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branch of engineering concerned mainly with moving liquids. The term is applied commonly to the study of the mechanical properties of water, other liquids, and even gases when the effects of compressibility are small. Hydraulics can be divided into two areas, hydrostatics and hydrokinetics. Hydrostatics, the consideration of liquids at rest, involves problems of buoyancy and flotation, pressure on dams and submerged devices, and hydraulic presses. The relative incompressibility of liquids is one of its basic principles. Hydrodynamics, the study of liquids in motion, is concerned with such matters as friction and turbulence generated in pipes by flowing liquids, the flow of water over weirs and through nozzles, and the use of hydraulic pressure in machinery.



the science that deals with the laws of motion and equilibrium for liquids and with methods of applying these laws to solve practical engineering problems. In contrast to hydromechanics, hydraulics takes a fundamental approach to the study of phenomena of fluid flow; it establishes approximate relationships, which in many cases are restricted to consideration of one-dimensional motion, and makes use of experiments under both laboratory and natural conditions. At the same time, hydromechanics and hydraulics appear to be drawing closer together: on the one hand, hydromechanics is turning more often to experiment, and on the other, the methods of hydraulic analysis are becoming more rigorous.

Hydraulics studies liquids, usually treating them as incompressible. However, the conclusions of hydraulics are applied to gases in cases in which the pressure in them, as well as their density, is nearly constant. Gas flow at high velocities is investigated in gas dynamics. Since hydraulics mainly considers the so-called internal problem—that is, the motion of a fluid within solid boundaries—it scarcely touches upon the question of the distribution of forces on the surface of aerodynamic bodies, which is dealt with in detail in aerodynamics.

Hydraulics is subdivided into two parts—the theoretical foundations, where the most important aspects of the science of equilibrium and fluid motion are set forth, and practical hydraulics, which applies these statements to the solution of particular problems in engineering practice. The main divisions of practical hydraulics are the flow in tubes (tube hydraulics), the flow in canals and rivers (hydraulics of open channels), the discharge of fluids from orifices and through spillways, the movement in porous mediums (filtration), and the interaction between a stream and a solid obstruction (hydraulics of structures). In all these divisions the motion of the fluid is treated from both the steady-state and unsteady (nonstationary) points of view.

In dealing with the equilibrium of fluids, hydraulics studies the general laws of hydrostatics, as well as particular questions, such as the pressure of a fluid on the walls of various vessels, pipes, dams, the piers and abutments of bridges, and other structures; the pressure on bodies immersed in a fluid (Archimedes’ principle); and the equilibrium conditions of floating bodies. In the treatment of the motion of fluids, hydraulics utilizes the fundamental equations of hydrodynamics, the most important of which are Bernoulli’s equation for a real fluid (which defines the overall relationship of pressure, height, fluid flow velocity, and pressure losses) and the equation of discontinuity in hydraulic form. Hydraulics treats in detail the question of hydraulic resistances that arise under various fluid flow conditions, as well as the conditions of transition from one mode to the other. Tube hydraulics indicates methods of calculating the dimensions required to pass a given rate of flow under given conditions, as well as for solving a number of problems that arise in the design and construction of pipelines for various purposes (water mains, pressure pipes for hydroelectric stations, and oil pipelines). The question of the velocity distribution in pipes, which is very important for heat transfer calculations, for pneumatic and hydraulic transportation devices, and in measuring discharges, is also considered. The theory of unsteady flow in tubes studies the phenomenon of hydraulic impact.

The hydraulics of open channels studies the flow of water in canals and rivers. Methods are given for the determination of the water depth in canals with a given flow rate and bottom slope; they are used extensively in planning navigation, irrigation, drainage, and hydraulic power-engineering canals and sewer pipelines, as well as in straightening operations. The hydraulics of open channels also deals with the question of velocity distribution through the cross section of a stream, which is extremely important for hydrometry and the calculation of the movement of detritus. The theory of nonuniform motion in open channels makes it possible to define curves of the free surface of water, and the theory of unsteady flow is important in taking account of the phenomena associated with the maneuvering of dam gates, the diurnal regulation of hydroelectric power plants, and the release of water from reservoirs. In the branches of hydraulics concerned with the discharge of a fluid from orifices and through spillways, design relationships are provided to determine the necessary dimensions of openings in various reservoirs, locks, dams, and pipes, as well as for finding the velocities of discharge of the fluid and the time required to empty reservoirs. The hydraulic theory of filtration provides methods for calculating the yield and flow velocity of water under various nonpressured and pressured flow conditions (water filtration through dams, filtration of petroleum, gas, and water in strata, filtration from canals, and inflows to underground wells).

Hydraulics also treats the movement of detritus in open streams and of pulp in pipes, the methods used in hydraulic measurements, and simulation of hydraulic phenomena. The hydraulics of nonuniform and unsteady motion in open channels and pipes, variable-rate flow, filtration, and some other questions, which are sometimes combined under the general names “engineering hydraulics” or “hydraulic-engineering works,” are of very great importance for the calculation of hydraulic-engineering structures. Thus, the scope of problems covered by hydraulics is very broad, and its laws are applied to a greater or lesser degree in all fields of engineering, particularly in hydraulic engineering, reclamation, water supply, drainage, heating gas supply, hydromechanization, hydraulic power engineering, and water transportation.

Some principles of hydrostatics were established by Archimedes, and the origin of hydrodynamics also dates to ancient times, but hydraulics began to take shape as a science in the mid-15th century, when Leonardo da Vinci laid down the basis of the experimental method in laboratory hydraulic tests. During the 16th and 17th centuries S. Stevin, Galileo, and B. Pascal developed the principles of hydrostatics as a science, and E. Torricelli gave the well-known formula for the velocity of a fluid flowing from an orifice. Later, I. Newton formulated the main theorems for viscous friction in liquids. During the 1700’s, D. Bernoulli and L. Euler developed the general equations of motion for an ideal fluid that served as a basis for the further development of hydromechanics and hydraulics. However, the application of these equations to the solution of practical problems (just as the equations of motion for a viscous fluid, which were proposed somewhat later) gave satisfactory results in only a few cases. In view of this, in the late 18th century many scientists and engineers (A. de Chézy, H. Darcy, H. Bazin, and J. Weisbach) performed experimental studies of the motion of water for various special cases, thus enriching hydraulics with a considerable number of empirical formulas. The practical hydraulics thus developed moved farther and farther away from theoretical hydrodynamics. They began to draw closer together only toward the end of the 19th century as a result of the formation of new views on the motion of fluids based on studies of flow patterns. The work of O. Reynolds merits special mention, for it gave a deeper understanding of the complicated process of flow in a real fluid and the physical nature of hydraulic resistance by laying the foundation for the study of turbulent flow. Through the studies of L. Prandtl and T. von Kármán, this study culminated in the creation of semiempirical theories of turbulence, which have found extensive practical application. The research of N. E. Zhukov-skii belongs to this same period; his work on hydraulic impact and the movement of groundwater was of the greatest value for hydraulics. In the 20th century, the rapid growth of hydraulic engineering, power engineering, hydraulic machine design, and aeronautical engineering brought about intensive development of hydraulics, which is characterized by a synthesis of theoretical and experimental methods. Soviet scientists, including N. N. Pavlovskii, L. S. Leibenzon, and M. A. Velikanov, made a large contribution to this development.

The practical significance of hydraulics has grown because of modern technology’s need to solve the problems of transporting various types of liquids and gases and of utilizing them for various purposes. Although in the past only one liquid, water, was studied, under modern conditions more and more attention is being given to the laws of motion for viscous liquids (petroleum and its products), gases, and the nonuniform and so-called non-Newtonian liquids. The methods of analyzing and solving problems in hydraulics are also changing. Comparatively recently, in hydraulics, empirical relationships were given the principal role, although they were only valid for water and often for just a narrow range of variation of the velocities, temperatures, and geometric parameters of the flow; at present, general rules that are valid for all fluids and that meet the requirements of the theory of similarity, as well as other theories, are taking on greater significance. In this case, individual instances can be treated as the result of generalized principles. Hydraulics is gradually being converted into one of the applied branches of the general science of fluid motion—fluid mechanics.

Research in the field of hydraulics is coordinated by the International Association for Hydraulic Research. Its organ is the Journal of the International Association for Hydraulic Research (Delft, since 1937). Periodical publications in the field include the journals Gidrotekhnicheskoe stroitel’stvo (Hydraulic-engineering Construction; since 1930) and Gidro-tekhnika i melioratsiia (Hydraulic Engineering and Reclamation; since 1949), Izv. Vsesoiuznogo n.-i. in-ta gidro-tekhniki im. B. E. Vedeneeva (Transactions of the B. E. Vedeneev All-Union Scientific Research Institute of Hydraulic Engineering; since 1931), Trudy koordinatsionnykh soveshchanii po gidrotekhnike (Transactions of the Coordinating Conferences on Hydraulic Engineering; since 1961), the collection Gidravlika i gidrotekhnika (Hydraulics and Hydraulic Engineering; since 1961), Houille Blanche (Grenoble, since 1946), Journal of the Hydraulics Division: American Society of Civil Engineers (New York, since 1956), and L’energia elettrica (Milan, since 1924).


Idel’chik, I. E. Spravochnik po gidravlicheskim soprotivleniiam. Moscow-Leningrad, 1960.
Kiselev, P. G. Spravochnik po gidravlicheskim raschetam, 3rd ed. Moscow-Leningrad, 1961.
Bogomolov, A. I., and K. A. Mikhailov. Gidravlika. Moscow, 1965.
Al’tshul, A. D., and P. G. Kiselev. Gidravlika i aerodinamika. Moscow, 1965.
Chugaev, R. R. Gidravlika. Moscow-Leningrad, 1970.
Rouse, H., and J. Howe. Basic Mechanics of Fluids. New York-London, 1953.
King, H. W., and E. F. Brater. Handbook of Hydraulics, 5th ed. New York, 1963.
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Eck, B. Technische Strömungslehre, 7th ed. Berlin, 1966.



(fluid mechanics)
The branch of engineering that focuses on the practical problems of collecting, storing, measuring, transporting, controlling, and using water and other liquids.


The branch of engineering that focuses on the practical problems of collecting, storing, measuring, transporting, controlling, and using water and other liquids. It differs from fluid mechanics, which is more theoretical and includes the study of gases as well as liquids; and from hydrology, which is the study of the properties, distribution, and circulation of the Earth's water.

Many problems in hydraulics involve pipe flow. Pipe flow occurs in the direction of decreasing energy. The primary forms of energy in pipes are position energy (height of the fluid), pressure energy, and kinetic energy according to Bernoulli's theorem. Fluids can be forced to flow uphill if the pressure energy and kinetic energy are large enough to overcome the position energy. This can be accomplished with a pump that adds pressure energy to the fluid. See Pump

Liquids in motion produce forces whenever the velocity or flow direction changes. For example, forces develop at the nozzle of a fire hose, at pipe bends, and when flowing water is used to turn a turbine. The force is generally proportional to the flow rate, the mass density, and the velocity change.

Liquids are often transported in open channels instead of pipes. An energy imbalance produces flow in open channels, just as it does in pipes. The primary forms of energy are position energy, flow depth, and kinetic energy. Energy balance methods are used to solve many problems in gradually varied flow (that is, the depth changes slowly over short distances), but a momentum balance is required for rapidly varied flow.

Hydraulic principles apply to many other scientific and engineering endeavors. For example, ground-water flow is studied in geology but is governed by the principles of hydraulics. Coastal hydraulics is an important subset of oceanography. The design of certain structures, such as jetties, dams, spillways, locks, piers, levees, dry docks, and tanks, requires an understanding of hydraulic concepts. Scale models are often used to better understand some of the complex forces and currents associated with these large structures. See Coastal engineering, Dam, River engineering


The branch of engineering which treats the motion of fluids.
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