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Hydraulic shock (
colloquial Colloquialism (), also called colloquial language, everyday language or general parlance, is the linguistic style used for casual (informal) communication. It is the most common functional style of speech, the idiom normally employed in conve ...
: water hammer; fluid hammer) is a
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
surge or wave caused when a
fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
in motion, usually a liquid but sometimes also a gas is forced to stop or change direction suddenly; a
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass ...
change. This phenomenon commonly occurs when a valve closes suddenly at an end of a pipeline system, and a pressure wave propagates in the pipe. This pressure wave can cause major problems, from noise and vibration to pipe rupture or collapse. It is possible to reduce the effects of the water hammer pulses with accumulators, expansion tanks,
surge tank A Surge tank is a water storage device used as a pressure neutralizer in hydropower water conveyance systems in order to dampen excess pressure variance. A surge tank (or surge drum or surge pool) is a standpipe or storage reservoir at the downst ...
s, blowoff valves, and other features. The effects can be avoided by ensuring that no valves will close too quickly with significant flow, but there are many situations that can cause the effect. Rough calculations can be made using the Zhukovsky (Joukowsky) equation, or more accurate ones using the
method of characteristics In mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations, although more generally the method of characteristics is valid for any hyperbolic partia ...
.


History

In the 1st century B.C., Marcus Vitruvius Pollio described the effect of water hammer in lead pipes and stone tubes of the Roman public water supply. Water hammer was exploited before there was even a word for it. The
Alhambra The Alhambra (, ; ar, الْحَمْرَاء, Al-Ḥamrāʾ, , ) is a palace and fortress complex located in Granada, Andalusia, Spain. It is one of the most famous monuments of Islamic architecture and one of the best-preserved palaces of ...
, built by Nasrid Sultan Ibn al-Ahmar of Granada beginning AD1238, used a hydram to raise water. Through a first reservoir, filled by a channel from the Darro River, water emptied via a large vertical channel into a second reservoir beneath, creating a whirlpool that in turn propelled water through a much smaller pipe up six metres whilst most water drained into a second, slightly larger pipe. In 1772, Englishman
John Whitehurst John Whitehurst FRS (10 April 1713 – 18 February 1788), born in Cheshire, England, was a clockmaker and scientist, and made significant early contributions to geology. He was an influential member of the Lunar Society. Life and work Whit ...
built a hydraulic ram for a home in Cheshire, England. In 1796, French inventor Joseph Michel Montgolfier (1740–1810) built a hydraulic ram for his paper mill in
Voiron Voiron (; frp, Vouèron) is a commune (French municipality) in the ninth district of the Isère department in southeastern France. It is the capital of the canton of Voiron and has been part of the Grenoble-Alpes Métropole since 2010. Voiron i ...
. 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 "blow of the ram". As the 19th century witnessed the installation of municipal water supplies, water hammer became a concern to civil engineers. Water hammer also interested physiologists who were studying the circulatory system. Although it was prefigured in work by Thomas Young, the theory of water hammer is generally considered to have begun in 1883 with the work of German physiologist Johannes von Kries (1853–1928), who was investigating the pulse in blood vessels. However, his findings went unnoticed by civil engineers. Kries's findings were subsequently derived independently in 1898 by the Russian fluid dynamicist
Nikolay Yegorovich Zhukovsky Nikolay Yegorovich Zhukovsky ( rus, Никола́й Его́рович Жуко́вский, p=ʐʊˈkofskʲɪj;  – March 17, 1921) was a Russian scientist, mathematician and engineer, and a founding father of modern aero- and hydrodyna ...
(1847–1921), in 1898 by the American civil engineer
Joseph Palmer Frizell Joseph Frizell (13 March 1832 – 4 May 1910) was an American engineer. He is notable for having independently derived the fundamental equations to describe the velocity of a shock wave (Water hammer equations) in 1898, and for his book Water-Powe ...
(1832–1910), and in 1902 by the Italian engineer
Lorenzo Allievi Lorenzo Allievi (November 18, 1856 – October 30, 1941) was an Italian engineer known for being one of the first to explain the water hammer problem.Kaveh Hariri Asli, Faig Bakhman Ogli Naghiyev, Reza Khodaparast Haghi, Hossien Hariri Asli, Ad ...
(1856–1941).


Cause and effect

Water flowing through a pipe has momentum. If the moving water is suddenly stopped - such as by closing a valve downstream of the flowing water, the pressure can rise suddenly with a resulting
shock wave In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
. In domestic
plumbing Plumbing is any system that conveys fluids for a wide range of applications. Plumbing uses pipes, valves, plumbing fixtures, tanks, and other apparatuses to convey fluids. Heating and cooling (HVAC), waste removal, and potable water delive ...
this shock wave is experienced as a loud banging resembling a hammering noise. Water hammer can cause pipelines to break if the pressure is sufficiently high. Air traps or stand pipes (open at the top) are sometimes added as dampers to water systems to absorb the potentially damaging forces caused by the moving water. For example, the water traveling along a tunnel or pipeline to a turbine in a hydroelectric generating stations may be slowed suddenly if a valve in the path is closed too quickly. If there is of tunnel of diameter full of water travelling at , that represents approximately of kinetic energy. This energy can be dissipated by a vertical surge shaft into which the water flows which is open at the top. As the water rises up the shaft its kinetic energy is converted into potential energy, avoiding sudden high pressure. At some hydroelectric power (HEP) stations, such as the Saxon Falls Hydro Power Plant In Michigan, what looks like a
water tower A water tower is an elevated structure supporting a water tank constructed at a height sufficient to pressurize a distribution system for potable water, and to provide emergency storage for fire protection. Water towers often operate in conju ...
is a surge drum. In residential plumbing systems, water hammer may occur when a dishwasher,
washing machine A washing machine (laundry machine, clothes washer, washer, or simply wash) is a home appliance used to wash laundry. The term is mostly applied to machines that use water as opposed to dry cleaning (which uses alternative cleaning fluids and ...
or
toilet A toilet is a piece of sanitary hardware that collects human urine and feces, and sometimes toilet paper, usually for disposal. Flush toilets use water, while dry or non-flush toilets do not. They can be designed for a sitting position popu ...
suddenly shuts off water flow. The result may be heard as a loud bang, repetitive banging (as the shock wave travels back and forth in the plumbing system), or as some shuddering. Other potential causes of water hammer: * A pump stopping * A
check valve A check valve, non-return valve, reflux valve, retention valve, foot valve, or one-way valve is a valve that normally allows fluid ( liquid or gas) to flow through it in only one direction. Check valves are two-port valves, meaning they have ...
which closes quickly (i.e., "check valve slam") due to the flow in a pipe reversing direction on loss of motive power, such as a pump stopping. "Non-slam" check valves can be used to reduce the pressure surge. * Filling an empty pipe that has a restriction such as a partially open valve or an orifice that allows air to pass easily as the pipe rapidly fills, but with the pressure increasing once full the water encounters the restriction.


Related phenomena

''Steam hammer'' can occur in steam systems when some of the steam condenses into water in a horizontal section of the piping. The steam forcing the liquid water along the pipe forms a "
slug Slug, or land slug, is a common name for any apparently shell-less terrestrial gastropod mollusc. The word ''slug'' is also often used as part of the common name of any gastropod mollusc that has no shell, a very reduced shell, or only a ...
" which impacts a valve of pipe fitting, creating a loud hammering noise and high pressure. Vacuum caused by condensation from thermal shock can also cause a steam hammer. Steam hammer can be minimized by using sloped pipes and installing steam traps. On
turbocharged In an internal combustion engine, a turbocharger (often called a turbo) is a forced induction device that is powered by the flow of exhaust gases. It uses this energy to compress the intake gas, forcing more air into the engine in order to pr ...
internal combustion engine An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal co ...
s, a "gas hammer" can take place when the throttle is closed while the turbocharger is forcing air into the engine. There is no shockwave but the pressure can still rapidly increase to damaging levels or cause compressor surge. A pressure relief valve placed before the throttle prevents the air from surging against the throttle body by diverting it elsewhere, thus protecting the turbocharger from pressure damage. This valve can either recirculate the air into the turbocharger's intake (recirculation valve), or it can blow the air into the atmosphere and produce the distinctive hiss-flutter of an aftermarket turbocharger ( blowoff valve).


Mitigation measures

Water hammer has caused accidents and fatalities, but usually damage is limited to breakage of pipes or appendages. An engineer should always assess the risk of a pipeline burst. Pipelines transporting hazardous liquids or gases warrant special care in design, construction, and operation. Hydroelectric power plants especially must be carefully designed and maintained because 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 recommend flow velocity at or below . * Fit slowly closing valves. Toilet fill valves are available in a quiet fill type that closes quietly. *Non-slam check valves do not rely on fluid flow to close and will do so before the water flow reaches significant velocity. * High pipeline pressure rating (does not reduce the effect but protects against damage). * Good pipeline control (start-up and shut-down procedures). *
Water tower A water tower is an elevated structure supporting a water tank constructed at a height sufficient to pressurize a distribution system for potable water, and to provide emergency storage for fire protection. Water towers often operate in conju ...
s (used in many
drinking water Drinking water is water that is used in drink or food preparation; potable water is water that is safe to be used as drinking water. The amount of drinking water required to maintain good health varies, and depends on physical activity level, ...
systems) or
surge tank A Surge tank is a water storage device used as a pressure neutralizer in hydropower water conveyance systems in order to dampen excess pressure variance. A surge tank (or surge drum or surge pool) is a standpipe or storage reservoir at the downst ...
s help maintain steady flow rates and trap large pressure fluctuations. * Air vessels such as expansion tanks and some types of
hydraulic accumulator A hydraulic accumulator is a pressure storage reservoir in which an incompressible hydraulic fluid is held under pressure that is applied by an external source of mechanical energy. The external source can be an engine, a spring, a raised weigh ...
s work in much the same way as water towers, but are pressurized. They typically have an air cushion above the fluid level in the vessel, which may be regulated or separated by a bladder. Sizes of air vessels may be up to hundreds of cubic meters on large pipelines. They come in many shapes, sizes and configurations. Such vessels often are called accumulators or expansion tanks. * A hydropneumatic device similar in principle to a
shock absorber A shock absorber or damper is a mechanical or hydraulic device designed to absorb and damp shock impulses. It does this by converting the kinetic energy of the shock into another form of energy (typically heat) which is then dissipated. Most ...
called a 'Water Hammer Arrestor' can be installed between the water pipe and the machine, to absorb the shock and stop 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 the system, which is often unwanted. Blowoff valves may be used as an alternative. * Shorter branch pipe lengths. * Shorter lengths of straight pipe, i.e. add elbows, expansion loops. Water hammer is related to the 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. With looped piping, lower velocity flows from both sides of a loop can serve a branch. *
Flywheel A flywheel is a mechanical device which uses the conservation of angular momentum to store rotational energy; a form of kinetic energy proportional to the product of its moment of inertia and the square of its rotational speed. In particular, as ...
on a pump. * Pumping station bypass.


Magnitude of the pulse

One of the first to successfully investigate the water hammer problem was the Italian engineer
Lorenzo Allievi Lorenzo Allievi (November 18, 1856 – October 30, 1941) was an Italian engineer known for being one of the first to explain the water hammer problem.Kaveh Hariri Asli, Faig Bakhman Ogli Naghiyev, Reza Khodaparast Haghi, Hossien Hariri Asli, Ad ...
. Water hammer can be analyzed by two different approaches—''rigid column theory'', which ignores compressibility of the fluid and elasticity of the walls of the pipe, or by a full analysis that includes elasticity. When the time it takes a valve to close is long compared to the propagation time for a pressure wave to travel the length of the pipe, then rigid column theory is appropriate; otherwise considering elasticity may be necessary. Below are two approximations for the peak pressure, one that considers elasticity, but assumes the valve closes instantaneously, and a second that neglects elasticity but includes a finite time for the valve to close.


Instant valve closure; compressible fluid

The pressure profile of the water hammer pulse can be calculated from the Joukowsky equation : \frac = \rho a \frac. So for a valve closing instantaneously, the maximal magnitude of the water hammer pulse is : \Delta P = \rho a_0 \Delta v, where Δ''P'' is the magnitude of the pressure wave (Pa), ''ρ'' is the density of the fluid (kg/m3), ''a''0 is the speed of sound in the fluid (m/s), and Δ''v'' is the change in the fluid's velocity (m/s). The pulse comes about due to
Newton's laws of motion Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in mo ...
and the
continuity equation A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. ...
applied to the deceleration of a fluid element.


Equation for wave speed

As the speed of sound in a fluid is a = \sqrt, the peak pressure depends on the fluid compressibility if the valve is closed abruptly. : B = \frac, where : ''a'' = wave speed, : ''B'' = equivalent bulk modulus of elasticity of the system fluid–pipe, : ''ρ'' = density of the fluid, : ''K'' = bulk modulus of elasticity of the fluid, : ''E'' =
elastic modulus An elastic modulus (also known as modulus of elasticity) is the unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is ...
of the pipe, : ''D'' = internal pipe diameter, : ''t'' = pipe wall thickness, : ''c'' = dimensionless parameter due to on wave speed.


Slow valve closure; incompressible fluid

When the valve is closed slowly compared to the transit time for a pressure wave to travel the length of the pipe, the elasticity can be neglected, and the phenomenon can be described in terms of inertance or rigid column theory: : F = m a = P A = \rho L A . Assuming constant deceleration of the water column (''dv''/''dt'' = ''v''/''t''), this gives : P = \rho L v/t. where: : ''F'' = force : ''m'' = mass of the fluid column g : ''a'' = acceleration /s2 : ''P'' = pressure a : ''A'' = pipe cross-section 2 : ''ρ'' = fluid density g/m3 : ''L'' = pipe length : ''v'' =
flow velocity In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...
/s : ''t'' = valve closure time The above formula becomes, for water and with imperial unit, : P = 0.0135\, V L/t. For practical application, a safety factor of about 5 is recommended: : P = 0.07\, V L/t + P_1, where ''P''1 is the inlet pressure in psi, ''V'' is the flow velocity in ft/ s, ''t'' is the valve closing time in seconds, and ''L'' is the upstream pipe length in feet. Hence, we can say that the magnitude of the water hammer largely depends upon the time of closure, elastic components of pipe & fluid properties.


Expression for the excess pressure due to water hammer

When a valve with a volumetric flow rate ''Q'' is closed, an excess pressure Δ''P'' is created upstream of the valve, whose value is given by the Joukowsky equation: : \Delta P = Z Q. In this expression: : Δ''P'' is the overpressurization in Pa; : ''Q'' is the volumetric flow in m3/s; : ''Z'' is the hydraulic impedance, expressed in kg/m4/s. The hydraulic impedance ''Z'' of the pipeline determines the magnitude of the water hammer pulse. It is itself defined by : Z = \frac, where : ''ρ'' the density of the liquid, expressed in kg/m3; : ''A'' cross sectional area of the pipe, m2; : ''B'' equivalent 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 ''B''l, resulting from the equation of state of the liquid generally available from thermodynamic tables; * the elasticity of the walls of the pipe, which defines an equivalent bulk modulus of compressibility for the solid ''B''s. In the case of a pipe of circular cross-section whose thickness ''t'' is small compared to the diameter ''D'', the equivalent modulus of compressibility is given by the formula B = \frac E, in which ''E'' is the Young's modulus (in Pa) of the material of the pipe; * possibly compressibility ''B''g of gas dissolved in the liquid, defined by B_\text = \frac P, *: γ being the
specific heat ratio In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volu ...
of the gas, *: α the rate of ventilation (the volume fraction of undissolved gas), *: and ''P'' the pressure (in Pa). Thus, the equivalent elasticity is the sum of the original elasticities: : \frac = \frac + \frac + \frac. As a result, we see that we can reduce the water hammer by: * increasing the pipe diameter at constant flow, which reduces the flow velocity and hence the deceleration of the liquid column; * employing the solid material as tight as possible with respect to the internal fluid bulk (solid Young modulus low with respect to fluid bulk modulus); * introducing a device that increases the flexibility of the entire hydraulic system, such as a hydraulic accumulator; * where possible, increasing the fraction of undissolved gases in the liquid.


Dynamic equations

The water hammer effect can be simulated by solving the following partial differential equations. : \frac + \frac \frac = 0, : \frac + \frac \frac + \frac V , V, = 0, where ''V'' is the fluid velocity inside pipe, \rho is the fluid density, ''B'' is the ''equivalent'' bulk modulus, and ''f'' is the Darcy–Weisbach friction factor.


Column separation

Column separation is a phenomenon that can occur during a water-hammer event. If the pressure in a pipeline drops below the
vapor pressure Vapor pressure (or vapour pressure in English-speaking countries other than the US; see spelling differences) or equilibrium vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed pha ...
of the liquid,
cavitation Cavitation is a phenomenon in which the static pressure of a liquid reduces to below the liquid's vapour pressure, leading to the formation of small vapor-filled cavities in the liquid. When subjected to higher pressure, these cavities, ca ...
will occur (some of the liquid vaporizes, forming a bubble in the pipeline, keeping the pressure close to the vapor pressure). This is most likely to occur at specific locations such as closed ends, high points or knees (changes in pipe slope). When subcooled liquid flows into the space previously occupied by vapor the area of contact between the vapor and the liquid increases. This causes the vapor to condense into the liquid reducing the pressure in the vapor space. The liquid on either side of the vapor space is then accelerated into this space by the pressure difference. The collision of the two columns of liquid (or of one liquid column if at a closed end) causes a large and nearly instantaneous rise in pressure. This pressure rise can damage
hydraulic machinery Hydraulic machines use liquid fluid power to perform work. Heavy construction vehicles are a common example. In this type of machine, hydraulic fluid is pumped to various hydraulic motors and hydraulic cylinders throughout the machine ...
, individual pipes and supporting structures. Many repetitions of cavity formation and collapse may occur in a single water-hammer event.


Simulation software

Most water hammer
software Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work. At the lowest programming level, executable code consist ...
packages use the
method of characteristics In mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations, although more generally the method of characteristics is valid for any hyperbolic partia ...
to solve the
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...
s involved. This method works well if the wave speed does not vary in time due to either air or gas entrainment in a pipeline. The wave method (WM) is also used in various software packages. WM lets operators analyze large networks efficiently. Many commercial and non-commercial packages are available. Software packages vary in complexity, dependent on the processes modeled. The more sophisticated packages may have any of the following features: * Multiphase flow capabilities. * An
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
for
cavitation Cavitation is a phenomenon in which the static pressure of a liquid reduces to below the liquid's vapour pressure, leading to the formation of small vapor-filled cavities in the liquid. When subjected to higher pressure, these cavities, ca ...
growth and collapse. * Unsteady friction: the pressure waves dampen as turbulence is generated and due to variations in the flow velocity distribution. * Varying bulk modulus for higher pressures (water becomes less compressible). * Fluid structure interaction: the pipeline reacts on the varying pressures and causes pressure waves itself.


Applications

* The water hammer principle can be used to create a simple water
pump A pump is a device that moves fluids (liquids or gases), or sometimes slurries, by mechanical action, typically converted from electrical energy into hydraulic energy. Pumps can be classified into three major groups according to the method they ...
called a hydraulic ram. * Leaks can sometimes be detected using water hammer. * Enclosed air pockets can be detected in pipelines. * The water hammer from a
liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, ...
jet created by a collapsing microcavity is studied for potential applications noninvasive transdermal drug delivery.


See also

*
Blood hammer The blood hammer phenomenon is a sudden increase of the upstream blood pressure in a blood vessel (especially artery or arteriole) when the bloodstream is abruptly blocked by vessel obstruction. The term "blood-hammer" was introduced in cerebral h ...
*
Cavitation Cavitation is a phenomenon in which the static pressure of a liquid reduces to below the liquid's vapour pressure, leading to the formation of small vapor-filled cavities in the liquid. When subjected to higher pressure, these cavities, ca ...
*
Fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) a ...
* Hydraulophone – musical instruments employing water and other fluids * Impact force * Transient (civil engineering) * Watson's water hammer pulse


References


External links


What Is Water Hammer and Why Is It Important That You Prevent it?

Use accumulator to prevent water hammer in pipeline



"Water hammer"
��YouTube (animation)
"Water Hammer Theory Explained"
��YouTube; with examples {{DEFAULTSORT:Water Hammer Hydraulics Irrigation Plumbing Physical phenomena