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The Chézy Formula is a semi-empirical resistance equation [1] [2] which estimates mean flow velocity in open channel conduits. [3] The relationship was conceptualized and developed in 1768 by French physicist and engineer Antoine de Chézy (1718–1798) while designing Paris's water canal system.
In numerical analysis, the Runge–Kutta methods (English: / ˈ r ʊ ŋ ə ˈ k ʊ t ɑː / ⓘ RUUNG-ə-KUUT-tah [1]) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. [2]
The Chézy equation is a pioneering formula in the field of fluid mechanics, and was expanded and modified by Irish engineer Robert Manning in 1889 [1] as the Manning formula. The Chézy formula concerns the velocity of water flowing through conduits and is widely celebrated for its use in open channel flow calculations. [ 2 ]
Equation is a form of the Kutta–Joukowski theorem. Kuethe and Schetzer state the Kutta–Joukowski theorem as follows: [ 5 ] The force per unit length acting on a right cylinder of any cross section whatsoever is equal to ρ ∞ V ∞ Γ {\displaystyle \rho _{\infty }V_{\infty }\Gamma } and is perpendicular to the direction of V ∞ ...
In a letter to Flamant, Manning stated: "The reciprocal of C corresponds closely with that of n, as determined by Ganguillet and Kutter; both C and n being constant for the same channel." On 4 December 1889, at the age of 73, Manning first proposed his formula to the Institution of Civil Engineers (Ireland).
Fehlberg, Erwin (1969) Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems. Vol. 315. National aeronautics and space administration. Fehlberg, Erwin (1969). "Klassische Runge-Kutta-Nystrom-Formeln funfter und siebenter Ordnung mit Schrittweiten-Kontrolle". Computing. 4: 93– 106.
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The discharge formula, Q = A V, can be used to rewrite Gauckler–Manning's equation by substitution for V. Solving for Q then allows an estimate of the volumetric flow rate (discharge) without knowing the limiting or actual flow velocity. The formula can be obtained by use of dimensional analysis.