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Water hammerFrom Wikipedia, the free encyclopedia

For a hammer powered by water, see Trip hammer.

Water hammer (or, more generally, fluid hammer) is a pressure surge or wave caused when afluid (usually a liquid but sometimes also a gas) in motion is forced to stop or change directionsuddenly (momentum change). A water hammer commonly occurs when a valve closes suddenly atan end of a pipeline system, and a pressure wave propagates in the pipe. It is also called hydraulicshock.

This pressure wave can cause major problems, from noise and vibration to pipe collapse. It ispossible to reduce the effects of the water hammer pulses with accumulators, expansion tanks andother features.

Rough calculations can be made either using the Joukowsky equation,[1] or more accurate onesusing the method of characteristics.[2]

Contents [hide]

1 Cause and effect1.1 Related phenomena

2 Water hammer during an explosion3 Mitigating measures4 The magnitude of the pulse

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4 The magnitude of the pulse4.1 Instant valve closure; compressible fluid

4.1.1 Equation for wave speed4.2 Slow valve closure; incompressible fluid

5 Expression for the excess pressure due to water hammer6 Dynamic equations7 Column separation8 Simulation software9 Applications10 History11 See also12 References13 External links

Cause and effect [edit]

When a pipe is suddenly closed at the outlet (downstream), the mass of water before the closure isstill moving, thereby building up high pressure and a resulting shock wave. In domestic plumbingthis is experienced as a loud banging, resembling a hammering noise. Water hammer can causepipelines to break if the pressure is high enough. Air traps or stand pipes (open at the top) aresometimes added as dampers to water systems to absorb the potentially damaging forces causedby the moving water.

In hydroelectric generating stations, the water travelling along the tunnel or pipeline may beprevented from entering a turbine by closing a valve. However, if, for example, there is 14 km oftunnel of 7.7 m diameter, full of water travelling at 3.75 m/s,[3] that represents approximately 8000Megajoules of kinetic energy that must be arrested. This arresting is frequently achieved by asurge shaft[4] open at the top, into which the water flows; as the water rises up the shaft, its kineticenergy is converted into potential energy, which decelerates the water in the tunnel. At some HEP

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stations, what looks like a water tower is actually one of these devices, known in these cases as asurge drum.

In the home, water hammer may occur when a dishwasher, washing machine, or toilet shuts offwater flow. The result may be heard as a loud bang, repetitive banging (as the shock wave travelsback and forth in the plumbing system), or as some shuddering.

On the other hand, when an upstream valve in a pipe closes, water downstream of the valveattempts to continue flowing, creating a vacuum that may cause the pipe to collapse or implode.This problem can be particularly acute if the pipe is on a downhill slope. To prevent this, air andvacuum relief valves, or air vents, are installed just downstream of the valve to allow air to enterthe line for preventing this vacuum from occurring.

Other causes of water hammer are pump failure, and check valve slam (due to suddendeceleration, a check valve may slam shut rapidly, depending on the dynamic characteristic of thecheck valve and the mass of the water between a check valve and tank).

Related phenomena [edit]

Steam distribution systems may also bevulnerable to a situation similar to waterhammer, known as steam hammer. In a steamsystem, water hammer most often occurswhen some of the steam condenses into waterin a horizontal section of the steam piping.Subsequently, steam picks up the water,forms a "slug" and hurls it at high velocity intoa pipe fitting, creating a loud hammering noiseand greatly stressing the pipe. This condition

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Expansion joints on a steam line that have beendestroyed by steam hammer

is usually caused by a poor condensatedrainage strategy.

Where air filled traps are used, theseeventually become depleted of their trappedair over a long period of time through absorption into the water. This can be cured by shutting offthe supply, opening taps at the highest and lowest locations to drain the system (thereby restoringair to the traps), and then closing the taps and re-opening the supply.

Water hammer during an explosion [edit]

When an explosion happens in an enclosed space, water hammer can cause the walls of thecontainer to deform. However, it can also impart momentum to the enclosure if it is free to move.An underwater explosion in the SL-1 nuclear reactor vessel caused the water to accelerateupwards through 0.76 m (2.5 ft) of air before it struck the vessel head at 49 m/s (160 ft/s) with apressure of 680 atm (69,000 kPa). This pressure wave caused the 12,000 kg (26,000 lb) steelvessel to jump 2.77 m (9.1 ft) into the air before it dropped into its prior location.[5]

Mitigating measures [edit]

Water hammer has caused accidents and fatalities, but usually damage is limited to breakage ofpipes or appendages. An engineer should always assess the risk of a pipeline burst. Pipelinestransporting hazardous liquids or gases warrant special care in design, construction, andoperation. Hydroelectric power plants especially must be carefully designed and maintainedbecause the water hammer can cause water pipes to fail catastrophically.

The following characteristics may reduce or eliminate water hammer:

Reduce the pressure of the water supply to the building by fitting a regulator.Lower fluid velocities. To keep water hammer low, pipe-sizing charts for some applications

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Lower fluid velocities. To keep water hammer low, pipe-sizing charts for some applicationsrecommend flow velocity at or below 1.5 m/s (4.9 ft/s)Fit slowly closing valves. Toilet fill valves are available in a quiet fill type that closes quietly.High pipeline pressure rating (expensive).Good pipeline control (start-up and shut-down procedures).Water towers (used in many drinking water systems) help maintain steady flow rates and traplarge pressure fluctuations.Air vessels work in much the same way as water towers, but are pressurized. They typicallyhave an air cushion above the fluid level in the vessel, which may be regulated or separated bya bladder. Sizes of air vessels may be up to hundreds of cubic meters on large pipelines. Theycome in many shapes, sizes and configurations. Such vessels often are called accumulators orexpansion tanks.A hydropneumatic device similar in principle to a shock absorber called a 'Water HammerArrestor' can be installed between the water pipe and the machine, to absorb the shock andstop the banging.Air valves often remediate low pressures at high points in the pipeline. Though effective,sometimes large numbers of air valves need be installed. These valves also allow air into thesystem, which is often unwanted.Shorter branch pipe lengths.Shorter lengths of straight pipe, i.e. add elbows, expansion loops. Water hammer is related tothe speed of sound in the fluid, and elbows reduce the influences of pressure waves.Arranging the larger piping in loops that supply shorter smaller run-out pipe branches. Withlooped piping, lower velocity flows from both sides of a loop can serve a branch.Flywheel on pump.Pumping station bypass.

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Typical pressure wave caused by closing a valve ina pipeline

The magnitude of the pulse[edit]

One of the first to successfully investigate thewater hammer problem was the Italianengineer Lorenzo Allievi.

Water hammer can be analyzed by twodifferent approaches—rigid column theory,which ignores compressibility of the fluid andelasticity of the walls of the pipe, or by a fullanalysis that includes elasticity. When the timeit takes a valve to close is long compared tothe propagation time for a pressure wave totravel the length of the pipe, then rigid column theory is appropriate; otherwise consideringelasticity may be necessary.[6] Below are two approximations for the peak pressure, one thatconsiders elasticity, but assumes the valve closes instantaneously, and a second that neglectselasticity but includes a finite time for the valve to close.

Instant valve closure; compressible fluid [edit]

The pressure profile of the water hammer pulse can be calculated from the Joukowsky equation [7]

So for a valve closing instantaneously, the maximum magnitude of the water hammer pulse is:

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where ΔP is the magnitude of the pressure wave (Pa), ρ is the density of the fluid (kgm−3), a0 isthe speed of sound in the fluid (ms−1), and Δv is the change in the fluid's velocity (ms−1). Thepulse comes about due to Newton's laws of motion and the continuity equation applied to thedeceleration of a fluid element.[8]

Equation for wave speed [edit]

As the speed of sound in a fluid is the , the peak pressure

depends on the fluid compressibility if the valve is closed abruptly.

where

a = wave speedK = bulk modulus of elasticity of the fluidρ = density of the fluidE = elastic modulus of the pipeD = internal pipe diametert = pipe wall thicknessc = dimensionless parameter due to system pipe-constraint condition on wavespeed[8][page needed]

Slow valve closure; incompressible fluid [edit]

When the valve is closed slowly compared to the transit time for a pressure wave to travel thelength of the pipe, the elasticity can be neglected, and the phenomenon can be described in terms

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of inertance or rigid column theory:

Assuming constant deceleration of the water column (dv/dt = v/t), gives:

where:

F = force, Nm = mass of the fluid column, kga = acceleration, m/s2

P = pressure, PaA = pipe cross section, m2

ρ = fluid density, kg/m3

L = pipe length, mv = fluid velocity, m/st = valve closure time, s

The above formula becomes, for water and with imperial unit: P = 0.0135 V L/t. For practicalapplication, a safety factor of about 5 is recommended:

where P1 is the inlet pressure in psi, V is the flow velocity in ft/sec, t is the valve closing time inseconds and L is the upstream pipe length in feet.[9]

Expression for the excess pressure due to water hammer [edit]

When a valve with a volumetric flow rate Q is closed, an excess pressure δP is created upstream

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of the valve, whose value is given by the Joukowsky equation:

In this expression:[10]

overpressurization δP is expressed in Pa;Q is the volumetric flow in m3/s;Zh is the hydraulic impedance, expressed in kg/m4/s.

The hydraulic impedance Zh of the pipeline determines the magnitude of the water hammer pulse.It is itself defined by:

with:

ρ the density of the liquid, expressed in kg/m3;A cross sectional area of the pipe, m2;Beff effective modulus of compressibility of the liquid in the pipe, expressed in Pa.

The latter follows from a series of hydraulic concepts:

compressibility of the liquid, defined by its adiabatic compressibility modulus Bl, resulting fromthe equation of state of the liquid generally available from thermodynamic tables;the elasticity of the walls of the pipe, which defines a modulus of equivalent compressibility Beq.In the case of a pipe of circular cross section whose thickness e is small compared to thediameter D, the equivalent modulus of compressibility is given by the following formula:

; in which E is the Young's modulus (in Pa) of the material of the pipe;

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possibly compressibility Bg of gas dissolved in the liquid, defined by:

γ being the ratio of specific heats of the gasα the rate of ventilation (the volume fraction of undissolved gas)and P the pressure (in Pa).

Thus, the effective compressibility modulus is:

As a result, we see that we can reduce the water hammer by:

increasing the pipe diameter at constant flow, which reduces the inertia of the liquid column;choosing to use a material with a reduced Young's modulus;introducing a device that increases the flexibility of the entire hydraulic system, such as ahydraulic accumulator;where possible, increasing the percentage of undissolved air in the liquid.

Dynamic equations [edit]

The water hammer effect can be simulated by solving the following partial differential equations.

where V is the fluid velocity inside pipe, is the fluid density and is the equivalent bulkmodulus, f is the friction factor.

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Column separation [edit]

Column separation is a phenomenon that can occur during a water-hammer event. If the pressurein a pipeline drops rapidly to the vapor pressure of the liquid, the liquid vaporises and a "bubble"of vapor forms in the pipeline. This is most likely to occur at specific locations such as closed ends,high points or knees (changes in pipe slope). When the pressure later increases above the vaporpressure of the liquid, the vapor in the bubble returns to a liquid state, which leaves a vacuum inthe space formerly occupied by the vapor. The liquid either side of the vacuum is then acceleratedinto this space by the pressure difference. The collision of the two columns of liquid, (or of oneliquid column if at a closed end,) results in cavitation and causes a large and nearly instantaneousrise in pressure. This pressure rise can damage hydraulic machinery, individual pipes andsupporting structures. Many repetitions of cavity formation and collapse may occur in a singlewater-hammer event.[11]

Simulation software [edit]

Most water hammer software packages use the method of characteristics [8] to solve thedifferential equations involved. This method works well if the wave speed does not vary in time dueto either air or gas entrainment in a pipeline. The Wave Method (WM) is also used in varioussoftware packages. WM lets operators analyze large networks efficiently. Many commercial andnon commercial packages are available.

Software packages vary in complexity, dependent on the processes modeled. The moresophisticated packages may have any of the following features:

Multiphase flow capabilitiesAn algorithm for cavitation growth and collapseUnsteady friction - the pressure waves dampens as turbulence is generated and due to

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variations in the flow velocity distributionVarying bulk modulus for higher pressures (water becomes less compressible)Fluid structure interaction - the pipeline reacts on the varying pressures and causespressure waves itself

Applications [edit]

The water hammer principle can be used to create a simple water pump called a hydraulic ram.Leaks can sometimes be detected using water hammer.Enclosed air pockets can be detected in pipelines.

History [edit]

Water hammer was exploited before there was even a word for it: Marcus Vitruvius Pollio describesin the 1st century B.C.E the effect of water hammer in lead pipes and stone tubes of the Romanpublic water supply.[12] In 1772, Englishman John Whitehurst built a hydraulic ram for a home inCheshire, England.[13] In 1796, French inventor Joseph Michel Montgolfier (1740–1810) built ahydraulic ram for his paper mill in Voiron.[14] In French and Italian, the terms for "water hammer"come from the hydraulic ram: coup de bélier (French) and colpo d’ariete (Italian) both mean "blowof the ram".[15] As the 19th century witnessed the installation of municipal water supplies, waterhammer became a concern to civil engineers.[16] Water hammer also interested physiologists whowere studying the circulatory system.

The theory of water hammer began in 1883 with the work of German physiologist Johannes vonKries (1853–1928), who was investigating the pulse in blood vessels.[17] However, his findingswent unnoticed by civil engineers.[18] Kries's findings were subsequently derived independently in1898 by the Russian fluid dynamicist Nikolay Yegorovich Zhukovsky (1847–1921),[19] in 1898 bythe American civil engineer Joseph Palmer Frizell (1832–1910),[20] and in 1902 by the Italian

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engineer Lorenzo Allievi (1856–1941).[21]

See also [edit]

Blood hammerCavitationFluid dynamicsHydraulic ram – makes constructive use of the water hammer effectHydraulophone – musical instruments employing water and other fluidsImpact forceWatson's water hammer pulse

References [edit]

1. ^ Kay, Melvyn (2008). Practical Hydraulics (2nd ed.). Taylor & Francis. ISBN 0-415-35115-4.2. ^ Shu, Jian-Jun (2003). "Modelling vaporous cavitation on fluid transients". International Journal of

Pressure Vessels and Piping 80 (3): 187–195. doi:10.1016/S0308-0161(03)00025-5 .3. ^

http://communities.bentley.com/products/hydraulics___hydrology/f/5925/p/60896/147250.aspx#1472504. ^ http://cr4.globalspec.com/thread/736465. ^ Flight Propulsion Laboratory Department, General Electric Company, Idaho Falls, Idaho (November

21, 1962), Additional Analysis of the SL-1 Excursion: Final Report of Progress July through October1962 , U.S. Atomic Energy Commission, Division of Technical Information, IDO-19313; also TM-62-11-707

6. ^ Bruce, S.; Larock, E.; Jeppson, R. W.; Watters, G. Z. (2000), Hydraulics of Pipeline Systems,CRC Press, ISBN 0-8493-1806-8

7. ^ Thorley, A. R. D. (2004), Fluid Transients in Pipelines (2nd ed.), Professional EngineeringPublishing, ISBN 0-79180210-8[page needed]

a b c

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8. a b c Streeter, V. L.; Wylie, E. B. (1998), Fluid Mechanics (International 9th Revised ed.), McGraw-Hill Higher Education[page needed]

9. ^ "Water Hammer & Pulsation"10. ^ Faisandier, J., Hydraulic and Pneumatic Mechanisms, 8th edition, Dunod, Paris, 1999 (ISBN

2100499483)11. ^ Bergeron, L., 1950. Du Coup de Bélier en Hydraulique - Au Coup de Foudre en Electricité.

(Waterhammer in hydraulics and wave surges in electricity.) Paris: Dunod (in French). (Englishtranslation by ASME Committee, New York: John Wiley & Sons, 1961.)

12. ^ Ismaier, Andreas (2011), Untersuchung der fluiddynamischen Wechselwirkung zwischenDruckstößen und Anlagenkomponenten in Kreiselpumpensystemen [Investigation of the fluiddynamic interaction between system components and pressure surges in centrifugal pumpingsystems], Schriftenreihe des Lehrstuhls für Prozessmaschinen und Anlagentechnik, UniversitätErlangen; Nürnberg Lehrstuhl für Prozessmaschinen und Anlagentechnik (in German) 11, Shaker,ISBN 978-3-8322-9779-4

13. ^ Whitehurst, John (1775), "Account of a machine for raising water, executed at Oulton, in Cheshire,in 1772" , Philosophical Transactions of the Royal Society of London 65: 277–279 See also platepreceding page 277.

14. ^ Montgolfier, J. M. de (1803), "Note sur le bélier hydraulique, et sur la manière d’en calculer leseffets" [Note on the hydraulic ram, and on the method of calculating its effects] , Journal desMines (in French) 13 (73): 42–51

15. ^ Tijsseling, A. S.; Anderson, A. (2008), "Thomas Young's research on fluid transients: 200 yearson" , Proceedings of the 10th International Conference on Pressure Surges (Edinburgh, UK): 21–33 see page 22.

16. ^ See, for example:Ménabréa, L. F. (1858) "Note sur les effects de choc de l’eau dans les conduites," (Note onthe effects of water shocks in pipes), Comptes rendus, 47 : 221–224.Michaud, J. (1878) "Coups de bélier dans les conduites. Étude des moyens employés pour enatténeur les effects" (Water hammer in pipes. Study of means used to mitigate its effects),Bulletin de la Société Vaudoise des Ingénieurs et des Architects, 4 (3,4) : 56–64, 65–77.

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17. ^ See:J. von Kries (1883) "Ueber die Beziehungen zwischen Druck und Geschwindigkeit, welche bei derWellenbewegung in elastischen Schläuchen bestehen" (On the relationship between pressureand velocity, which exist in connection with wave motion in elastic tubing), Festschrift der 56.Versammlung Deutscher Naturforscher und Ärzte (Festschrift of the 56th Convention of GermanScientists and Physicians), (Tübingen, Germany: Akademische Verlagsbuchhandlung, 1883),pages 67-88.J. von Kries, Studien zur Pulslehre (Studies in Pulse Science) (Tübingen, Germany:Akademische Verlagsbuchhandlung, 1892).

18. ^ See:Arris S. Tijsseling and Alexander Anderson (2004) "A precursor in waterhammer analysis –rediscovering Johannes von Kries," Proceedings of the 9th International Conference on PressureSurges, Chester, UK, pages 739-751. Available on-line at: Technical University of Eindhoven .Arris S. Tijsseling and Alexander Anderson (2007) "Johannes von Kries and the history of waterhammer," Journal of Hydraulic Engineering, 133 (1) : 1-8.

19. ^ See:Joukowsky, N. (1898). "Über den hydraulischen Stoss in Wasserleitungsröhren" (On thehydraulic hammer in water supply pipes), Mémoires de l'Académie Impériale des Sciences deSt.-Pétersbourg (1900), series 8, 9 (5) : 1-71.Arris S. Tijsseling and Alexander Anderson, (2006) "The Joukowsky equation for fluids andsolids". Available on-line at: Technical University of Eindhoven .

20. ^ See:Frizell, J.P. (1898) "Pressures resulting from changes of velocity of water in pipes,"Transactions of the American Society of Civil Engineers, 39 : 1-18.R. A. Hale (Sept. 1911) Obituary: "Joseph Palmer Frizell, M. Am. Soc. C. E.," Transactions ofthe American Society of Civil Engineers, 73 : 501-503.

21. ^ Allievi, L. (1902), "Teoria generale del moto perturbato dell'acqua nei tubi in pressione (colpod’ariete)" [General theory of the perturbed motion of water in pipes under pressure (water hammer))],Annali della Società degli Ingegneri ed Architetti Italiani (Annals of the Society of Italian Engineersand Architects) (in Italian) 17 (5): 285–325

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