Chanson H. Jean-Baptiste Charles Joseph Belanger (1790-1874), the Backwater Equation and the Belanger Equation (796976), страница 5
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Although he succeeded, his treatise (BÉLANGER1828) is sometimes known for the treatment of the stationary hydraulic jump, nowadays called the Bélangerequation. It is shown herein that BÉLANGER (1828) correctly considered a hydraulic jump as a rapidly-15varied flow, but he applied the wrong basic principle at the time. The error was corrected ten years later andthe correct solution was first published by BÉLANGER (1841).The originality of BÉLANGER's (1828) work was the successful development of the backwater equation forsteady one-dimensional gradually-varied flows in an open channel.
His work outlined the fundamentalassumptions and he derived from momentum considerations an equation for gradually-varied open channelflows that is still in use today, but for the flow resistance model. In the same study, Jean-BaptisteBÉLANGER introduced two further modern concepts: the step method, distance calculated from depth, andthe critical flow conditions. He associated the notion of critical flow with one of the two singularities of thebackwater equation.
His technique of numerical integration was ahead of his time, when there was nocomputer nor electronic calculator.In 1828, Jean-Baptiste BÉLANGER was a young hydraulic engineer and his contribution (BÉLANGER1828) demonstrates the dynamism of practicing engineers at the time. In the second part of his career, JeanBaptiste BÉLANGER became a renowned academic at the leading French engineering schools.
He continuedto work in open channel hydraulics including on the hydraulic jump (BÉLANGER 1841). His contributionswere remarkable and influenced other leading hydraulic engineers including BRESSE (1860), DARCY andBAZIN (1865), BARRÉ de SAINT VENANT (1871), and BOUSSINESQ (1877).7.
AcknowledgementsThe writer thanks Dr Jerry R. ROGERS, University of Houston for his detailed review of the report, valuablecomments and encouragements. He acknowledges the helpful comments of many people, including Dr JerryL. ANDERSON, University of Memphis, Dr Glenn O. BROWN, Oklahoma State University, ProfessorColin J. APELT, University of Queensland, and Professor John D.
FENTON, University of Karlsruhe.He further acknowledges the assistance of Monsieur Jean-Yves JOUAN, Recherches historiques,Bibliothèque de l'Ecole Centrale de Paris, of Monsieur Guillaume SAQUET, Documentaliste du FondsAncien, Ecole Nationale des Ponts et Chaussées, of the Bibliothèque de l'Ecole Nationale Supérieure desPonts et Chaussées, and of the Archives Municipales de Valenciennes.16Appendix A - Birth certificate of Jean-Baptiste BÉLANGERThe Archives Municipales de Valenciennes provided the author with a copy of the birth certificate (1) ofJean-Baptiste BÉLANGER dated 4 April 1790 (Fig.
C-1), together with a facsimile of the marriagecertificate of his parents dated 21 April 1789. The birth certificate was handwritten and the French text isreproduced after Figure C-1, with the same spelling, punctuation and style as the original document. JeanBaptiste BÉLANGER was baptised on the day of his birth (4 April 1790). His godfather and godmother wererespectively his uncle and his aunt.The facsimile of his parents' marriage certificate is also reproduced, with the same spelling, punctuation andstyle as the original facsimile (Dated 26 June 2008).Fig.
C-1 - Birth certificate of Jean-Baptiste BÉLANGER, paroisse de St Vaast en Ville (Courtesy ofArchives Municipales de Valenciennes)TextBelangerL'an mil Sept cent quatre vingt dix le quatre avrilfur par maitre Carpentier, pretre grandeler, baptiséjeanbaptiste, charles joseph, né le même jour à Dixheures du matin, fils légitime de Charles antoine1The birth certificate acted as both birth and baptism certificates since it was common that the newborns were baptisedon the day of their birth by the local catholic priest.17aimé joseph Belanger, Serurrier et de jeanne françoisejoseph fauconnier.
fut parrain jean baptistelaurent honnis, maitre Serurrier, oncle du batiséde cette paroisse, marraine marie heleine fauconnier,tante maternelle du baptisé. laquelle avec le perea Signé. le parrain a déclaré ne Savoir lireCarpentier grandelerCharles BelangerHelene fauconnierNote : blue text = uncertain letters/words.Facsimile of marriage certificate of Charles Antoine Aimé Joseph BÉLANGER and Jeanne Françoise JosephFAUCONNIER on 21 April 1789Extrait d'acte de mariageActe rédigé le : 21/04/1789par:Maitre GOPEAU (Curé)Célébrant / Officier d'état civilà VALENCIENNES, Paroisse/Canton: St GéryConcernant le mariagede:Charles Antoine Aimé Joseph BELLANGERAgé(e) de:26 ans et 3 mois (natif de la paroisse de St Etienne à LilleExerçant la profession de :SerurrierFils / Fille de :feu Antoine Josephet de :Angélique GODEFROYet de :Jeanne Françoise Joseph FAUCONNIERAgé(e) de :27 ans (native de cette paroisse)Exerçant la profession de :Fils / Fille de :Pierre Josephet de :Marie Anne BERTON1er témoin:François FAUCONNIERParenté:Frère de l'épouse2ème témoin:Jean-Baptiste HONNISExerçant la profession de :SerurrierFait à Valenciennes, le 26/06/0818Appendix B - The names of the 72 scientists written around the Eiffel Tower, ParisThe names of 72 scientists were engraved around the first floor of the Eiffel Tower (Tour Eiffel, Paris) as atribute gesture from Gustave EIFFEL (Fig.
A-1 and A-2). The names disappeared during one of the EiffelTower's repaintings at the turn of the 20th century and they were re-established in 1986-87.NoNameNoName1Marc SÉGUIN (17861875)Joseph JérômeLEFRANCOIS deLALANDE (1732-1807)Henri TRESCA (18141885)Jean-Victor PONCELET(1788-1867)Jacques Antoine CharlesBRESSE (1822-1883)19Jules Célestin JAMIN(1818-1889)Louis Joseph GAYLUSSAC (1778-1850)2345678910111213141516171820NoNameNoName37 Augustin Louis CAUCHY 55 Jules Alexandre PETIET(1789-1857)(1813-1871)38Eugène BELGRAND56 Louis Jacques MANDÉ(1810-1878)DAGUERRE (1787-1851)21 Hippolyte FIZEAU (1819- 39 Henri Victor REGNAULT 57 Charles Adolphe WÜRTZ1896)(1810-1878)(1817-1884)22Eugène SCHNEIDER40 Augustin Jean FRESNEL 58 Urbain Jean Joseph LE(1805-1875)(1788-1827)VERRIER (1811-1877)23 Louis LE CHATELIER 41Gaspard de PRONY59Jean Albert Vincent(1815-1873)(1755-1839)Auguste PERDONNET(1808-1867)Joseph-Louis24 Pierre BERTHIER (1782- 42 Louis VICAT (1786-1861) 60Jean-Baptiste JosephLAGRANGE (1736-1813)1861)DELAMBRE (1749-1822)25 Jean-Augustin BARRAL 43Jacques-Joseph61 Étienne Louis MALUSJean-Baptiste-Charles(1819-1884)EBELMEN (1814-1852)(1775-1812)Joseph BÉLANGER(1790-1874)Henri de DION (182844Charles-Augustin de62 Louis BREGUET (1804Baron Georges Leopold 261878)COULOMB (1736-1806)1883)Chretien Frédéric DagobertCUVIER (1769-1832)Pierre-Simon LAPLACE 27Ernest GOUIN (181545 Louis POINSOT (1777- 63 Camille POLONCEAU(1749-1827)1885)1859)(1778-1847)Pierre Louis DULONG 28 Louis Didier JOUSSELIN 46Jean Bernard Léon64Jean Baptiste André(1785-1838)(1776-1838)FOUCAULT (1819-1868)DUMAS (1800-1884)Michel CHASLES (1793- 29Paul Pierre BROCA47Charles-Eugène65Benoît Paul Émile1880)(1824-1880)DELAUNAY (1816-1872)CLAPEYRON (17991864)Antoine Laurent de30 Antoine BECQUEREL 48Arthur MORIN (179566 Jean-Charles de BORDALAVOISIER (1743-1794)(1788-1878)1880)(1733-1799)André-Marie AMPÈRE 31Gaspard-Gustave49 René Just HAÜY (1743- 67Jean Baptiste Joseph(1775-1836)CORIOLIS (1792-1843)1822)FOURIER (1768-1830)Michel Eugène32Jean-François CAIL50 Charles COMBES (1801- 68Marie François XavierCHEVREUL (1786-1889)(1804-1871)1872)BICHAT (1771-1802)Eugène FLACHAT (1802- 33 Jacques TRIGER (1801- 51 Louis Jacques THÉNARD 69François Clément1873)1867)(1777-1857)SAUVAGE (1814-1872)Claude Louis Marie Henri 34 Henri GIFFARD (1825- 52 Dominique François Jean 70Théophile-JulesNAVIER (1785-1835)1882)ARAGO (1786-1853)PELOUZE (1807-1867)Adrien-Marie35 François PERRIER (1833- 53 Siméon Denis POISSON 71 Lazare Nicolas MargueriteLEGENDRE (1752-1833)1888)(1781-1840)CARNOT (1753-1823)Jean-Antoine CHAPTAL 36 Jacques Charles François 54 Gaspard MONGE (1746- 72Gabriel LAMÉ (1795(1756-1832)STURM (1803-1855)1818)1870)The names numbered between 1 and 18 are on the Facade Trocadéro.
The names numbered from 19 to 36 areengraved on the Facade Grenelle. The name numbers 37 to 54 are written on the Facade Ecole Militaire,while names numbered between 55 and 72 are listed on the Facade Paris.19Fig. A-1 - Eiffel Tower (Tour Eiffel), Paris, France on 8 July 2008 (Courtesy of Bernard CHANSON) View from Champ de Mars (Facade Ecole Militaire) with the Trocadéro in the background(A) Facade Ecole Militaire with the names of CAUCHY, BELGRAND, REGNAULT, FRESNEL, dePRONY, and VIGAT20(B) Facade Trocadéro with the names of PONCELET (incomplete), BRESSE, LAGRANGE, BÉLANGER,CUVIER, and LAPLACE(C) Facade Ecole Militaire with the names of COMBES (incomplete), THENARD, ARAGO, POISSON andMONGEFig.
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