# Petrov, Nikolay Pavlovich

# PETROV, NIKOLAY PAVLOVICH

(*b* . Trubchevsk, Orlovskaya Oblast, Russia, 25 May 1836; *d* . Tuapse, U.S.S.R., 15 January 1920)

*mechanics, engineering.*

The son of a military man, Petrov graduated in 1855 from the Konstantinovsky Military School in St. Petersburg with the rank of ensign. He immediately enrolled at the Nikolaevskaya Engineering Academy, where Vyshnegradsky guided his studies in applied mechanics and where he was especially influenced by Ostrogradsky. After graduating in 1858, Petrov was retained in the mathematics department, where he worked under Ostrogradsky. On the latter’s death in 1862 Petrov began teaching a course in higher mathematics at the Academy, while from 1866 he taught applied mechanics at the St. Petersburg Technological Institute. In 1867 he became adjunct professor of applied mechanics at the Engineering Academy.

In 1876 Petrov was invited to the U.S. Centennial Exposition in Philadelphia. On the basis of material collected during this trip, he published a work in 1882 on mechanical equipment for ports and cargo deposits at railroad stations; it presented methods for designing elevators and mechanical devices used in shipping grain and coal. In a paper published in 1878 on continuous braking systems of trains, he was the first to arrive at equations for the motion of wheels in the presence and absence of braking, as well as an equation for the motion of the center of gravity of a train during braking. As a result of his theoretical investigations, he found the true maximum speed for any possible braking system.

In 1888 Petrov was elected an honorary member of the Moscow Polytechnical Society and was awarded the gold medal of the Russian Technical Society for inventing an instrument to determine the internal and external friction of liquids. As chairman of the Department of State Railroads (1888-1892) he was active in the construction of the Trans-Siberian Railroad. In 1892 he became chairman of the Engineering Council of the Ministry of Means of Communication, and from 1893 to 1900 he was deputy minister of means of communication. In 1894 Petrov became an honorary member of the St. Petersburg Academy of Sciences, and from 1896 to 1905 he was chairman of the Russian Technical Society.

Petrov’s most important work was in the hydrodynamic theory of lubricants. His investigations were characterized by a masterful command of mathematical method and an outstanding gift for experiment. Petrov’s results were based on broad experimental study of friction in liquids and machines, the most important part of which he conducted himself.

Petrov accurately formulated the physical laws that might provide a basis for calculating elementary frictional forces. He demonstrated that the frictional force developed within a viscous liquid is proportional to the velocity of relative motion and to the surface area of contact; it does not depend on pressure, and the coefficient of proportionality depends only on the properties of the liquid.

Petrov also confirmed experimentally Newton’s formula for the force of resistance of a viscous liquid with one layer in motion relative to another layer, *F* = μ(∂ν/∂n) , where ν is the velocity, *n* is the distance between layers along the normal to the surface of constant velocity, and ∂ is the coefficient of viscosity. He determined that the internal friction of a liquid varies significantly with temperature; this relationship was experimentally determined for each type of lubricant.

Petrov also studied the effects of friction in a bearing in which the lubricating layer fills the intermediate space between two cylinders having a common geometrical axis. During rotation friction causes the shaft to carry along with it the nearest adjacent layer of lubricant. This layer moves more slowly than the shaft, since it is impeded by friction with the next adjacent layer of lubricant. The last layer, carried along by friction with the penultimate layer, is in turn retarded by friction with the surface of the bearing. Using this model, Petrov examined bearings that operate with only a thin layer of lubricant. Computing the equations of motion of a viscous liquid, integrating them, and using Newton’s formula presented above, he discovered the law of friction that bears his name.

Petrov’s works have formed the basis of the hydrodynamic theory of friction in the presence of lubrication and provided an impetus for the further development of theoretical and experimental research in this field.

## BIBLIOGRAPHY

I. Original Works. The basic ideas of Petrov’s hydrodynamic theory of lubricants were stated in the following works: “Trenie v mashinakh i vlianie na nego smazyvayushchey zhidkosti” (“Friction in Machines and the Influence of a Lubricating Liquid on It”), in *Inzhenernyi zhurnal*, **24** (1883), no. 1, 71–140; no. 2, 227–279; no. 3, 377–436; no. 4, 535-641; also published separately (St. Petersburg, 1883); *Opisanie i rezultaty opytov nad treniem zhidkostey i mashin* “Description and Results of Experiments on the Friction of Liquids and Machines” St. Petersburg, 1886); “Prakticheskie rezultaty opytov” (“Practical Results of Experiments”), in *Inzhenernyi zhurnal*, **26** (1887), also published separately; and “Frottement dans les machines,” in *Zapiski Imperatorskoi akademii nauk*, **10** , no. 4 (1900), 1–84.

His other writings include “Ochertanie zubstov kruglykh tailindricheskikh koles dugami kruga” (“Configuration of the Teeth of Round Cylindrical Wheels With Circular Arcs”), in *Inzhenernyi zhurnal*, **12** (1871), which was his first scientific paper; *O nepreryunykh tormoznykh sistemakh* “On Continuous Braking Systems” St. Petersburg, 1878); *Peregruzka i khranenie khlebnogo zerna, Peregruzka I kamenogo ugla* (“Shipmem and Storage of Cereal Grain. Shipment of Coal” St. Petersburg, 1882); *Résultats les plus marquants de l’étude theorique et expérimentale sur le frottement mediat* (St. Petersburg, 1889); “Sur le frottement des liquides,” in *Izvestiya Imperatorskoi akademii nauk*, **5** (1896), 365–373; *Un moyen de determiner les deformations du rail soutenu par des supports mobiles sous la pression d’une roue usée en mouvement* (St. Petersburg, 1910); and *Davlenie koles na relysy. Prochnost relsov i ustoychivost puti* (“The Pressure of Wheels on Rails. Strength of the Rails and Stability of the Track” St. Petersburg, 1915), a summary of his investigations.

Petrov’s writings are also included in L. S. Leybenzon, ed., *Gidrodinamicheskaya teoria smazki* (“The Hydrodynamic Theory of Lubricants” Moscow-Leningrad, 1934); and L. S. Leybenzon, ed., *Gidrodinamicheskaya teoria smazki*, in the series Klassiki Nauki (Moscow, 1948), an anthology.

II. Secondary Literature. On Petrov and his work, see A. S. Akhmatov, “Nikolay Pavlovich Petrov,” in *Lyudi russkoy nauki. Tekhnika* (“ Men of Russian Science;” Moscow, 1965), 240–246; A. T. Grigorian, *Ocherki istorii mekhaniki v Rossii* (“Sketches of the History of Mechanics in Russia” Moscow, 1961), 213–217; V. M. Kostomarov and A. G.Burgvits, *Osnovopolozhnik teorii gidrodinamicheskogo trenia v mashinakh N. P. Petrov* (“Petrov, the Founder of the Theory of Hydrodynamic Friction in Machines” Moscow, 1952); and L. S. Leybenzon and N. I. Glagolev, “Vydayushchysya ucheny i inzhener N. P. Petrov” (“The Outstanding Scientist and Engineer N. P. Petrov “), in *Izvestiya Akademii nauk* SSSR, no.7 (1946), 929–933.

A. T. Grigorian

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