POISEUILLE, JEAN LéONARD MARIE

(b. Paris, France, 22 April 1797; d. Paris, 26 December 1869)

physiology, physics.

Poiseuille was the son of Jean Baptiste Poiseuille, a carpenter, and Anne Victoire Caumont. From 1815 to 1816 he studied at the École Polytechnique in Paris. In 1828 he became doctor of science, but we do not know what kind of positions he held until 1860, when he was elected inspector of the primary schools in Paris. In 1829 he married a daughter of M. Panay de la Lorette, ingénieur en chef des ponts et chaussées. In 1842 Poiseuille was elected to the Académie de Médecine in Paris and to the Société Philomathique in Paris. He was also a member of several foreign societies, which included the societies of medicine in Stockholm, Berlin, and Breslau. He received the Montyon Medal in 1829, 1831, 1835, and 1843 for his researches in physiology.

Poiseuille’s name is permanently associated with the physiology of the circulation of blood through the arteries. Hales was the first to measure the blood pressure by allowing the blood to rise into a vertical glass tube. Poiseuille improved the experiment by using a mercury manometer instead of the long tube and by filling potassium carbonate into the connection to the artery in order to prevent coagulation. With this instrument, a hemodynamometer, he showed in his 1828 dissertation, “Recherehes sur la force du coeur aortique,” that the blood pressure rises and falls on expiration and inspiration. He also found that the dilatation of an artery at each heartbeat was about 1/23 of normal. Ludwig improved the instrument by adding a float, which he caused to write on a rotating drum.

Poiseuille’s interest in blood circulation led him to experiment on the flow and outflow of distilled water in capillary tubes with diameters ranging from 0.03 mm. to 0.14 mm. Such experiments had been carried out before, especially by Franz Joseph von Gerstner and Pierre-Simon Girard; but since they used tubes with larger diameters, their experiments were disturbed by turbulence. In his 1840 paper, “Recherches expérimentales sur le movement des liquides dans les tubes de très-petits diamètres,” Poiseuille announced the law Q = k(D⁴p/L), where Q is the volume discharged in unit time, k is a constant, p is the pressure difference in mm. of mercury at the two ends of the tube, D is the diameter, and L is the length. He also measured the variation of Q with the temperature T (from 0° C. to 45° C.) and found Q = 1836.724

× (1 + 0.0336793T + 0.0002209936T²)(D⁴p/L), which agrees within 0.5 percent with modern values. Poiseuille also found that the law was not valid if the length L (as a function of the diameter) was below a certain limit.

Poiseuille’s paper was reviewed by a committee consisting of Arago, Piobert, and Regnault. They persuaded him to make further experiments with ether and mercury, and these investigations were published in 1847. He found that ether yielded the same law as distilled water, whereas mercury obeyed a different law. In 1870 Emil Gabriel Warburg found that mercury obeys the Poiseuille law, except for certain anomalies caused by amalgamation in metal tubes.

In 1839 G. H. L. Hagen had already found the same law as Poiseuille, using brass tubes with diameters from 2.5 mm. to 6 mm., the temperature varying from 1° C. to l5° C. Poiseuille and the committee reviewing his paper indicated at no point any knowledge of Hagen’s researches, and it seems that Hagen’s work was not appreciated at this time, probably because he used—besides the correct experimental law—a wrong velocity profile (a wedge profile) in his theoretical investigations. In 1860 Jacob Eduard Hagenbach named the law after Poiseuille, and it was not until 1925 that Whilhelm Ostwald argued that the law should be renamed the Hagen-Poiseuille law.

A correct analytical derivation of the Hagen-Poiseuille law was given independently by Franz Neumann and Hagenbach in 1860, both of whom derived the parabolic expression for the velocity distribution and identified the constant k as an expression for the viscosity of the fluid. In 1845 Stokes calculated the discharge of long straight circular pipes and rectangular canals. Since he compared his formulas with the experiments of Bossut and Du Buat, which were complicated by turbulence, he did not evaluate the constant but obtained the parabolic velocity profile.

BIBLIOGRAPHY

I. Original Works. For Poiscuille’s dissertation of blood pressure, see “Recherehes sur la force du coeur aortique,”in Archives générales de médecine, 8 (1828), 550–554. The outflow law was published in “Recherches expérimentales sur le mouvement des liquides dans les tubes de très petits diamèstres,” in Comptes rendus hebdomadaires des séances de l’Académie des sciences, 11 (1840), 961–967, 1041–1048; 12 (1841), 112–115; also in Annalen der Physik und Chemie, 58 (1843), 424–447. His experiments on the flow of ether and mercury were published in “Recherches expérimentales sur le mouvement des liquides de nature différente dans les tubes de très-petits diamètres,” in Comptes rendus hebdomadaires des sèances de l’Académie des sciences, 24 (1847), 1074–1079, and in Justus Liebigs Annalen der Chimie, 21 (1847), 76–110.

II. Secondary Literaiure. René Taton and Mlle Cazenave have collected some of Poiseuille’s biographical dates in a MS at the Centre de Recherches Alexandre Koyré in Paris. Some biographies give 1799 or 1800 as his year of birth, but Taton has found Poiseuille’s birth certificate, his date of birth being 22 April 1797 C. Sachaile, Les médecins de Paris jugés par leurs oeuvres (Paris, 1845) mentions that Poiseuille was professor of experimental physics at the Institut de France but this is not corroborated by other evidence. Short biographies can be found in G. Vapereau, Dictionnaire universel des contemporains (Paris, 1861), 1408–1409; August Hirsch, ed., Biographisches Lexikon der hervorragende Ärzte, IV (Vienna, 1886), 599; Dechambre and Lereboullet, in Dictionnaire encyclopédigue des sciences médicales, 26 (1888), 425; and C. P. Callisen, Medicinisches Schriftsteller-Lexikon, XXXI (Copenhagen, 1843). 265. The Archives de l’Académie de Médecine in Paris has a short notice on the works of Poiseuille inMélanges scientifiques recueil de mémoires, discours, rapports, . . . 1 , no. 22; 40 , nos. 17, 18.

In “Ueber die Bestimmung der Zähigkeit einer Flüssigkeit durch den Ausfluss der Röhren;“in Annalen der Physikund Chemie, 109 (1860), 385–426, E. Hagenbach named the outflow law “Poiseuille’s law” whereas W. Ostwald, in Kolloidzeitschrift, 36 (1925), 99, argued in favor of naming it the Hagen-Poiseuille law. Much useful information can be found in L. Schiller, ed., Drei Klassiker der Strömungs Lehre: Hagen, Poiseuille, Hagenbach,Ostwalds Klassiker der exakten Wissenchaften no. 237 (Leipzig, 1933). See also Hunter Rouse and Simon Ince, History of Hydraulics (New York, 1963). C. Truesdell has commented on G. G. Stokes’s derivation of the Hagen-Poiseuille law in the intro. to the reprint of Stokes, Mathematical and Physical Papers (New York, 1966), pp. ivF., ivG. For the history of viscosity of liquids, see E. N. da C. Andrade, “The Viscosity of Liquids,” in Endeavour, 13 (1954), 117–127. For Poiseuille’s contribution to physiology, see Fielding H. Garrison, An Introduction to the History of Medicine, 4th ed. (Philadelphia-London, 1929).