontal Qo and the vertical AQ, it is true that we can express the horizontal and vertical velocities of any point o by p and q, that is to say by the functions of QA, as x, and Qo, as z. In addition, it will be found by the methods already explained, that if dq = Adx + Bdz, we will have dp = Bdx − Adz. Therefore, 1st, [It is possible to] know the quantities q and p with a coefficient, as in art.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Jean Le Rond D'Alembert: A New Theory of the Resistance of FluidsApplication of the Same Principles to Some Research on Streams in Rivers

Part of the Studies in History and Philosophy of Science Book Series (volume 47)
Editors: Calero, Julián Simón
Simón Calero, Julián
Jean Le Rond D'Alembert: A New Theory of the Resistance of Fluids — Jan 13, 2018
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Publisher
Springer International Publishing
Copyright
© Springer International Publishing AG 2018
ISBN
978-3-319-67999-0
Pages
117 –119
DOI
10.1007/978-3-319-68000-2_9
Publisher site
See Chapter on Publisher Site

Abstract

[156. Let be Bm (Fig. 9.1) the bottom of the river, CM its upper surface, and let it be assumed that the river flows from C to M, and that its riverbed is of equal width everywhere. Drawing at will the horizontal Qo and the vertical AQ, it is true that we can express the horizontal and vertical velocities of any point o by p and q, that is to say by the functions of QA, as x, and Qo, as z. In addition, it will be found by the methods already explained, that if dq = Adx + Bdz, we will have dp = Bdx − Adz. Therefore, 1st, [It is possible to] know the quantities q and p with a coefficient, as in art.]

Published: Jan 13, 2018

Keywords: Equal Width; River Flow; Vertical Velocity; Undetermined Coefficients; Vertical Force

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