a division of mechanics devoted to the study of the equilibrium and motion of liquid and gaseous mediums and their interaction with one another and with solids.

The development of hydroaeromechanics proceeded in a close relationship with practical problems. The first hydraulic-engineering devices (channels and wells) and floating structures (rafts and boats) appeared in prehistoric times. The invention of such relatively complicated aerodynamic and hydrodynamic devices as sails, oars, rudders, and pumps was also accomplished in the distant past. The development of navigation and military science served as a stimulus for the development of the foundations of mechanics and of hydroaeromechanics in particular.

From the outset, the main problem of hydroaeromechanics was the interaction between the medium (water or air) and a body that is either moving or at rest in the medium. The first scientist to make a significant contribution to hydroaeromechanics was Archimedes (third century B.C.), who discovered the fundamental law of hydrostatics and created the theory of equilibrium of liquids. The works of Archimedes formed the basis for the formation of a variety of hydraulic devices, particularly reciprocating pumps.

The next stage in the development of hydroaeromechanics dates to the period of the Renaissance (16th and 17th centuries). Leonardo da Vinci made the first significant step in the study of the motion of bodies in liquids and gases. From his observation of the flight of birds, he discovered the resistance of the medium. He believed that air, when it is compressed at the front end of the body, acts as if it were “thickened” and therefore resists the motion of bodies in it. As the air is compressed under a bird’s wing—in Leonardo’s opinion—it creates support for the wing, which generates a force that holds the bird up in flight; this force is called the lifting force. B. Pascal, while studying the force that acts at right angles to the contact surface of two elementary volumes of liquid (that is, pressure), concluded that at a given point in the liquid, the pressure acts with an equal force in all directions.

The first theoretical definition of the law of resistance was given by the English scientist I. Newton, who explained the resistance of a body during its motion in a gas by the impact of particles against the leading edge of the body and considered the magnitude of the resistance to be proportional to the square of the body’s velocity. Newton also observed that in addition to the force caused by the impact of particles, there is also a resistance from the friction of the fluid against the surface of the body (so-called frictional resistance). Having analyzed the force acting at the contact surface between two elementary liquid volumes, Newton found that the frictional stress between two layers of liquid is proportional to the relative velocity of glide of these layers over each other.

Having established the basic laws and equations of mechanics, Newton opened the way for the transition of hydroaeromechanics from the study of isolated problems to the investigation of the general laws of motion of liquids and gases. The creators of theoretical hydrodynamics were L. Euler and D. Bernoulli, who applied the laws of mechanics known at that time to the study of the flow of fluids. Euler was the first to derive the equations of the so-called ideal fluid—that is, one that is nonviscous. The works of the French scientists J. Lagrange and A. Cauchy, the German scientists G. Kirchhoff and H. Helmholtz, the English scientist G. Stokes, and the Russian scientists N. E. Zhukovskii, and S. A. Chaplygin, and others developed the analytical methods for the study of the ideal fluid flow. These methods were applied to the solution of numerous important problems related to the motion of fluids in channels of various forms, to the outflow of jets of liquid into spaces filled with liquids or gases, and to the motion of solids in liquids and gases. The development of the theory of waves generated on the surface of a liquid—for example, by the action of the wind or during the motion of ships—was of great importance for practical applications.

The main achievement of hydroaerodynamics during the 19th century was the transition to the study of the motion of viscous fluids, which was due to the development of hydraulics, hydraulic engineering, and machine building (lubrication of machine parts under friction). Experiments showed that at low speeds the resistance depends basically on the viscous forces. These forces also determine the resistance during the motions of liquids in channels and pipes. Stokes, in analyzing the deformation of the elementary volume of a liquid during its displacement, established that the viscous stresses arising in the liquid depend linearly on the rate of deformation of the liquid particle. This law, by generalizing Newton’s law for friction, made it possible to supplement Euler’s equation of motion with terms that take into account forces arising because of the viscous action of liquids or gases. The derivation of the equations of motion for viscous liquids and gases (the Navier-Stokes equations) made it possible to study the flow of real (viscous) continuous mediums. However, the solution of these equations in the general form still presents great difficulties; therefore, simplifications of the problem by eliminating from the equations those terms that are insignificant in the given case are frequently used in the study of viscous flow.

Experimental methods are of great importance in hydroaeromechanics. Another important difference between real and ideal gases and liquids that was discovered was the capability of transferring heat, which is characterized by the heat conductivity value. Hydroaeromechanical methods were also used to develop the theory of the filtration of liquids through soils, which is important in hydraulic engineering, petroleum extraction, and gasification.

The equation of the boundary layer, which was first derived by the German scientist L. Prandtl in 1904, was of decisive importance to the entire subsequent development of the science concerning the motion of real liquids and gases, which are viscous and are capable of transferring heat. According to Prandtl’s hypothesis, the entire effect of viscosity is manifested only in the thin layer of the liquid or gas adjacent to the surface over which the fluid is flowing. For this reason, the flow of a real viscous fluid outside of this layer does not differ in any way from the motion of an ideal (non-viscous) fluid. Thus, the problem of the motion of a viscous fluid or gas is divided into two problems: the study of the flow of the ideal fluid outside of the boundary layer and the study of the viscous fluid within the boundary layer.

Another branch of hydroaeromechanics—the study of the flow of a compressible continuous medium—began to develop during the second half of the 19th century. Almost all fluids are virtually incompressible, and their density, therefore, remains unchanged in the process of flowing. Gases, on the other hand, change their volume—and consequently their density—very readily under the influence of changes in pressure and temperature. The branch of hydroaeromechanics that is devoted to the study of continuous compressible mediums is called gas dynamics. The demands of aviation and rocket technology (first and second quarters of the 20th century, respectively) stimulated the development of aerodynamics and gas dynamics.

The creation of rockets and rocket motors using liquid and solid fuels of complex chemical composition, the advent of the era of the flight of spacecraft in the atmosphere of the earth and other planets, an increase in the speed of atomic submarines used as nuclear missile carriers, the creation of a worldwide weather service using artificial earth satellites, and the synthesis of various natural sciences, as well as other elements of scientific and technological progress during the 20th century, have significantly increased the role of hydroaeromechanics in the life of humanity.

Modern hydroaeromechanics is a diversified science that consists of many subdivisions and is closely associated with other sciences, above all mathematics, physics, and chemistry. The motion and equilibrium of incompressible fluids are studied in hydromechanics (fluid mechanics); the motion of gases and their mixtures, including air, are studied by gas dynamics and aerodynamics. Branches of hydroaeromechanics include the theory of filtration and the theory of the wave motion of a fluid. Technological applications of hydroaeromechanics include hydraulics and applied gas dynamics, and applications of the laws of hydroaeromechanics to the study of climate and weather are investigated in dynamic meteorology. The methods of hydroaeromechanics are being used for the solution of various problems in the areas of aeronautics, artillery and rocket technology, the theory of shipbuilding and power-engineering machine building, the design of chemical equipment, and the study of biological processes (for example, the circulation of blood), hydraulic-engineering structures, the theory of combustion, and meteorology.

The first main task of hydroaeromechanics consists in the determination of the forces acting on bodies or elements of bodies that are moving in liquids or gases and in the determination of the most advantageous shapes for the bodies. Knowledge of these forces makes it possible to determine the required power of the motors that move the bodies, as well as the trajectories of the bodies. The second task is the shaping (determination of the most advantageous form) of the channels of various machines involving the use of gases and liquids—jet engines and rocket motors in aircraft and rockets, centrifugal and axial compressors and pumps, and gas, water, and steam turbines in electric power plants. The third task is the determination of the gas or liquid parameters in the proximity of solid bodies, in order to take into account the effect of the force, thermal, and physicochemical actions on these bodies caused by the flow of gas or liquid. This task is related both to the flow of liquids or gases around the bodies and to the flow of liquids and gases through channels of various shapes. The fourth task is the study of the motion of air in the atmosphere and of water in the seas and oceans, which is undertaken by geophysics (meteorology, ocean physics) with the aid of the methods and equations of hydroaeromechanics. Problems of the propagation of shock and explosion waves and of the streams generated by the jet and rocket engines in air and water are related to this task.

The solution of practical problems of hydroaeromechanics in various branches of technology is achieved by experimental as well as theoretical methods. Modern technology sometimes leads to such parameters of gas or liquid flow that it is frequently impossible to generate conditions for a complete experimental study of the flow using models. In this case, partial simulation is performed experimentally—that is, the separate physical phenomena in the moving gas or liquid that occur in real flow are studied, a physical model of the flow is determined, and the required experimental relationships among the characteristic parameters are found. Theoretical methods based on precise or approximate equations that describe the flow make it possible, using the experimental data, to collect all of the significant physical phenomena in the moving gas or liquid and to determine the flow parameters, taking account of these phenomena in the given concrete problem. A high degree of perfection became possible with the appearance of high-speed electronic computers. The use of electronic computers in solving problems in hydroaeromechanics has also changed the methods of solution: solution by direct integration of the initial system of equations describing the motion of the gas or liquid and all of the physical processes accompanying this motion is frequently possible. Progress in the theoretical methods of hydroaeromechanics and the development of electronic computers make it possible to solve problems of ever-increasing complexity.

Theoretical and experimental studies in the area of hydroaeromechanics are concentrated at large institutes and scientific centers. The development of hydroaeromechanics in the USSR was promoted by the creation in 1918 of the Central Aerodynamic and Hydrodynamic Institute in Moscow, which became the principal center for studies related to aviation, hydraulic machine building, shipbuilding, and industrial aerodynamics.

Research in the area of hydroaeromechanics is conducted at Moscow State University, Leningrad State University, and other institutions of higher learning, as well as at many specialized research institutes of the various ministries and departments of the USSR.

In the USA, the main research activity in the area of hydroaeromechanics is carried out under the guidance of the National Aeronautics and Space Administration (NASA) at a number of centers (Marshall, Ames, Lewis, Langley, and Goddard), as well as in universities, in the laboratories of large firms, and at research centers of the US Air Force and Navy. Large centers of hydroaeromechanical studies in England are the Royal Aeronautical Society (RAS), the Royal Aviation Establishment (RAE) at Farnborough, the aerodynamics section of the National Physical Laboratory (NPL), and Cambridge and Oxford universities. In France, research in hydroaeromechanics is directed by the National Center for Scientific Research at the laboratories located in Modane-Avrieux, Chalais-Meudon, and other locations. In West Germany, these studies are concentrated at the Aviation and Space Center (DFL) in Braunschweig, the Experimental Aviation and Space Center (CVL) in Porz Wahn, and the Aerodynamics Research Center (AVA) in Göttingen. Important studies in hydroaeromechanics are being conducted in Italy, Japan, Switzerland, and other countries.

The results of theoretical and experimental studies in hydroaeromechanics are published in many scientific and engineering periodicals, the most important of which include Doklady Akademii Nauk SSSR (Reports of the Academy of Sciences of the USSR; mathematics and physics series—since 1922), Izvestiia Akademii Nauk SSSR (Transactions of the Academy of Sciences of the USSR; fluid and gas mechanics series—since 1966), and Prikladnaia matematika i mekhanika (Applied Mathematics and Mechanics, since 1933) in the USSR; Journal of the American Institute of Aeronautics and Astronautics (AIAA Journal, New York, since 1963; in Russian translation— Rake-tnaia tekhnika i kosmonavtika, Moscow, since 1963), Journal of Applied Mechanics (New York, since 1934; in Russian translation— Prikladnaia mekhanika: Seriia E, Moscow, since 1961), and Physics of Fluids (New York, since 1958) in the USA; Journal of the Royal Aeronautical Society (London, since 1923) and Journal of Fluid Mechanics (London, since 1956) in Great Britain; Comptes rendus hebdomadaires des séances de l’Académie des Sciences (Paris, since 1835) and La Recherche aéronautique: Bulletin bimestriel de l’Office national d’études et des recherches aéronautiques (Paris, since 1948) in France; Zeitschrift für Flugwissenschaften (Braunschweig, since 1953) in the Federal Republic of Germany; and Zeitschrift für angewandte Mathematik und Mechanik (Berlin, since 1921) in the German Democratic Republic.


Loitsianskii, L. G. Mekhanika zhidkosti i gaza, 3rd ed. Moscow, 1970.
Prandtl, L. Gidroaeromekhanika. Moscow, 1949.


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