# Dupuit, Jules

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## Dates

Arsène Jules Etienne Juveénal Dupuit May 18, 1804, (Fossano, Italy) - October 5 1866 (Paris, France)

## Biography

Jules Dupuit was born in Fossano, Italy then under the rule of Napoleon Bonaparte. At the age of ten he emigrated to France with his family where he studied in Versailles — winning a Physics prize at graduation. He then studied in the École Polytechnique as a civil engineer. He gradually took on more responsibility in various regional posts. He received a Légion d'honneur in 1843 for his work on the French road system, and shortly after moved to Paris. He also studied flood management in 1848 and supervised the construction of the Paris sewer system. He died in Paris.

Arsène Jules Etienne Juveénal Dupuit was born on May 18, 1804, at Fossano, then a part of France in Piedmont, where his father was an imperial inspector of finances. In 1822 he entered the Ecole Polytechnique, and continued his studies at the Ecole des Ponts et Chaussées. In 1829 he was appointed ordinary engineer of the Sarthe department. There, he was in charge of roads, and in 1833 and 1834 conducted experiments on the pulling of cars and thus investigated friction as a function of road surface and car-wheel characteristics. Another paper was directed at the effect of road curves on car friction Dupuit 1838b. In 1839 he was called to Paris to submit a report and to suggest a means for road maintenance. The administration was satisfied with his work and awarded him a gold medal. One year later, Dupuit was appointed engineer of the Marne department and in 1842 promoted to chief engineer. Here, he applied the methods proposed for road improvement writing a paper that was awarded a gold medal. In 1843, Dupuit was decorated a member of Légion d’Honneur for his contributions to road improvement.

After long governmental discussions on the optimum method for road improvement, the February 1848 revolution put an abrupt end to that research. In 1849, Dupuit was named secretary of the commission that investigated wheel-rolling resistance. In 1850, Dupuit was promoted to Officer of Légion d’Honneur for his research into this important question. During his stay in the Maine-et-Loire department, Dupuit witnessed the large 1846 floods of the River Loire and began investigating flood movement in its aftermath. This experience completely turned around his engineering career. Dupuit's 1948 book is the result of his work to improve rivers in order to reduce damage caused by large floods. He asked for detailed investigations of flood movements in rivers, a task later considered by Henry Bazin. The 1848 book was revised in 1963 to address both groundwater and river flows.

In 1850, he was at the city of Angers to design the water supply system based on a groundwater current of the Loire River and two bridges, one of which had 14 arches, each 25 m long Dupuit 1850. In May 1850, Dupuit received a call to return to Paris and head the municipal service in succession to Henry Darcy (1803–1858). Also, he arranged the reconstruction of large sewers and investigated the distribution and collection of waters. The results were published in a book (Dupuit, 1854) where detailed descriptions were presented of wells for a water supply, improved sewer cross-sectional shapes, and the sewer of the Se ́bastopol Boulevard, among other topics.

A second edition (Dupuit 1865) accounted for new findings relating to natural water filtration, groundwater prospect, and the installation and maintenance of steam machines used for pumping water. In 1855, Dupuit was appointed Inspector General, 2nd class, and a member of the commission on steam machines. During the years until his death, he also was a member of Council of the Ecole des Ponts et Chaussées. In 1857, he tried in vain to become a member of Académie des Sciences. During the rest of his life, Dupuit published works on political economics and hydraulics. He was an ardent polemist, always ready to attack the ideas of others that he saw differently. It was that liberty of mind paired with a difficult character that resulted in some discredit among colleagues. His opinions were described to have been always well founded but too absolute. He died in Paris at the premature age of 62 on October 5, 1866. A full life had come to the end, which did not have the influence on his contemporaries that it deserved. A book on the construction of arches and bridges was published posthumously. A lasting monument to Dupuit is in the Ecole des Ponts et Chaussées in Paris, where his bust has been placed in the entrance.

## Hydrological Achievements

In 1854, Dupuit published Traiteé théorique et pratique de la conduite et de la distribution des eaux (Theoretical and practical treatise on conduits and the distribution of water). The book is subdivided into two parts, the latter being the contribution of Jean-François d’Aubuisson de Voisins (1769–1841), well known for his work on natural filters and hydraulic experiments conducted at Toulouse. Genieys, a predecessor of Dupuit in the Paris municipal service, added a short history on water supplies. It should be noted that Dupuit’s work was published 2 years prior to that of Henry Darcy on a similar topic, and both used outstanding engravers that created lasting hydraulic engineering documents.

In Chapter 5, Dupuit introduces the hydraulics of networks and derived the by now standard chain relations for equivalent pipe diameters. These basic equations are then applied to urban water supply networks and to the flows of various reservoirs into a pipeline system. In all his computations, the flow formula of Gaspard de Prony ( (1755 – 1839) is adopted. In Chapter 11, unsteady pipe flow between two reservoirs of different head is considered. Today, the surge tank problem would be approached with the corresponding differential equation. Dupuit’s simplified approach neglected inertia and fluid friction forces, thus allowing for a closed form solution. He introduced dimensionless expressions for pipe velocity and time, to determine the extreme down- and up-surge conditions together with the period of one surge cycle. His results were finally applied to a then recently completed installation in Cornwall. To facilitate works of the practicing engineer, the book is accompanied with a number of documents, computational examples, and numerical tables.

In 1858 he presented a pamphlet following the second (1856) large flood on the Loire River. According to public opinion, floods were particularly common for rivers running between dikes. As a reaction, engineers had erected dams in the side valleys to retain the maximum wave from the main river. The Loire catchment was particular in this regard, with its 20-m-high Pinay dam that had been erected in 1711 for that purpose. It was located 33 km upstream from the city of Roanne and created a reservoir by which floodwater could be retained. After a description of its origin, and some aggressive remarks against two of his colleagues involved in the aftermath of the 1846 flood, Dupuit stated that a reservoir increases the flood period while the peak discharge is reduced. This principle results from the basic retention equation with the temporal change of reservoir volume being equal to the net storage divided by the reservoir surface. During low water, the flow is below a bridge; whereas, the water may overtop the dam during the flood season. Such structures retain considerable volumes of water but submerge large portions of land in the upstream reach, with considerable consequences for nearby reservoir residents. Dupuit continues that the difficulty was to find suitable locations for dams. He then considered the alternative of river dikes to reduce floods and their potential of destruction. His general conclusions were the following:

- Dams like Pinay have only a limited influence on floods of large rivers such as the Loire.
- Small reservoirs erected in mountains demand extraordinary design and costs, are inefficient for large floods, and may behave adversely when filled during a long storm period.
- River dikes have proved to be effective, although several were damaged during floods. Dams should thus be incorporated with dikes to result in a combined flood defense.
- The height of dikes is related to the damage produced under a breach. The government should control these works. The finances required should be collected from those who profit, with a system of assurances.

In the area of groundwater flows, The Dupuit-Forchheimer equation is a lasting contribution of Dupuit and the Austrian Philipp Forchheimer ( (1852–1933) a hydraulics professor at the University of Graz. They provided the first analytical solutions for groundwater flow in an aquifer. The Dupuit theory was criticized by Jaeger because it did not contain the vertical velocity component. His improved solution is mathematically more precise, but also lacks a definition of the active well extension. The other effect neglected is the outflow boundary condition at the interior well surface, which has a finite length in contrast to the Dupuit assumption. However Dupuit’s solution remains useful for preliminary analysis of isolated wells.

Dupuit’s 1863 book is one of the very first that was almost entirely devoted to channel flow. It should be noted that Chapter 8 was submitted in 1861 to Académie des Sciences in Paris as a paper for its Mémoires. The report by the reviewers was favorable, but Dupuit was asked to revise parts. Dupuit declined and added the chapter to the 1863 book. Depute provides an analysis of the velocity distribution in an open channel. His analysis results in a parabolic distribution. Such distributions were determined experimentally by Darcy and Bazin. Once the general velocity distribution is available, other quantities such as the discharge, the ratio between bed and surface velocities, and the location of average velocity may be determined. The analysis assumes a finite bottom velocity was assumed, although scientists such as Jean Poiseuille (1797–1869) had demonstrated that for laminar flow the bottom velocity goes to zero. Dupuit also established relations for the energy correction for the Coriolis coefficient and then proceeds to derive the gradually varied flow equation.

Dupuit of course realized the significance of the ratio q2/(gh3), actually referred to as the square of the Froude number F. He stated that for F<1, flows may produce a backwater. Dupuit also integrated hydraulic jumps into his analysis, by following the procedure outlined by Jean-Baptiste Bélanger (1790–1874). He analyzed the effect of cross-sectional shape and thus was able to portray almost completely 1D open channel flows. In Chapter 4, flows in non-prismatic channels are analyzed using a step-by-step method. The next two chapters addressed spatially varied and unsteady flows, with application to flood movement in rivers. From a hydraulic point of view, the basic equations were presented in 1871 by Adhémar Barré de Saint-Venant (1797– 1886). Chapter 7, on mobile bed rivers, was mainly a qualitative description, and Dupuit ends it by noting that, ‘‘We do not expand furthese important questions. Maybe it is regrettable that we have not concise and simple formulas which would respond to the needs of practice, as formulas in algebra. ... Today, knowledge has not advanced sufficiently, however....’’ In the last chapter of the book he rederived the Darcy equation.

Dupuit also considered confined groundwater flow from Artesian wells. Further analysis was directed to the Darcy groundwater experiment, flows across layered material, and emptying flow from a tank. Then, well hydraulics is presented and the Passy well project of Paris was described, for which Dupuit was responsible as the municipal engineer. The book reviews the main hydraulic chapters written by Dupuit over his engineering career. It represents a classical text of open channel and groundwater hydraulics.

## Reference Material

Source: Jules Dupuit Wikipedia Page

Source: Hager, W.H. (2004): Jules Dupuit—Eminent Hydraulic Engineer. Journal of Hydraulic Engineering, Volume 130, Issue 9, pp. 843–848. doi:10.1061/(ASCE)0733-9429(2004)130:9(843)[1]

Combes, C. 1854. ‘‘Traité théorique et pratique de la conduite et de la distribution de eaux by M. Dupuit.’’ Comptes Rendus de l’Académie des Sciences, 39, 41–43.

Combes, C. 1861. ‘‘Rapport sur un mémoire de M. Dupuit intitulé: Mémoire sur le mouvement de l’eau à travers les terrains perméables.’’ Comptes Rendus de l’Académie des Sciences, 52, 1121–1131.

Brown, G O, 2004, Jules Dupuit's Contributions in Water Resources, in Jerry R. Rogers; Glenn O. Brown; and Jürgen D. Garbrecht(Eds.), Water Resources and Environmental History, 104-110, ISBN: 978-0-7844-0738-7; DOI: 10.1061/40738(140)14

## Major Publications

Dupuit, J. 1843. Etablissement des fontaines publiques de Rheims, d’après les plans et sous la direction de M. J. M. Cordier, Luton, Rheims.

Dupuit, J. 1848. Etudes théoriques et pratiques sur le mouvement des eaux courantes, Dunod, Paris.

Dupuit, J. 1854. Traité théorique et pratique de la conduite et de la distribution des eaux, Carilian-Goeury et Dalmont, Paris.

Dupuit, J. 1857. Mouvement de l’eau à travers le terrains perméables. Comptes Rendus de l’Académie des Sciences, 45, 92–96.

Dupuit, J. 1858. Des inondations—Examen des moyens proposés pour en prévenir le retour, Dalmont, Paris.

Dupuit, J. 1858. Mémoire sur les inondations et les moyens proposés pour en prévenir le retour. Comptes Rendus de l’Académie des Sciences, 46, 935–936.

Dupuit, J. 1863. Etudes théoriques et pratiques sur le mouvement des eaux dans les canaux découverts et àtravers les terrains perméables, Dunod, Paris.

Dupuit, J. 1865. Traité théorique et pratique de la conduite et de la distribution des eaux, 2nd Ed., Dunod, Paris.