KSB Know-how, Volume 1

Water Hammer
2 × Di
> DN2 + 150

0,75 × Di CCW
Di
CCp

CW

CO

CO

CB

CO
 Contents
Table of Contents Page

1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 General - The Problem of Water Hammer . . . . . . . . . . . . . . .4

2.1 Steady and Unsteady Flow in a Pipeline. . . . . . . . . . . . . . . . . 4

3 Water Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.1 Inertia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2 Elasticity of Fluid and Pipe Wall. . . . . . . . . . . . . . . . . . . . . . 7

3.3 Resonance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4 The Joukowsky Equation. . . . . . . . . . . . . . . . . . . . . . . . . . .11

4.1 Scope of the Joukowsky Equation. . . . . . . . . . . . . . . . . . . . 12

5 Numerical Simulation of Water Hammer . . . . . . . . . . . . . . 15

5.1 Accuracy of Numerical Surge Analysis . . . . . . . . . . . . . . . . 15

5.2 Forces Acting on Pipelines as a Result of Water Hammer….16

6 Computerised Surge Analysis . . . . . . . . . . . . . . . . . . . . . . . 17

6.1 Technical Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6.2 Interaction between Ordering Party and Surge Analyst……17

7 Advantages of Rules of Thumb and Manual Calculations…18

8 Main Types of Surge Control. . . . . . . . . . . . . . . . . . . . . . . . 20

8.1 Energy Storage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

8.1.1 Air Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

8.1.2 Standpipes, One-Way Surge Tanks . . . . . . . . . . . . . . . . . . . 21

8.1.3 Flywheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

8.2 Air Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

8.3 Actuated Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

8.4 Swing Check Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

9 Case Studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

9.1 Case Study: Long-Distance Water Supply System . . . . . . . . 25

9.2 Case Study: Stormwater Conveyance Pipeline. . . . . . . . . . . 26

Model Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Calculation of Actual Duty Data, First Results . . . . . . . . . .27

Surge Control Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

10 Additional Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30

Authors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

1
Introduction 1

1 Introduction the photos taken of some “acci- in this brochure:

Most engineers involved in the dents” (Figs. 1-a, 1-b, 1-c) one
planning of pumping systems are thing is clear: the damage caused • How can we know whether
familiar with the terms “hydrau- by water hammer by far exceeds there is a risk of water hammer
lic transient”, “surge pressure” or, the cost of preventive analysis and or not?
in water applications, “water surge control measures. • How significant are approxima-
hammer”. The question as to tion formulas for calculat­ing
whether a transient flow or surge The ability to provide reliably de- water hammer?
analysis is necessary dur­ing the signed surge control equipment, • Can the surge analysis of one
planning phase or not is less rea- such as an air vessel or accumula- piping system be used as a b
­ asis
dily answered. Under unfavoura- tor1, flywheel and air valve, has for drawing conclusions for
ble circumstances, dam­age due to long been state of the art. The similar systems?
water hammer may occur in pipe- technical instruction leaf­let W • Which parameters are required
lines measuring more than one 303 “Dynamic Pres­sure Changes for a surge analysis?
hundred metres and conveying in Water Supply Sys­tems” publis- • What does a surge analysis cost?
only several tenths of a litre per hed by the German Association • How reliable is the surge
second. But even very short, un- of the Gas and W
­ ater Sector control equipment available and
supported p
­ ipelines in pumping clearly states that pressure transi- how much does it cost to
stations can be damaged by reso- ents have to be considered when operate it?
nant ­vibrations if they are not designing and operating water • How reliable is a computerised
properly anchored. By contrast, supply systems, because they can analysis?
the phenomenon is not very cause extensive damage. This me-
System designer and surge ­analyst
­common in building services ans that a surge analysis to indus-
have to work together closely to
­systems, e.g. in heating and try standards has to be performed
save time and money. ­Water
­drinking water supply pipelines, for every hydraulic piping system
hammer is a complex phenome-
which typically are short in length at risk from water hammer. Dedi-
non; the purpose of this bro-
and have a small cross-section. cated software is available for this
chure is to impart a ­basic know-
The owners or operators of sys­ purpose – an important tool for
ledge of its many aspects wit-
tems affected by water hammer the specialist surge analyst to use.
hout oversimplifying them.
are usually reluctant to pass on Consultants and system ­designers
information about any surge are faced with the ­following que-
­damage suffered. But studying stions, which we hope to answer

Fig. 1-a: Completely destroyed DN Fig. 1-b: Destroyed support (double Fig. 1-c: DN 800 check valve
600 discharge pipe (wall thickness T profile 200 mm, permanently following a pressure surge in the
12 mm) deformed) discharge pipe
1
Air vessels, sometimes also called “accumulators”, store potential energy by accumulating a quantity of pressurised hydraulic
fluid in a suitable enclosed vessel.

3
2 General – The Problem of Water Hammer

2 General – The problem of time. Fig. 2.1-a shows a typical commonly referred to as unstea-
water hammer steady flow profile: dy or ­transient. Referring speci-
2.1 Steady and unsteady With a constant pipe diameter fically to pressures, they are
flow in a pipeline and a constant surface rough- sometimes ­called dynamic pres-
When discussing the pressure of ness of the pipe’s inner walls, the sure changes or pressure transi-
a fluid, a distinction has to be pressure head curve will be a ents. The main ­causes of transi-
made between pressure above straight line. In simple cases, a ent flow ­conditions are:
atmospheric [p bar], absolute pump’s steady-state operating • Pump trip as a result of switch­
pressure [p bar(a)] and pressure point can be determined graphi- ing off the power supply or a
head h [m]. Pressure head h de- cally. This is done by determin­ power failure.
notes the height of a homogene- ing the point where the pump • Starting or stopping up one or
ous liquid column which gener­ curve intersects the piping cha- more pumps whilst other
ates a certain pressure p. Values racteristic. pumps are in operation.
for “h” are always referred to a A pumping system can never be • Closing or opening of shut-off
datum, (e.g. mean sea level, axi- operated in steady-state conditi- valves in the piping system.
al centreline of pipe and pipe on all the time, since starting up • Excitation of resonant vibra
crown etc.). and stopping the pump alone tions by pumps with an
will change the duty conditions. unstable H/Q curve.
As a rule, system designers start ­Generally speaking, every • Variations of the inlet water
by determining the steady-state ­change in operating conditions level.
operating pressures and volume and every disturbance cause Fig. 2.1-b may serve as a repre-
rates of flow. In this context, the pressure and flow variations or, sentative example showing the
term steady2 means that volume put differently, cause the flow pressure envelope3 with and
rates of flow, pressures and conditions to c­ hange with time. ­without an air vessel following
pump speeds do not change with Flow conditions of this kind are pump trip.

Metres
Koteabove
m sea level

Stead
y-sstta
attioenpr
äresD
suru
reckhe
höahdecu
nlin
r viee

hNN+m hm

Length
Länge

Fig. 2.1-a: Steady-state pressure head curve of a pumping system

2
Not to be confused with the term “static".
3
The term “pressure envelope” refers to the area defined by the minimum and maximum head curves along the fixed datum
ine resulting from all dynamic pressures occurring within the time period under review
4
General – The Problem of Water Hammer 2

hsteady in Fig. 2.1-b is the steady- the pipe PN 16 (curve marked We will come back to the sub-
state pressure head curve. “PN pipe“) and is, therefore, ject of macro-cavitation, i.e.
Pressure head envelopes hminWK inadmissibly high. As a rule, ­liquid column separation, in
and hmaxWK were obtained from vapour pressure is a most ­section 3.1.
an installation with, hmin and undesirable phenomenon. It can
hmax from an installation have the following harmful
without air vessel. Whereas effects:
hminWK and hmaxWK are within the • Dents in or buckling of thin-
permissible pressure range, hmin walled steel pipes and plastic
gives evi­dence of vapour tubes.
pressure (macro-cavitation) over • Disintegration of the pipe’s ­
a pipe distance from 0 m to cement lining.
approximately • Dirty water being drawn into
800 m. Almost across the entire drinking water pipelines
length of the pipe, the value of through leaking connecting
hmax exceeds the maximum sockets.
permissible nominal pressure of

Pipe length
Rohrlänge L: L: 26242624
m m
Inside diameter of
Rohrinnendurchmesser pipe Di:
Di: 605,2 mm 605.2 mm
stationäre Fördermenge:
Steady-state flow rate: 500 l/s
500 l/s
h-Pumpensumpf: 287,5 m
Hpump sump:
h-Auslauf: 400 m
287.5 m
Houtlet:
Windkesselzuleitung 400 m 3
mit Bypass und Rückstromdrossel:
vessel inlet pipe with a VLuft = 3,8 m , V Wasser = 6,2 m
3
Air
bypass and a non-return valve: Vair = 3.8 m , Vwater = 6.2 m3
D1

Z2 Z1

700 D2

hmax

600
Metres above sea level [m]

PN-Pipe
500

hmax WK
400
hsteady
hmin WK

Elevation of
300
hmin pipe

200
0 500 1000 1500 2000 2500
Length of Pipe [m]
Fig. 2.1-b: Pressure head envelope of pressure transients following pump trip

5
3 Water Hammer · Inertia

3 Water Hammer disconnected flanges. The root v = 3 m/s, the vol­ume of water in
Pressure transients are also re­ cause of damage then tends to the pipeline is calculated by
ferred to as surge pressure or, if remain in the dark. Some 0,22p .
mwater = 900 · 1000 = 28274 kg
­referring to water systems, water representative incidents caused by 4
hammer. The latter term suitably water hammer are listed in the This is more or less the same as
reflects the harmful effects that following: the weight of a truck; v = 3 m/s
the hammer-like blows accom­ corresponds to 11 km/h. In ­other
panying the pressure surges can Pressure rise: words, if the flow is suddenly
­have on pipes and system com­ • Pipe rupture stopped, our truck – to put it in
ponents. Water hammer causes • Damaged pipe fixtures less abstract terms – runs into a
­piping, valves, pipe fixtures, • Damage to pumps, wall (closed valve) at 11 km/h
supports, system components, foundations, pipe internals (water mass inside the pipe). In
etc. to suffer the added strain of and valves terms of our pipeline, this means
dynamic loads. The term “water Pressure fall: that the sequence of events taking
hammer” is used to describe the • Buckling of plastic and thin- place inside the p
­ ipe will result in
phenomenon occurring in a walled steel pipes high pressures and in high forces
closed conduit when there is • Disintegration of the cement acting on the shut-off valve.
either an acceleration or lining of pipes As a further example of inertia,
retardation of the flow. In • Dirty water or air being drawn Fig. 3.1-a shows a pump dis­
contrast to a force, pressure is into pipelines through charge pipe. At a very small
non-directional; i.e. it does not flanged or socket connections, ­moment of inertia of pump and
have a vector. Not until a gland packing or leaks motor, the failing pump comes to
hydrostatic pressure starts acting • Water column separation a sudden standstill, which has the
on a limiting area, is a force followed by high increases in same effect as a suddenly closing
exerted in the direction of the pressure when the separate ­ gate valve, only this time on the
area normal. liquid columns recombine downstream side of the gate val-
As it is not possible to altogether (macro-cavitation) ve. If mass inertia causes the fluid
avoid pressure transients when flow on the down­stream side of
operating a piping system, the art 3.1 Inertia the pump to c­ ollapse into sepa-
lies in keeping the pressure The sudden closure of a valve in rate columns, a cavity containing
transients within controllable a pipeline causes the mass inertia a mixture of water vapour and
­limits. What makes matters even of the liquid column to exert a air coming out of solution will be
more complex is the fact that the force on the valve’s shut-off ele- formed. As the separate liquid
damage caused by impermissibly ment. This causes the pressure on columns subsequently move
high surge pressures is not always the upstream side of the valve to backward and recombine with a
visible. Often the consequences increase; on the downstream side hammer-like impact, high pres-
do not become apparent until of the valve the pressure decre- sures develop. The phenomenon
long after the event, for example ases. Let us consider an example: is referred to as liquid column se-
a pipe rupture, loose or for a DN 200 pipe, L = 900 m, paration or macro-cavitation4.

4
Macro-cavitation in pipelines is not to be confused with microscopic cavitation causing pitting corrosion on pump and turbine blades. The
latter always strikes in the same place and is characterised by local high pressures of up to 1000 bar or more that develop when the
microscopically small vapour bubbles collapse.
With macro-cavitation, repetitive strain of this kind, or the bombarding of a sharply contoured area of the material sur­face, does not occur
6 since the pressure rises are considerably lower.
Elasticity of Fluid and Pipe Wall 3

1. Steady-state condition prior 2. Formation of a vapour pocket 3. High-impact reunion of separate

to pump trip (cavitation cavity) following pump trip liquid columne accomparied
by surge pressures

Fig. 3.1-a: Macro-cavitation following pump trip

3.2 Elasticity of fluid and ­

pipe wall
The attempt at visualising water
hammer resulting from the
inertia of a body of water made
s1 in t1
in section 3.1 is only partly
correct, because no allowance
was made for the elasticity of
s2 in t2
fluid and ­pipe wall. As long as
safety belts are worn and the
barrier impact speed is not too
s3 in t3
high, even a h­ ead-on collision
will not put drivers in too much Fig. 3.2-a: Sudden closure of gate valve, visualised by a heavy steel spring
danger ­today, because the
vehicle’s ­momentum is converted stopped (Fig. 3.2-a): subject, we will now go back to
to harmless deformation heat5. The front end deformation trav­ the real situation inside the pipe,
Contrary to the body of a car, els in the opposite direction to which is shown in Fig. 3.2-b,
however, water and pipe walls the original direction of with friction being neglected.
are elastic, even though they are movement at the speed typical The shut-off valve installed at
so hard that this property is not for the steel spring, i.e. wave the downstream end of a
notice­able in every day use.
propagation velocity a in m/s. In horizontal pipeline with a
the compression zone, the constant inside diameter, which
What actually goes on inside the
velocity of the steel spring is is fed from a reservoir at
pipe will, therefore, be described
using the following example of a v = 0 e­ verywhere. constant pressure, is suddenly
heavy steel spring sliding through Following these, admittedly closed:
a pipe. This spring suffers elastic poor but hopefully helpful,
deformation when it is suddenly examples chosen to illustrate the

5
To withstand the regular pushing and shoving over rare parking spaces, cars have to be elastic. To minimise the damage of a
collision at high speed, however, carmakers spend vast amounts of time and money to make their products as inelastic as possi-
ble!

7
3 Elasticity of Fluid and Pipe Wall

1 For t = 0, the pressure profile velocity changes sign and is

t=0 L 1
is steady, which is shown by the now headed in the d
­ irection of
pressure head curve running the reservoir
horizontally because of the 4 A relief wave with a head of
assumed lack of friction. Under -Dh travels downstream ­
v = v0
0 < t < 1/2Tr 2 steady-state conditions, the towards the gate valve and ­
∆h flow velocity is v0. reaches it at a time t = Tr. It is
2 The sudden closure of the gate accompanied by a change of
ve at the downstream end of the velocity to the value -v0.
v = v0 v=0 pipeline causes a pulse of high 5 Upon arrival at the closed ­
t = 1/2Tr
3 pressure Dh; and the pipe wall gate valve, the velocity ­
∆h is stretched. The pressure wave changes from -v0 to v = 0.
generated runs in the opposite This causes a sudden negative
direction to the steady-state change in pressure of -Dh.
v=0 direction of the flow at the 6 The low pressure wave -Dh
1/ 2T < t < Tr
r
4 speed of sound and is ac travels upstream to the
-∆h
companied by a reduction of reservoir in a time
the fow velocity to v = 0 in the Tr < t < 3/2Tr, and at the same
high pressure zone. The process time, v adopts the value v = 0.
v = - v0 v=0
takes place in a period of time 7 The reservoir is reached in a
t = Tr
5 0 < t < /2Tr , where Tr is the
1
time t = 3/2Tr, and the pres­sure
amount of time needed by the resumes the reservoir’s
pressure wave to travel up and pressure head.
down the entire length of the 8 In a period of time 3/2Tr < t <
v = - v0
Tr < t < 3/2Tr
pipeline. The important 2Tr , the wave of increased
6 parameter Tr is the reflection pressure originating from the
-∆h time of the pipe. It has a ­value reservoir runs back to the ­
of 2L/a. gate valve and v once again
v = - v0 v=0 3 At t = 1/2
Tr the pressure wave adopts the value v0
t= 3/ 2T
r has arrived at the reservoir. As 9 At t = 2Tr , conditions are
7 the reservoir pressure p = exactly the same as at the ­
-∆h constant, there is an unbal­ instant of closure t = 0, and
anced condition at this point. the whole process starts over
v=0 With a change of sign, the again.
3/ 2T
r < t < 2Tr pressure wave is reflected in the
8 opposite direction. The flow
-∆ h

Fig. 3.2-b: Pressure and velocity waves in a single-conduit, frictionless pipe-

v = v0 v=0 line following its sudden closure. The areas of steady-state pressure head are
t = 2Tr 9 shaded medium dark, those of increased pressure dark, those of reduced pres-
sure light. The expansion and contraction of the pipeline as a result of rising
and falling pressure levels, respec­tively, are shown. To give an idea of the rela-
tionship involved: With a 100 bar pressure rise, the volume of water will de-
crease by about 0.5%.
v = v0
8
Elasticity of Fluid and Pipe Wall 3

So, one might ask, what hap­ en­ergy conversion in reverse also example given in Fig. 3.2-b for a
pened to the original steady- becomes apparent from ­ real p
­ ipeline with the following
state kinetic energy of the fluid Fig. 3.2-b – specifically from the parameters: L = 100 m, DN 100,
follow­ing the sudden closure of condition prevailing at t = 2Tr. k = 0.1 mm, hinlet = 200 m, linear
the gate valve? A closer look at If the gate valve were to be sud- throttling of Q = 10 l/s at the
Fig. 3.2-b will reveal the an- denly opened at this point, we outlet of the p
­ ipe to Q = 0,
swer. According to the law of would have the old ­steady-state starting at t = 0.1 s in a period of
the conservation of energy, it condition at t = 0 again ­without time Dt = 0.01 s.
cannot simply disap­pear. First it ­change, and there would be no
is con­verted into elas­tic energy elastic energy left. Based on Fig. 3.2-b, the reflec-
of the fluid and the pipe wall, tion of pressure waves at the
then changes into kinetic energy Without friction, the pressure upstream and downstream ends
again as a result of reflection, fluctuations would not diminish. of the pipeline can be explained
then becomes elastic energy In actual fact, no system is ever in a general manner as follows:
again, and so forth. Let’s look at entirely without friction, but the
Fig. 3.2-b up to the point where reduction in pressure fluctuation • If a pressure wave Dp reaches
t = 1/2Tr. The conversion into is relatively small in reality, the closed end of a pipe, Dp be
elastic energy takes place within because the energy conversion comes twice the amount with
this period of time. Im­mediately into frictional heat as a result of the same sign, i.e. p = ­
preceding the reflection of the fluid rubbing against the p ± 2·Dp. The velocity at the
the wave at the reservoir, the pipe walls, the inherent fluid pipe ends is always v = 0.
vel­oc­ity of the liquid column friction and, finally, the • At the open end of a pipe with
is v = 0 everywhere, and it is deformation of pipe walls and a constant total head (e.g. res­
­totally devoid of kinetic energy. fixtures is rela­tively small. ervoir with a constant water
Instead, the kinetic ­energy has To show the process in a less level), the pressure change
been changed into elastic energy, ­abstract manner, Fig. 3.2-c always equals zero.
comparable to the situation of provides the results of a • At valves, throttling sections,
a compressed steel spring. The computerised simulation of the pumps and turbines, pressure
and velocity are always found
360
Pressure head above pipe centreline at pipe outlet [m l.c]

on the resistance or machine

characteristic curve.
300
Fig. 3.2-c: Pressure head up­stream
of gate valve. Compared with the si-
240
tuation shown in Fig. 3.2-b, small
differences are apparent. For examp-
180
le, the pres­sure flanks are not per-
fectly perpendicular, because of the
120 finite closing time of Dt = 0.01 s. As
a result of friction, the pressure­
­planes are not perfectly horizontal –
60
0 0,20 0,40 0,60 0,80 1,00 this phenomenon will be discussed
Time [s]
in greater detail in section 4.1.

9
3­ Elasticity of Fluid and Pipe Wall • Resonance

Water hammer occurs when the kinetic energy of a fluid is converted into elastic energy. But
­only rapid6 changes of the flow velocity will produce this effect, for example the sudden
closure of a gate valve or the sudden failure or tripping of a pump. Due to the inertia of the
fluid, the flow velocity of the liquid column as a whole is no longer capable of adjusting to
the new situation. The fluid is deformed, with pressure transients accompanying the
deformation process. The reason why surge pressure is so dangerous is that it travels at the
almost undiminished speed of sound (roughly 1000 m/s for a large number of pipe materials)
and causes destruction in every part of the piping system it reaches.

Surge pressures travel at a very lowing a pump trip would take air vessel oscillations to die away,
high wave propagation velocity, place at the pump outlet, which in ­longer pipelines in particular.
for example a = 1000 m/s in duc- could cause the ­liquid col­umn to
tile or steel piping (see 4.1). They separate
dampen out only gradually and, (Fig. 3.1-a). However, this does 3.3 Resonance
therefore, remain danger­ous for not happen, because the energy Resonant vibrations are an
a long time. The time needed to stored in the air cushion in the ­exception. These occur when ex-
subside depends on the length of vessel takes over the work of the citer frequencies of whatever ori-
the pipeline. In an urban water pump. Immediately following gin, generated, for example, by
supply installation, they only last pump trip, the air cushion starts the pump drive or by flow
several seconds. In long pipe- expanding and takes over the ­separation phenomena in valves
lines, it can take a few minutes pump’s job of discharging the and pipe bends, happen to
until a pressure surge has dam- water into the pipeline. Provided ­coincide with a natural frequency
pened out. that the vessel is properly of the pipeline. Improperly an-
Knowing these facts, the basic ­designed, it will prevent rapid chored, unsupported pipeline
working principles of all surge changes in the flow velocity in sections in pumping installations
control equipment, such as air the pipeline. Instead, the water are particularly prone to reso-
vessel or accumulator, flywheel, level in the vessel and the nant vibrations transmitted by
standpipe and air valves can be ­­­­un­deformed liquid column in the the fluid pumped and by the
deduced. They prevent the dan- ­pipeline will continue to rise and ­piping structure. By contrast,
gerous conversion of steady-­state fall over a longer period of time. ­resonance is all but negligible for
kinetic energy into elastic defor- The process is kept in ­motion by buried piping. In order to ­design
mation energy. Air vessels are the energy discharged by the air adequately dimensioned ancho-
ideally suited to explain the un- cushion each time ­fluid flows out ring, all pipe anchors in pumping
derlying principle. The pressuri- of the vessel and by the energy installations should be examined
sed air cushion in the air v­ essel absorbed again by the air using structural ­dynamics analy-
stores potential energy. If there cushion on the fluid’s ­return. The sis, with the pump speed serving
were no air vessel, the d
­ readed energy stored in the air ­cushion as the ­exciter frequency.
conversion of kinetic energy into is only gradually ­dissipated. That
elastic deformation energy fol- is why it takes ­many minutes for

6
The adjective “rapid” is to be seen in relation to the system’s operating conditions. For example, the pressure transients caused
by the closure of a valve in a 2 km long pipeline may well stay within the permissible range, whereas the same closing process
could generate unacceptably high pres­sures in a 20 km long pipeline.
10
The Joukowsky Equation 4

4 The Joukowsky equation consider the fluid mass to judge

The pressure change DpJou in a the risk of water hammer, al­
fluid caused by an instantaneous though that does not seem
change in flow velocity Dv is ­necessary after a superficial
calculated by: glance at Joukowsky’s equation.
At the same time, this explains
(4.1) why the pressure surges occurring
in domestic piping systems
∆v: Flow velocity change in m/s with their small diameters and
r: Density of the fluid in kg/m3 lengths are usually negligible. In
a: Wave propagation velocity these systems, the kinetic energy
through the fluid in the levels and fluid masses are very
­pipeline in m/s Nikolai Egorovich Joukowsky small. In addition, it is practically
DpJou: pressure change in N/m 2 dia­meters: 7620 m / 50 mm, impossible to close a valve within
The DpJou: formula is referred to 305 m / 101.5 mm and 305 m / the very short reflection time of a
as the Joukowsky equation. As 152.5 mm. He published the domestic water system.
well as Dv, equation (4.1) contains results of his various experiments The Joukowsky equation can be
the density r and wave propaga- and theoretical studies in 1898. used to calculate simple esti­mates.
tion velocity a. The relationship Let’s consider three examples:
only applies to the pe­riod of time It may seem inconsistent that
in which the veloc­ity change DpJou in the Joukowsky equation Example 1:
Dv is taking place. If Dv runs in (4.1) seems to have nothing to do In a DN 500 pipeline, L = 8000
opposite direction to the flow, the with the mass of the flow inside m, a = 1000 m/s and v = 2 m/s,
pressure will rise, other­wise it will the pipeline. For example, if the a gate valve is closed in 5 seconds.
fall. If the ­liquid pumped is water , 7 water hammer described in the Calculate the pressure surge. Calcu-
i.e. ­ first example in section 3.1 had late the force exerted on the gate.
r = 1000 kg/m3, equation (4.1) been based on a pipe dia­meter
will look like this: twice that of the diameter used, Answer:
A = D2p/4 would have caused the 5 s < Tr = 16 s, i.e. Joukowsky’s
(4.2) fluid mass and its ­kinetic energy equation may be applied. If the
to turn out four times as large. flow velocity is reduced from
g: Acceleration due to gravity What seems to be a paradox is 2 m/s to zero as the valve is
9.81 m/s 2 instantly resolved if one considers ­closed, Dv = 2 m/s. This gives us
DhJou: Pressure head change in m the force exerted on the shut-off a pressure increase Dh = 100 · 2 =
valve, i.e. force ­ 200 m or approximately Dp =
In 1897, Joukowsky conducted a F = Dp · A, the defining para­meter 20 · 105 N/m2, which is 20 bar.
series of experiments on Mos­cow for the surge load. Because of A, it The valve cross-section measures
drinking water supply ­pipes is now in actual fact four times as A = D2 · 0.25 · p ≈ 0.2 m2. The
of the following lengths / large as before. force acting on the gate is p·A =
This shows that one must also 0.2 · 20 · 105 = 4·105 N= 400 kN.

7
Despite the high flow velocities common in gas pipes, these do not experience surge problems, because p · a is several thousand times
smaller than for water.

11
4 The Joukowsky Equation

Example 2: Dh = 100 · 2.4 = 240 m, which is ­reach the pump until after the
A pump delivers water at the equivalent to 24 bar. speed has dropped to zero and it
Q = 300 l/s and a head Dh = 40 is too late for the relieving effect
m through a DN 400 discharge Example 3: to take place. It is, therefore,
­pipe measuring L = 5000 m into A pump delivers water at Q = ­probably safe to say that macro-
an overhead tank; a = 1000 m/s. 300 l/s and a head Dh = 40 m cavitation will develop.
The inertia moments of pump ­into a 2000 m long pipeline DN
and motor are negligible. Is 400; a = 1000 m/s. The mass
­there a risk of liquid column moment of inertia8 of all rotat­ 4.1 Scope of the Joukowsky

­separation, i.e. macro-cavi­ta­ ing components (pump, motor, equation

tion, following pump trip? If so, etc.) is J = 20 kgm2 , the speed of The Joukowsky equation only
what is the anticipated pressure rotation n0 = 24 s-1 and the total applies to:
increase? efficiency = 0.9, i.e. 90%. Is • Periods of time which are
Answer: ­there a risk of liquid column equal to or shorter than the ­
Q = 300 l/s in a DN 400 pipe­ ­separation, i.e. macro-cavitati- reflection time of the piping Tr
line roughly corresponds to a on, following pump trip? • The period of time which falls
flow velocity v = 2.4 m/s. As a within the velocity change Dv
result of pump trip and the loss Answer: • Pipes characterised by friction
of mass inertia moment, the For the instant of pump failure, losses within the limits typical
pump comes to a sudden stand- the change in speed n. may be of water transport systems
still, i.e. Dv = 2.4 m/s. According derived from the inertia equati-
to the Joukowsky equation, this on as follows: Reflection time Tr:
causes a head drop of Dh = Mp = 2·p·J·n.
-100 · 2.4 m = -240 m. Since the In Fig. 3.2-b the wave of re­duced
steady-state head is just 40 m, Assuming as an (extremely pressure reflected by the tank
vacuum is reached, the liquid co- rough) approximation a linear has arrived at the gate ­valve af-
n0 ter Tr has lapsed, and evens out
lumn collapses and macro-­ speed reduction n= , then, if
Dt
cavitation sets in. Following the some of the pressure increase
Dp·Q Dp. If the change in flow takes
liquid column separation near Mp= ,
2p·n0·h
the pump outlet, the two liquid place in a period of time Dt lon-
columns will recombine with we obtain a time Dt in which the ger than Tr, the rise in pressure
great impact after some time. speed has dropped to zero, and, DpJou will only occur at the
For reasons of energy conserva- if Dp = 1000 · 9.81 · Dh, wave’s source, whereas it will
tion, the highest velocity of the have diminished to the ­value gi-
(2 · n0)2 · J · n2 · J · ven by the boundary condition
backward flow cannot exceed t= Ä 4· 0 = 3.4 s
p· 0.001· Q h·Q
the original velocity of the by the time it reaches the opposi-
­steady-state flow of 2.4 m/s. Un- The reflection time of the pipe­ te end of the pipeline.
der the most unfavourable con- line is Tr = 4 s (for a = 1000 m/s), Fig. 4.1-a shows the pressure en-
ditions, the cavitation-induced which means that the reflected velope, which applies to a case
pressure rise will, therefore, be pressure relief wave will not of this kind:

8
Mass moment of inertia J: J expressed in kgm 3 is the correct physical quantity. Flywheel moment GD2 , which was used in the past, should no
longer be used, because it can easily be confused with J!

12
The Joukowsky Equation · Wave Propagation Velocity 4

hmax
∆ hJou

hmin ∆ hJou

Fig. 4.1-a: Pressure head envelope for closing times > reflection time Tr

Friction gate valve can be several ­times caused by line packing. Line pa-
If the liquid pumped is highly that of DpJou as calculated by the cking is only of significance for
­viscous or if the pipeline is ex­ Joukowsky equation! The phe- long pipelines or highly v­ iscous
tremely long (say, 10 km and nomenon caused by the pipe media. It is unlikely to occur in
­more), the work done by the friction is commonly called line urban water supply and waste
pump only serves to overcome packing. The following flow water disposal plants.
the friction produced by the ­simulation calculation gives an
­pipeline. Changes of geodetic example of this:
head due to the pipe profile, by The gate valve in the example
comparison, are of little or no shown in Fig. 4.1-b closes 20 s
importance. The Joukowsky after the start of the calculation.
equation no longer. applies, not The first steep increase by ap-
even within the reflection time prox. 20 bar to approx. 55 bar is
of the pipeline. In a case like DpJou according to the Jou-
this, the actual pressure rise fol- kowsky equation; the continued
lowing the sudden closure of a increase to almost 110 bar is

120
Initial pressure, absolute, in bar (approx.)

100

80
Fig. 4.1-b: Pressure curve at the outlet
of a 20 km long crude oil pipeline fol-
60 lowing a sudden gate valve closure.
Calculation para­meters:
DN 300, k = 0.02 mm, inlet pressure
40
88 bar constant, Q = 250 l/s, fluid
pumped: crude oil, r = 900 kg/m3
20
0 80 160 240 320 400
Time [s]

13
4 The Joukowsky Equation · Wave Propagation Velocity

Wave propagation velocity Gas content a

% by volume m/s
The wave propagation velocity is 0 1250
one of the elements of the
0,2 450
Joukowsky equation and,
0,4 300
therefore, a vital parameter for
defining the intensity of a surge. 0,8 250

It is calculated by solving 1 240

equation (4.1). Table 4-1: “a” as a function of the
gas content at a static water
pressure of approximately 3 bar
m/s
(4.1)

r Density of the fluid in kg/m3 “a” is estimated. The volume of

EF Modulus of elasticity of the air contained by the fluid, which
fluid in N/m2 equation (4.1) does not take into
ER Modulus of elasticity of the account, can have a strong im-
pipe wall in N/m 2
pact on “a”, as is shown by ­some
di Inside pipe diameter in mm examples in Table 4-1: In drinking
s Pipe wall thickness in mm water supply pipelines the gas
m Transverse contraction content is negligible; in waste
number water installations it normally is
not. Further elements of uncer-
Equation (4.1) produces a range tainty with regard to “a” mainly
of values from approximately concern pipes made of synthetic
1400 m/s for steel pipes to material. An unknown and va-
around 300 m/s for ductile plas­ rying modulus of elastic­ity, ma-
tic pipes. Wave propagation nufacturing tolerances, the age
­velocity “a” in an unconfined of the pipeline and, in particu-
body of water is approximately lar, the question whether the
1440 m/s. pipeline is laid in the ground or
To all intents and purposes, the not, all play a part. A buried
validity of equation (4.1) should ­pipeline has considerably higher
not be over­estimated; surge ana- values of “a” than a pipe laid
lyses are o
­ ften performed with- above ground.
out it, in which case the value of

14
Numerical Simulation of Water Hammer
Accuracy of Numerical Surge Analysis
5

5 Numerical simulation
( 5.1)
of water hammer
In current theory, the dependent
model variables are the pressure
p and the flow velocity v in the
two partial differential equations
(5.1) for every single pipe of a pi- 5.1. Accuracy of numerical ­ are somewhat larger than the
ping system; the time t and an
surge analysis ­forecast supplied by simu­lation.
unrolled reach of pipe x are inde- Computer programs based on The first pressure peaks and
pendent variables. Equations the characteristics method ­val­leys, therefore, tend to be si-
(5.1) are generally ­valid and co- produce solutions whose mulated very precisely, whereas
ver the effects of both ­inertia and accuracy by far exceeds that the pressures further down the
elasticity. Mathema­tically, the which is called for in practice. line are on the whole depicted
pipe ends serve as the boundary This is evidenced by ­numerous with an increasing lack of
conditions of equations (5.1); dif- comparisons with ­actual dampen­ing. But imperfections of
ferent types of boundary condi- measurements. Significant dif­ this kind are negligible compa-
tions are introduced to include ferences were only found for red with inaccuracies caused by
internal components such as pipe ­calculations aimed at predicting ­entering wrong or insufficient
branches, vessels, pumps and macro-cavitation or dampening input data.
valves in the model. For examp- of pressure waves inside a pipe.
le, the creation of a complete pi- Some of the potential sources of
ping system by connecting a For example, the pressures error are:
number of individual pipes is computed using the standard • Inaccurate valve and/or pump
done by taking a pipe node to be model of vapour cavitation characteristics.
the boundary condition. The derived from equations (5.1), i.e. • Lack of knowledge about the
starting condition of equation the ­assumption of a simple actual wave propagation
(5.1) is the steady-­state flow in- cavity of low pressure following veloc­ity inside the pipeline.
side the pipe con­cerned before liquid c­ olumn separation, are • Lack of information about
the onset of the dis­turbance. always higher than what they are tapping points in a main pipe.
Equations (5.1) are ­solved by me- in real­ity. However, the • Unawareness of the degree of
ans of the character­istics me- advantage of the conservative in crustation inside the pipes.
thod, which provides the basis outcome is that one is always on
for almost all surge analysis soft- the safe side. This shows that the quality of the
ware available. The time frame The real energy losses due to surge analysis stands or falls with
covered by equations (5.1) is less friction, and the degree of warp­ the accuracy of the input data.
appro­priate for computing reso- ing of pipeline and pipe fix­tures
nant vibrations. These can be
calcu­lated much more precisely
A surge analysis can only be as accurate as the system data
using the impedance method, or,
­entered as inputs. Only if the input is accurate, and the
in ­other words, by looking at the
computation model is a faithful reproduction of the real system
frequency range.
conditions, will the analysis yield a high degree of accuracy.

15
5 Accuracy of Numerical Surge Analysis
Forces Acting on Pipelines as a Result of Water Hammer

In practice, it is often impossible 5.2 Forces acting on pipe-

to obtain exact data. If this is lines as a result of
the case, one has to estimate the water hammer
required inputs. After computing the time-depen-
dent pressure gradients, it takes
An example: a further separate step to calcu-
For a valve manufacturer, a late the forces acting on the el-
small individual loss coefficient bows and connections of unsup-
in the open condition of a valve ported pipes. The interaction
is a powerful sales argument. By between fluid and pipe wall does
contrast, for a surge analysis the not enter into the computation
values obtained immediately (separate calculation). Apart
preceeding total closure of a from the odd exception, which
valve are of the essence, and is of no relevance in the field of
measuring these is a time-con- water supply and waste water
suming and complex affair. As a disposal anyhow, this method
result of this, many individual tends to produce forces which
loss characteristics available for are somewhat higher than what
valves do not extend far enough they are in reality, so that the
into the closing range. For cost conclusions drawn from the cal-
reasons, the individual loss culation results will definitely be
curves provided by most manuf- on the safe side.
acturers are extrapolations,
rather than curves plotted on the
basis of original measurements.
When designing a plant with the
aid of surge analyses, inaccura-
cies of this kind should be ac-
counted for by designing the
surge control equipment sligh
on the conservative side.

16
Computerised Surge Analysis 6

6 Computerised surge ten analyses per year, the cost in- - Piping elevation profile
analysis volved in doing their own will - Lengths
probably not be worthwhile. - Diameters
6.1 Technical procedure
A surge analysis will not provide - Wall thickness
6.2 Interaction between
direct solutions for the required - Materials of construction, lining
ordering party and
parameters, such as, for example, material, pipe connections
surge analyst
the optimum air vessel size, com- - Pressure class, design pressure
First of all, a distinction has to be
pressor settings, valve clos ure made between the quotation head curve
characteristics, flywheel dimensi- phase and the calculation itself. - Permissible internal pipe
ons, etc. Instead, the surge ana- During the quotation phase, the pressures (pmin, pmax)
lyst must specify the type of sur- surge analyst requires the follow - Method used to lay the pipes:
ge control to be employed and ing information from the plant buried or placed on supports
provide estimates of the relevant engineering contractor to compute - Modulus of elasticity of pipe
parameters. After check ing the the cost involved: materials
outcome of the surge analysis, 1. A rough flow diagram of the - Surface roughness coefficient
the original parameters are sui- installation indicating all - Provision of air valves at the
tably adjusted and a complete re- important equipment, such as highest points of the piping
run of the surge analysis is made pumps, valves, additional inlet - Branch connections
for the system. After several runs, and outlet points, as well as any - Zeta or flow factors as well as
the values supplied will come existing safety devices, such as valve closing characteristices
very close to the technical and aerators, air vessels, etc. The - Characteristic curves or
economical optimum. As surge flow diagram can by all means performance charts and
analyses necessarily need to be be in the form of a quick sketch, characteristic data of all
performed by surge specialists, which does not take more than hydraulic equipment
they remain time and labour in- a couple of minutes to draw.
- Mass moments of inertia of all
tensive despite the use of modern 2. A rough list of all main para-
hydroelectric generating sets
computer technology. Conside- meters, i.e. principal pipe lengths,
- Characteristic curves and data
ring that powerful surge analysis diameters and flow rates.
on surge control equipment
software is now commercially 3. A list of all major operation and
already installed in the system
available, users may wonder downtime periods.
whether they cannot do their - Characteristic values of all aer-
4. A list of all known incidents
own analysis just as well. As reli- ation and deaeration equipment
that could have been caused by
able9 surge analysis software is - Settings of control equipment
water hammer.
far from a mass product, the low - Water levels in tanks and
5. Irregularities observed during
sales volume makes it expensive. reservoirs
operation.
Add to this the high cost of trai- If a surge analysis is to be - Rates of flow in the individual
ning and hands-on practice. Also performed, additional data to be piping branches
if the software is not used for specified by the surge analyst will - Degrees of opening of all shutoff
some time, operators usually have to be obtained. Some ex­ and throttling valves
have to brush up their skills. So, amples of additionally required - Operating pressures
if users require fewer than, say, data are:
9
Users are in the uncomfortable position of not being able to verify the workings of surge analysis software. It is, therefore, im-
portant that a reputable manufacturer vouch for the quality of the product. Surge analysis software, as a rule, is developed by spe-
cialist university institutes. There are some examples of programs that were bought by commercial enterprises and provided with
a sophisticated user interface, which makes them easier to handle for the user. 17
7 Rules of Thumb and Manual Calculations

7 Advantages of rules of same pipe lengths, they cannot It takes lots of experience to be
thumb and manual normally be scaled. A simple able to judge whether
calculations example shows why: approximation formulas can be
A rough estimate can be a very The only difference between two used to reliably calculate
useful tool to quickly assess the otherwise completely identical transient flow conditions. For
risk of water hammer. This leads water supply systems are the every day engineering purposes,
us to the validity of rules of elevation profiles of the main approximation formulas should
thumb and to the question pipes; one system has a high be used exclusively to roughly
whether the surge characteristics point, the other does not. The estimate the potential risk in a
of one system can be applied to system without the high point system (examples, see section 4).
another, similar installation can be safely protected by an air Using them as a basis for a
(scalability). To answer that vessel. A vessel of the same size serious surge analysis or, even
question,we should start by will not adequately protect the worse, for designing the surge
pointing outthat there is a great second system, however, because control equipment, would have
variety of water supply and the falling water level in the air to be regarded as highly
waste water disposal plants, and vessel would cause the minimum irresponsible. A brief description
that these are so different from dynamic pressure head to of all known processes of
each other that approximation intersect the pipeline’s high approximation and estimation
formulas cannot be applied. point. formulas is given below:
Even if the characteris tic values The low pressures thus created
of different systems are very would pose a risk of dirty water
similar, i.e. same rates of flow, being drawn into the system.

Fig. 7-1: Graphical method developed by Schnyder-Bergeron

18
Rules of Thumb and Manual Calculations 7

• Before the days of modern These are the only manual

computer software, the calculation methods. This
graphical Schnyder-Bergeron apparent lack is more easily
method was often employed understood if we take another
and produced relatively look at the air vessel, our
reliable surge analysis. For representative example of before.
practical reasons, use of this Reading the total volume of the
method is limited to systems vessel from a design curve is not
comprising a single pipeline. all that is required. The way the
Friction can only be taken into air vessel works depends to a
account by complex large extent on the ratio of water
procedures. Besides, it takes a volume to air volume in the
specialist to apply this method vessel, or, in other words, on the
and obtain the desired results. question whether
Fig. 7.1 is an example of a prepressurisation ofthe vessel is
typical Schnyder-Bergeron “hard” or “soft”. The pre-
diagram, which shows how the pressurisation level has an impact
pressure wave propagation due on the total vessel volume
to the closure of a valve is required. The pipeline profile also
determined by graphical plays a significant part. For
means. example, if it has a high point
• Application of the Joukowsky which should not be intersected
equation for rapid changes in by the minimum dynamic
flow velocity v (examples pressure head curve following
under 4). pump trip (area of low pres sure),
• Graphical method to determine the basic conditions for designing
the required air vessel the vessel will be dif ferent, even
sizes.*) if the plant para meters are
• Graphical method used to otherwise the same. The vessel
estimate the condition of line will have to be con siderably
packing.*) larger. In many cases, the swing
• The largely ideal valve closing check valve and throttle installed
characteristics for the except­- in a bypass will keep the reverse
ional case of a single-conduit pressure wave from causing an
pipeline can be calculated by impermissible rise in pressure
approximation.*) levels in the air vessel. It is
impossible to determine these
crucial variables using rules of
thumb or graphical design
methods.

*) Expertise required.

19
8 Surge Control Systems

8 Main types of surge 8.1 Energy storage 8.1.1 Air vessels

control With air vessels and standpipes, Air vessels come in the form of
The purpose of surge control is energy is stored as pressure en - compressor vessels (Fig. 8.1.1-a),
to stop kinetic energy from being ergy; when a flywheel is instal- [bag-type] accumulators (Fig.
converted into elastic deformati- led, the energy stored takes the 8.1.1-b) and vessels with a vent
on energy. This can be done by form of rotational energy. There pipe. Compressor- and accumu-
the following basic methods: is a sufficient amount of energy latortype air vessels basically
– Energy storage stored to maintain the steadys- work on the same operating
– One-way surge and venting tate flow for a relatively long principle. The reason for choos -
facilities time and to make sure the de - ing one or the other is based on
– Optimisation of valve closing crease in flow velocity due to technical or commercial conside-
characteristics10 dissipation will be slow to take rations. Because of their design,
– Optimisation of the strategy full effect. A rapid pressure drop maccumulators are only suitable
designed to control the piping is thus prevented. If air vessels for small volumes.
system and standpipes are installed As explained earlier, the vessel
upstream of a pump in a long in- volume is not the only important
let pipe, they not only prevent a factor. If the water-to-air volume
pressure transient by means of ratio is carefully chosen, a vessel
energy dissipation, but also the with a substantially lower total
other way around, by absorbing volume may be used.
energy.

D0

Va
Compressor on
100 mm
HWIN
Compressor off

Vw WSH

ZB

Z1
Hgeo

D1 D2

Z2

Fig. 8.1-a: Schematic layout of a compressor-type air vessel. To avoid excessive pressures on return of the vessel water,
the connecting pipe may have to be fitted with a swing check valve with a throttled bypass.

10
The valve closing characteristics describe the closing angle of a valve as a function of time.

20
Surge Control Systems 8

• There is a major risk of

Membrane
Membran
incrustations, deposits and
Gas
blokkages.
Provided they are adequately
monitored, the operating
reliability of air vessels is high.
GridBegrenzungsgitter
to limit the expansion
of the
der membrane
Gasmembran During their operation,
Flüssigkeit
Liquid attention has to be paid to the
Fig. 8.1.1-b: Schematic of an accumulator following:
To make sure compressor vessels the inlet end of the pump provides • Monitoring of the water level
are always filled to the correct effective surge control. If the in the vessel.
levels, they can be equipped with pump fails or trips, an upstream • For reasons of hygiene, the
sensors which will switch the vessel will absorb energy, while a water volume must be
compressor on or off as required. downstream vessel will dissipate continuously or regularly
Bag-type accumulators are typi­ energy. Air vessels or accumulators replaced.
cally adjusted by prepressu­ri­sing are not suitable for waste water • The compressed air must not
the gas inside the bag or mem­ disposal systems , because
11
contain any oil.
brane enclosure to a certain initial • With waste water, it is not • To be able to take the air vessel
pressure prior to installation. Air possible to measure the water out of service for an inspect ion,
vessels are not just installed at the level needed to set the spare vessels should be
pump discharge end to guard compressor. available.
against the consequences of pump • The bag-like enclosure in an • It must be possible to lock the
trips. They can also be installed in accumulator would be shut-off valves in the connecting
other suitable places in a piping punctured by the sharp objects pipeline against unintentional
system. For example in long inlet contained in the waste water, closure; the open position has to
pipes, an additional air vessel at such as razor blades, nails, etc. be monitored.
• Maintenance of the compressor
(compressor vessel).

8.1.2 Standpipes, one-way

surge tanks
Standpipes can only be installed at
points of a piping system
characterised by low-pressure
heads. As a rule, a standpipe
cannot replace a downstream air
vessel. Fitted with a swing check
valve in the direction of the flow
and a filling mechanism (oneway
surge tank), it is used to stop the
Fig. 8.1.1-c: Accumulators pressure falling below atmospheric
11
An exception is a vessel fitted with a vent pipe; this arrangement, comprising an air vessel, a standpipe and a vent valve, is
very rarely used in Germany.

21
8 Surge Control Systems

at the high points of long clean-

water pipelines. Because of the
possibility of mal odorous
fumes, standpipes are rarely
found in waste water installa-
tions. Standpipes and oneway
surge tanks are highly reliable pi-
eces of equipment provided the
following points are observed:
• Continuous or regular changes
of water (problem of hygiene).
• Filtering of air flow.
Fig. 8.1.3-a: The V-belt pulleys in this arrangement are solid discs
• Functional tests of the check
valve on one-way surge tank the running down time of the other pump types, it must be
arrangements. kind which is suitable for a checked in advance that the
• Monitoring of water level or relatively short pipeline, or, put flywheel will not interfere with
differently, with a short the starting procedure of the
filling device on one-way surge
reflection time Tr. The limits for pump driver. Flywheels are
tank arrangement.
employing a flywheel are in the probably the safest and most
region of 1 to 2 km pipeline elegant types of surge control.
8.1.3 Flywheels
length. Example 3 in section 4 Their reliability beats that of all
Mounted on the driver, a fly -
includes a rough estimate other surge control methods.
wheel prolongs the rundown
performed to check whether a With the exception of the
time of a pump to standstill by
flywheel can be used. For bearings of larger-scale systems,
means of the stored rotational
reasons of design, the flywheel they do not require any in-
energy:
solution is not suitable for operation monitoring.
submersible motor pumps. On
Ekin = 12– · J · v2 (8.1)

J - Mass moment of inertia of

flywheel in kgm2
v - Angular velocity s-1

For a homogeneous solid disc

with a radius r and a mass m,
for example, the mass moment
of inertia is
m · r2
J=
2
Figs. 8.1.3-a and 8.1.3-b show
several practical applications.
However, with a type of
flywheel that is economically
and technically feasible, one can Fig. 8.1.3-b: Vertically mounted flywheel (driven by means of cardan
only achieve a prolongation of shaft, D = 790 mm)

22
Surge Control Systems 8

8.2 Air valves tors and deaerators have different te safety elements, such as orifice
Air valves should not be used nominal diameters depending on plates or flow control valves, are
until every other solution has which way the air flows. Air nor- used. Proper valve functioning
been ruled out. Their drawbacks mally flows in through a large has to be checked at regular inter-
are: cross-section and out through a vals with regard to the actuating
• They require regular small crosssection. The reliability times and closing characteristics.
maintenance. of aerators /deaerators depends
• If arranged in the wrong place on their design and is the lowest
or mounted incorrectly, they of all surge control equipment.
can aggravate pressure varia- They have to be tested for proper
tions instead of alleviating functioning in regular intervals
them. and it may be necessary to filter
• Under certain circumstances, the incoming air.
operation of the plant may be
limited, because the air drawn 8.3 Actuated valves
into the system has to be Suitable actuation schedules for
removed again. the opening and closing of valves
• The handling of waste water are calculated and verified by me-
calls for special designs. ans of a surge analysis on the ba-
sis of the valve characte ristic. Fig. 8.2-a: Duojet*) two-way air
Air valves (Fig. 8.2-a) have to be The valves will give very reliable valve with a medium-operated
single-compartment valve. Large
carefully designed. On large dia- service if, on valves with electric
vent cross-section for drawing in
meter pipelines, one has to arran- actuator, adequate protection is and venting large amounts of air
ge air outlet valves on top of provided for the actuating times during start-up and shutdown of
domes, to make sure that the air and the break points of the actua- pumping systems. Small cross-
drawn into the system will collect tion schedules or if, on valves section for removing small amounts
of air during operation against full
there. As long as the fluid flow with hydraulic actuators, adequa-
internal pressure
has not reached the steady state,
air drawn into pipes can, under
unfavourable conditions, have a
very negative effect. Air cushions
normally have a dampening ef-
fect. However, the air drawn into
the pipeline can also give rise to
dangerous dynamic pressure in-
creases. It has to be pressed out of
the piping slowly; a large air out-
let cross-section would lead to
sudden pressure variations to-
wards the end of the air outlet
operation. For this reason, aera-
Fig. 8.3-a: Motorised shut-off butterfly valve
*) With the friendly permission of VAG-Armaturen GmbH.

23
8 Surge Control Systems

8.4 Swing check valves ing valve discs can have a very tion are designed to throttle the
The dynamics of swing check unfavourable effect, because they reverse flow in a controlled man-
valves often have a major influ- take a long time to close, which ner after the pump trips. This
ence on the development of sur- means reverse flow sets in while feature is important on pumps
ge, because the valve’s closure, they are still partly open, and the operated in parallel, when one
after reversal of flow, generates valve disc re-seats with consi- pump fails whilst the remaining
velocity changes which, accor- derable impact. The phenomenon pumps continue to run and deli-
ding to Joukowsky’s equation is known by the term “check val- ver flow against the tripped
(4.1), produce pressure variations. ve slam” and is much dreaded. pump. In a case like this, control-
Since the closing time is the main led closing is achieved by adjusta-
Check valves generally have to criterion for check valve slam, li- ble hydraulic actuators without
meet the following two contra- mit position dampers will impro- external supply but with a lever
dictory requirements: ve the situation, but not eliminate and counterweight, with the free-
the risk altogether. In waste wa- swinging valve disc opening in
• bring the reverse flow to a ter systems, nozzle check valves the direction of the flow and,
standstill as quickly as possible, cannot be used because they tend upon actuation, closing in one or
• keep the pressure surge gene- to clog up. This means that val- two stages according to a set clo-
rated during the process as ves with free-swinging discs and sing characteristic.
small as possible. limit position dampers are the
only remaining option, despite The operating reliability of check
Drinking water pumping installa- their drawbacks. valves is relatively high. In opera-
tions protected by air vessels tion, they have to be chekked for
should ideally be equipped with Pump check valves installed in proper functioning at regular in-
nozzle check valves. Free-swing - the cooling pipes of a power sta- tervals.

Fig. 8.4-a: Swing check valve equipped with a hydraulic actuator and counterweight

24
Case Studies 9

9 Case studies the development of areas of low vessel. The maximum head
The case studies below were pressure, the water column in curve obtained with an air vessel
taken from surge analyses the pipeline swinging back will hmaxWK is now only slightly above
performed by KSB. Although we still produce dynamic pressure the steady-state head curve
have altered the system para- peaks in excess of 16 bar. hsteady and the associated
meters, so that the installations Therefore, the reverse flow into minimum head curve hminWK
concerned remain anonymous, the air vessel has to be additio- runs at a wide safety margin
the problems involved and the nally throttled; a schematic above the peak point of the pipe.
way these were resolved have diagram of the operating Fig. 9.1 shows the head and flow
not been altered. principle is shown in Fig. 8.1.1-a. curves of the system protectedby
In the present case, the an air vessel arrangement
9.1 Case study: long-distance throttling action is achieved plotted against time (heads
water supply system with the aid of a short length of expressed in m above mean sea
The system parameters are DN 200 pipe fitted with a stan- level).
indicated in Fig. 2.1-b. A dard DN 80 orifice. Fig. 2.1-b
steadystate flow Qsteady = 500 shows the calculated pressure
l/s is pumped through a DN 600 envelope with and without air
pipeline of ductile cast material
Hinlet [m above MSL]:KN=1/Pipe No. System with air vessel
with a total length of L = 2624
by three centrifugal pumps
operating in parallel at a total
head of the pumps hsteady =
122.5 m into an overhead tank.
The disturbance under
investigation, which leads to Qinlet [l/s]:KN=1/Pipe No. 1 System with air vessel
excessive dynamic pressures, is
the simultaneous failure of all
three pumps. The dynamic
pressure peaks produced by far
exceed the permissible nominal
pressure of PN 16 (see hmax
Water vol. [m3]:KN=1/Air vessel No. System with air vessel
curve) in Fig. 2.1-b; the
minimum pressures drop to
vapour pressure in wide areas of
the system (see hmin curve) in
Fig. 2.1-b. The system can be
protected by installing an air
vessel at the inlet of the long-
distance pipeline. Although the Fig. 9.1: Time plots for the long-distance water supply pipeline (Fig. 2.1-b); the
vessel dimensioned as shown in example shows the head and flow curves of an air vesselprotected system as
Fig. 2.1-b will initially prevent functions of time (heads expressed in m above mean sea level)

25
9 Case Studies

9.2 Case study : stormwater

conveyance pipeline
Starting from a waste water
pumping installation, a new DN
350 stormwater pipeline with a
ae
total length of L = 590 m was ra o
r

laid to an aeration structure. Im

p ro
ve d
Pumping operation was by me- sys
te m
wi
th
ae
ans of three identical pumps ra o
ra
nd
by p
ass
running in parallel, each equip-
ped with a non-return valve and Fig. 9.2-a: Schematic diagram of the stormwater conveyance pipeline
a motorised gate valve to control • to determine what caused the Pump characteristic shown in
pump start-up and run-down. surge pressures and forces that Fig. 9.2-c
The first 100 m of pipe made of had been observed,
high-density polyethy lene were Model pipeline L1:
• to devise some protective
laid under ground, the remain - Material: high-density
measures or surge control equip-
ing 490 m were of steel and laid polyethylene (HDPE)
ment that would prevent the
above ground sup ported on Dinside: 354.6 mm
excessive dynamic pressures
pipe bridges. Fig. 9.2-a shows a k: 0.1 mm
produced by a pump failure
schematic of the model installa- a: 600 m/s
from occurring, and to prove
tion. The nodes connecting the (estimated value)
their effectiveness mathematically.
aboveground single pipes of the Min. permissible pressure:
model are 90° elbows. The engi- vacuum
Model parameters
neering firm in charge of plan- Pressure class: PN 6
Besides the parameters indicated
ning the plant neither performed in Fig. 9.2-a, the following sys -
nor ordered a surge analysis to tem data were entered into the
accompany the project planning calculation:
phase.
During the first operating tests
following the plant’s completion,
Stormwater pump 1470 rpm
several incidents, among them a
power failure which caused all
three pumps to fail at the same
time, caused the part of the pi-
ping laid above ground to shake
considerably, damaging pipe fix-
tures and tearing off some pipes
altogether. When a surge analy-
sis was finally ordered, its objec-
tive was:

Fig. 9.2-c: Characteristic curve of the pump used in the stormwater

conveyance system

26
Case Studies 9

Model pipeline L2 to L10: n [1/s]: KN=1/Pump-No. 1 Pump failure without surge control
Material: steel
Dinside: 349.2 mm
k: 0.1 mm
a: 1012 m/s
(from equation 4.1)
Time (s)
Min. permissible pressure: vacuum
Hinlet [m]:KN=1/Pipe No. 1 Pump failure without surge control
Pressure class: PN 10

Nothing was known about the

pump check valves. For the pur-
pose of the model, it was there-
fore assumed – correctly so, as it Time (s)

turned out – that the valves Qinlet [l/s]:KN=1/Pipe No. 1 Pump failure without surge control

would suddenly close upon rev

erse of the flow direction.

Calculation of actual duty

data, first results
Time (s)
The steady-state flow calculated
Fig. 9.2-d: Operating characteristics of the stormwater line without
by the surge software for the surge control plotted over time
parallel operation of three
pumps amounted to Qsteady = 187 Longitudinal force acting on L8 without surge control
Längskraft auf L8 ohne Druckstoß -Sicherungen

l/s. The first surge calculation of 40

the simultaneous failure of all 20

three pumps showed that macro- 0

0 5 10 15 20 25 30 35 40 45 50

cavitation and, as a result of it, -20

Kraft(kN)
kN

dynamic pressure peaks as high -40

Force

as 15 bar would occur inside the -60

HDPE pipeline, i.e. considerably -80

in excess of the given nominal -100

-120
pressure of the pipe of PN 6. Time
Zeit s(s)

The calculation showed that the Fig. 9.2-e: Longitudinal force acting on L8 if the stormwater line is
pipe bridges between each pair without surge control
of 90° elbows had to temporarily
withstand longitudinal forces of tem behaviour without surge curve in Fig. 9.2-e shows the
just under 100 kN, or in terms control plotted over time. axial forces acting on L8. This
of weight, the equivalent of a Fig. 9.2-d shows the pump explained the violent shaking
thrust somewhere in the region speed, head and flow at the ent- and resulting damage observed.
of 10 t. Figs. 9.2-d and 9.2-e rance of model pipe L1 (head in
show some examples of the sys- m above pipe centreline); the

27
9 Case Studies

Pump failure in a system equipped with an aerator Surge control measures

n [1/s]:KN=2/Pump No. 1 and a bypass as surge control devices

To eliminate the macro-cavitati-

on developing after pump failure,
a second simulation calculation
was run with a DN 150 aerator
at the outlet of L2, the highest
Time (s)
point of the piping. Despite the
Pump failure in a system equipped with an aerator addition of a surge control de-
Hinlet [m]:KN=2/Pipe No. 1 and a bypass as surge control devices
vice, the HD-PE pipe was still
found mathematically to contain
unacceptably high pressure incre-
ases a few seconds after pump
failure. In order to eliminate the-
se highly undesirable pressure
Time (s) peaks, it was eventually decided
Pump failure in a system equipped with an aerator to add a shut-off valve with a by-
Qinlet [l/s]:KN=2/Pipe No. 1 and a bypass as surge control devices
pass between the inlet of L1 and
the pump suction tank which
would be automatically opened
by a maintenancefree electro-hy-
draulic lever and weight type ac-
tuator if all three pumps were to
Time (s) fail at once. To valve manufactu-
rers today, systems like this are
Fig. 9.2-f: Operating characteristics of the stormwater line with more or less part of their stan-
surge control plotted over time dard product range. After adding
surge control devices, i.e. an aera-
tor and a bypass fitted with an
Längskraft
Longitudinal auf L8 acting
forces mit Belüfter
on L8undifBypass
the system is
automatically opening shut-off
protected by an aerator/bypass combination valve, the simulation finally sho-
40
wed that the dynamic pressure
20 peaks remained below the stea-
0
dy-state initial pressure, and that
0 5 10 15 20 25 30 35 40 45 50 the longitudinal forces acting on
-20
the pipe bridge sections laid abo-
kN
Karft kN
Force

-40 ve ground had diminished to no

more than 5% of the initial va-
-60
lue. The calculation further
-80 revealed that the existing check
valves could be dispensed with.
-100
Time (s)s
Zeit
Fig. 9.2-f shows – on the same
Fig. 9.2-g: Longitudinal force acting on L8 if the stormwater line is scale as in Figs. 9.2-d and 9.2-e to
suitably protected facilitate comparison – the n, H
and Q curves of the surgepro-
tected system plotted over time;
Fig. 9.2-g shows the forces of the

28
Case Studies 9

surge-protected system plotted

over time. The global pressure
envelope of the rehabilitated in-
stallation, as well as the curves of
the system without surge control,
are shown in Fig. 9.2-h.

Druckeinhüllenden
Pressure mit and
envelope with und without
ohne Druckstoß-Sicherungen (DS) (SC)
surge control equipment

220

200
Elevation in m above mean sea level

180
hmax ohne
h DS SC
without
max
160
Kote müNN

140

120

100
hhmax with
mit DSSC
max
80

60
hmin ohne
h DS SC
without
max
h with SC Elevation of
Rohrkote
hmin
maxmit DS
pipeline
40
0 100 200 300 400 500 600
Pipeline section in m covered
abgewickelte by the
Rohrlänge m analysis

Fig. 9.2-h: Pressure envelope of the stormwater conveyance pipeline with and without surge control

29
10 Additional Literature
Authors

Additional literature turen und Rohrleitungen (In- the engineering division of KSB
teraction between pumps, AG, in charge of surge analyses
  1. D
 ynamische Druckänder­
valves and pipelines), KSB and complex flow modelling for
ungen in Wasserversorgungs-
1983 waste water systems. Since 2002,
anlagen (Dynamic pressure
10. R
 aabe, J.: Hydraulische Manager Sales Support of the
changes in water supply sy-
­Maschinen und Anlagen ­Waste Water Competence Center
stems), Techn. M
­ itteilung,
(Hydraulic machines and at Halle.
Merkblatt W303, DVGW,
Sept. 1994 ­systems), VDI Verlag, 1989

  2. H
 orlacher, H.B., Lüdecke,
H.J.: Strömungsberechnung Authors
für Rohrsysteme (Flow mod­
elling for piping systems), ex- Prof. Dr. Horst-Joachim Lüdecke,

pert Verlag, 1992 born in 1943, Diplom-Physiker,

developed process engineering
  3. Z
 ielke, W.: Elektronische
and fluid dynamics software
­Berechnung von Rohr- und
whilst employed with BASF AG,
Gerinneströmungen (Compu-
Ludwigshafen; professor at
ter analysis of flows in pipes
Hochschule für Technik und
and channels), Erich Schmidt
Wirtschaft (HTW) des Saarlandes
Verlag, 1974
(University for Technology and
  4. W
 ylie, E.B., Streeter, V.L.: Economics of Saarland) since
Fluid Transients, FEB Press, 1976; numerous publications on
Ann Arbor, MI, 1983 the subject of fluid flows in pipe-
  5. C
 haudry, H.M.: Applied Hy- lines; co-author of the book
draulic Transients, Van No- “Strömungsberechnung für Rohr-
strand Reinhold Com­pany, systeme” (Flow modelling for pi-
New York, 1987 ping systems) (expert Verlag); as
  6. Sharp, B.B.: Water Hammer, a member of the Water Hammer
Edward Arnold, 1981 Committee of DVGW (German
  7. Parmarkian, J.: Water­ Association of the Gas and Water
hammer Analysis, Dover Sector), involved in the revision
­Publications, 1963 of Surge Guideline W 303; cur-
rently supports and ­advises KSB
  8. Publication of all papers pre-
in the field of surge analysis.
sented at the International
Conference on “Pressure Sur- Dipl.-Ing. Bernd Kothe, born in
ges” held by bhra fluid engi- 1955; graduate from “Otto von
neering, Great Britain, in the Guericke” Technical University at
Edited by:
years 1976, 1980, 1986, Magdeburg; joined Pumpenwerke
1992, 1996, 2000 Halle as a development engineer KSB Aktiengesellschaft,
for power station pumps. From ­Communications
  9. Engelhard, G.: Zusammen-
wirken von Pumpen, Arma- 1993 to 1998, whilst employed in Dipl.-Ing. (FH) Christoph P. Pauly

30
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