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The propagation in a liquid of an acoustic wave that is caused by a rapid change in fluid velocity. Such relatively sudden changes in the liquid velocity are due to events such as the operation of pumps or valves in pipelines, the collapse of vapor bubbles within the liquid, underwater explosions, or the impact of water following the rapid expulsion of air from a vent or a partially open valve. Alternative terms such as pressure transients, pressure surge, hydraulic transients, and hydraulic shock are often employed. Although the physics and mathematical characterization of water hammer and underwater acoustics (employed in sonar) are identical, underwater sound is always associated with very small pressure changes compared to the potential of moderate to very large pressure differences associated with water hammer. See Cavitation, Sound, Underwater sound
A pressure change Δp is always associated with the rapid velocity change ΔV across a water hammer wave, as formulated from the basic physics of mass and momentum conservation by the Joukowsky equation, Δp = -ρaΔV. Here &rgr; is the liquid mass density and a is the sonic velocity of the pressure wave in the fluid medium. In a pipe, this velocity depends on the ratio of the bulk modulus of the liquid to the elastic modulus of the pipe wall, and on the ratio of the inside diameter of the pipe to the wall thickness. In water in a very rigid pipe or in a tank, or even the sea, the acoustic velocity is approximately 1440 m/s (4720 ft/s), a value many times that of any liquid velocity.
Liquid-handling systems are designed so that water hammer does not result from sudden closure, but is limited to more gradual flow changes initiated by valves or other devices. The dramatic pressure rise (or drop) results can be significantly reduced by reflections of the original wave from pipe-area changes, tanks, reservoirs, and so forth. Although the Joukowsky equation applies across every wavelet, the effect of complete valve closure over a period of time greater than a minimum critical time can be quite beneficial. This critical time is the time required for an acoustic wave to propagate twice the distance along the pipe from the point of wave creation to the location of the first pipe-area change. See Hydrodynamics
the phenomenon of a sharp change in pressure in a fluid caused by an instantaneous change in its flow velocity in a pressure pipe (for example, in case of rapid closing of the pipeline by a shutoff device).
The pressure rise in water hammer is defined according to the theory of N. E. Zhukovskii by the formula
Δp = ρ(v0 - vx)c
where Δp is the pressure rise in newtons per sq m, and ρ is the fluid density in kg/m3; v0 and vt are the mean velocities in the pipeline (in m/sec) before and after the closing of the slide valve, and c is the speed of propagation of the shock wave through the pipeline. If the walls are absolutely rigid, c = a, the velocity of sound in the fluid (in water, a= 1,400 m/sec). In tubes with elastic walls, , where D and δ are the diameter and thickness of the tube’s wall, and E and e are the elastic moduli of the material of the walls of the tube and of the liquid, respectively.
Water hammer is a complex process of formation of elastic deformations in a liquid and their propagation through a tube. If the pressure rise is very great, the impact can cause damage. Safety devices (equalizing reservoirs, air domes, valves, and so on) are installed in pipelines to prevent such damage.
The theory of water hammer, which was developed by N. E. Zhukovskii, promoted technological progress in hydraulic engineering, mechanical engineering, and other fields.
REFERENCESZhukovskii, N. E. O gidravlicheskom udare v vodoprovodnykh trubakh. Moscow-Leningrad, 1949.
Mostkov, M. A., and A. A. Bashkirova. Raschety gidravlicheskogoudara. Moscow-Leningrad, 1952.
V. V. LIASHEVICH