Water hammer is a pressure surge or wave caused when a fluid in motion is forced to stop or
change direction suddenly. A water hammer commonly occurs when a valve closes suddenly
at an end of a pipeline system, and a pressure wave propagates in the pipe. It is also called
hydraulic shock. This pressure wave can cause major problems,
from noise and vibration to pipe collapse. It is possible to reduce the effects of the
water hammer pulses with accumulators, expansion tanks, surge tanks, and other features.
Rough calculations can be made either using the Joukowsky equation, or more accurate ones
using the method of characteristics.
Cause and effect When a pipe is suddenly closed at the outlet,
the mass of water before the closure is still moving, thereby building up high pressure
and a resulting shock wave. In domestic plumbing this is experienced as a loud banging, resembling
a hammering noise. Water hammer can cause pipelines to break if the pressure is high
enough. Air traps or stand pipes are sometimes added as dampers to water systems to absorb
the potentially damaging forces caused by the moving water.
In hydroelectric generating stations, the water travelling along the tunnel or pipeline
may be prevented from entering a turbine by closing a valve. However, if, for example,
there is 14 km of tunnel of 7.7 m diameter, full of water travelling at 3.75 m/s, that
represents approximately 8000 Megajoules of kinetic energy that must be arrested. This
arresting is frequently achieved by a surge shaft open at the top, into which the water
flows; as the water rises up the shaft, its kinetic energy is converted into potential
energy, which decelerates the water in the tunnel. At some HEP stations, what looks like
a water tower is actually one of these devices, known in these cases as a surge drum.
In the home, water hammer may occur when a dishwasher, washing machine, or toilet shuts
off water flow. The result may be heard as a loud bang, repetitive banging, or as some
shuddering. On the other hand, when an upstream valve
in a pipe closes, water downstream of the valve attempts 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 and vacuum relief valves,
or air vents, are installed just downstream of the valve to allow air to enter the line
for preventing this vacuum from occurring. Other causes of water hammer are pump failure,
and check valve slam. Related phenomena
Steam distribution systems may also be vulnerable to a situation similar to water hammer, known
as steam hammer. In a steam system, water hammer most often occurs when some of the
steam condenses into water in a horizontal section of the steam piping. Subsequently,
steam picks up the water, forms a "slug" and hurls it at high velocity into a pipe fitting,
creating a loud hammering noise and greatly stressing the pipe. This condition is usually
caused by a poor condensate drainage strategy. Where air filled traps are used, these eventually
become depleted of their trapped air over a long period of time through absorption into
the water. This can be cured by shutting off the supply, opening taps at the highest and
lowest locations to drain the system, and then closing the taps and re-opening the supply.
Water hammer during an explosion When an explosion happens in an enclosed space,
water hammer can cause the walls of the container 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 accelerate upwards through 0.76 m of air before it struck the
vessel head at 49 m/s with a pressure of 680 atm. This pressure wave caused the 12,000 kg
steel vessel to jump 2.77 m into the air before it dropped into its prior location.
Mitigating 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 1.5 m/s
Fit slowly closing valves. Toilet fill valves are available in a quiet fill type that closes
quietly. High pipeline pressure rating.
Good pipeline control. Water towers help maintain steady flow rates
and trap large pressure fluctuations. Air vessels 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 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.
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 on pump.
Pumping station bypass.
The magnitude of the pulse One of the first to successfully investigate
the water hammer problem was the Italian engineer Lorenzo Allievi.
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
So for a valve closing instantaneously, the maximum magnitude of the water hammer pulse
is:
where ΔP is the magnitude of the pressure wave, ρ is the density of the fluid, a0 is
the speed of sound in the fluid, and Δv is the change in the fluid's velocity. The pulse
comes about due to Newton's laws of motion and the continuity equation applied to the
deceleration of a fluid element. Equation for wave speed
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 speed
K = bulk modulus of elasticity of the fluid ρ = density of the fluid
E = elastic modulus of the pipe D = internal pipe diameter
t = pipe wall thickness c = dimensionless parameter due to system
pipe-constraint condition 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:
Assuming constant deceleration of the water column, gives:
where: F = force, N
m = mass of the fluid column, kg a = acceleration, m/s2
P = pressure, Pa A = pipe cross section, m2
ρ = fluid density, kg/m3 L = pipe length, m
v = fluid velocity, m/s t = valve closure time, s
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:
where P1 is the inlet pressure in psi, V is the flow velocity in ft/sec, t is the valve
closing time in seconds and L is the upstream pipe length in feet.
Expression for the excess pressure due to water hammer
When a valve with a volumetric flow rate Q is closed, an excess pressure δP is created
upstream of the valve, whose value is given by the Joukowsky equation:
In this expression: overpressurization δP is expressed in Pa;
Q is the volumetric flow in m3/s; Zh is the hydraulic impedance, expressed in
kgs. 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 from the 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 the diameter D, the equivalent modulus
of compressibility is given by the following formula: ; in which E is the Young's modulus
of the material of the pipe; possibly compressibility Bg of gas dissolved
in the liquid, defined by: γ being the ratio of specific heats of the gas
α the rate of ventilation and P the pressure.
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 velocity and hence the deceleration
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 a hydraulic accumulator;
where possible, increasing the percentage of undissolved air in the liquid.
Dynamic equations 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
bulk modulus, f is the friction factor. Column separation
Column separation is a phenomenon that can occur during a water-hammer event. If the
pressure in 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. When the pressure later increases above the
vapor pressure of the liquid, the vapor in the bubble returns to a liquid state, which
leaves a vacuum in the space formerly occupied by the vapor. The liquid either side of the
vacuum is then accelerated into this space by the pressure difference. The collision
of the two columns of liquid, results in cavitation and causes a large and nearly instantaneous
rise in pressure. This pressure rise can damage hydraulic machinery, 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 packages use the method of characteristics to solve the differential
equations 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 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 for cavitation growth and collapse
Unsteady friction - the pressure waves dampens as turbulence is generated and due to variations
in the flow velocity distribution Varying bulk modulus for higher pressures
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 called a hydraulic ram.
Leaks can sometimes be detected using water hammer.
Enclosed air pockets can be detected in pipelines. History
Water hammer was exploited before there was even a word for it: Marcus Vitruvius Pollio
describes in the 1st century B.C.E the effect of water hammer in lead pipes and stone tubes
of the Roman public water supply. In 1772, Englishman John Whitehurst built a hydraulic
ram for a home in Cheshire, England. In 1796, French inventor Joseph Michel Montgolfier
built a hydraulic ram for his paper mill in Voiron. In French and Italian, the terms for
"water hammer" come from the hydraulic ram: coup de bélier and colpo d’ariete 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.
The theory of water hammer began in 1883 with the work of German physiologist Johannes von
Kries, 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, in 1898 by the American
civil engineer Joseph Palmer Frizell, and in 1902 by the Italian engineer Lorenzo Allievi.
See also Blood hammer
Cavitation Fluid dynamics
Hydraulic ram – makes constructive use of the water hammer effect
Hydraulophone – musical instruments employing water and other fluids
Impact force Watson's water hammer pulse
References
External links What is Water Hammer/Steam Hammer?