8 Transient Analysis: 8.1. SYNOPSIS

AWWA MANUAL M32
Chapter 8
Transient Analysis
8.1. SYNOPSIS _____________________________________________

Transients can introduce large pressure forces and rapid fluid accelerations into a
piping system. These disturbances may result in pump and device failures, system
fatigue or pipe ruptures, and backflow/intrusion of untreated and possibly hazardous
water. Many transient events can lead to water-column separation, which can result
in catastrophic pipeline failures. Thus, transient events can cause health risks and
can lead to increased leakage, interrupted service, decreased reliability, and breaches
in the piping system integrity. Transient flow simulation has become an essential
requirement for assuring safety and the safe operation of drinking water supply and
distribution systems.
This chapter introduces the concept and fundamentals of hydraulic transients,
including the causes of transients, general rules to help determine whether or not the
system may be exposed to unacceptable conditions under a transient event, governing
transient equations, numerical solution methods, guidelines for control and suppres-
sion of transients, transient modeling considerations, and transient data requirements.
Illustrative examples are also discussed and conclusions are stated.
The chapter is therefore geared toward engineers involved in the planning, design,
and operation of water supply and distribution systems, and engineers who need an
insight into the most common causes of hydraulic transients and suitable methods that
can be applied to alleviate their consequences. Such capabilities will greatly enhance
the ability of water utilities to evaluate cost-effective and reliable water supply protec-
tion and management strategies for preserving system hydraulic and water quality
integrity, preventing potential problems, and safeguarding public health.
8.2. INTRODUCTION _______________________________________

Most people have been in an older house with pipes that rattle when someone turns off
a faucet. When the faucet handle turns, closing the valve almost instantaneously, the
pipes rattle against the walls. This is called water hammer, which is also referred to as
a surge or as a hydraulic transient. Water hammer refers to rapid and often large pres-
sure and flow fluctuations resulting from transient flow conditions in pipes transporting
173
Copyright (C) 2012 American Water Works Association All Rights Reserved
174 COMPUTER MODELING OF WATER DISTRIBUTION SYSTEMS
fluids. Transient flow analysis of the piping system is often more important than the
analysis of the steady-state operating conditions that engineers normally use as the
basis for system design. Transient pressures are most significant when the rate of flow
is changed rapidly, such as rapid valve closures or pump stoppages. Such flow distur-
bances, whether caused by design or accident, may create traveling pressure waves of
excessive magnitude. These transient pressures are superimposed on the steady-state
conditions present in the line at the time the transient occurs. The total force acting
within a pipe is obtained by summing the steady-state and transient pressures in the
line. The severity of transient pressures must thus be accurately determined so that
the pipes can be properly designed to withstand these additional shock loads. In fact,
pipes are often characterized by pressure ratings (or pressure classes) that define their
mechanical strength and have a significant influence on their cost.
Transient events may be associated with equipment failure, pipe rupture, sepa-
ration at bends, and the introduction of contaminated water into the distribution sys-
tem via unprotected cross-connections or intrusion. High-flow velocities can remove
protective scale and tubercles and increase the contact of the pipe with oxygen, all of
which will increase the rate of corrosion. Uncontrolled pump shutdown can lead to the
undesirable occurrence of cavitation and water-column separation, which can result in
catastrophic pipeline failures due to severe pressure rises following the collapse of the
vapor cavities. Vacuum conditions can create high stresses and strains that are much
greater than those occurring during normal operating regimes. They can cause the col-
lapse of thin-walled pipes or reinforced concrete sections, particularly if these sections
were not designed to withstand such strains (e.g., pipes with a low pressure rating).
Cavitation occurs when the local pressure is lowered to the value of vapor pres-
sure at the ambient temperature. At this pressure, gas within the liquid is released
and the liquid starts to vaporize. When the pressure recovers, liquid enters the cavity
caused by the gases and collides with whatever confines the cavity (i.e., another mass
of liquid or a fixed boundary) resulting in a pressure surge. In this case, both vacuum
and strong pressure surges are present, a combination that may result in substantial
damage. The main difficulty here is that accurate estimates are difficult to achieve,
particularly because the parameters describing the process are not yet determined
during design. Moreover, the vapor cavity collapse cannot be effectively controlled.
In less drastic cases, strong pressure surges may cause cracks in internal lining or
damage connections between pipe sections and, in more serious cases, can destroy
or cause deformation to equipment such as pipeline valves, air valves, or other surge
protection devices. Sometimes the damage is not realized at the time but results in
intensified corrosion that, combined with repeated transients, may cause the pipeline
to collapse in the future. Transient events in pipelines also damage seals that often
lead to increase leakage and significant water loss.
Transient events can have significant water quality and health implications.
These events can generate high intensities of fluid shear and may cause resuspension
of settled particles as well as biofilm detachment. Moreover, low pressure caused by
transients may promote the collapse of water mains; leakage into the pipes at loose
joints, cracks, and seals under subatmospheric conditions; backsiphonage at cross-
connections; and potential intrusion of untreated, possibly contaminated groundwater
in the distribution system. Pathogens or chemicals in close proximity to the pipe can
become potential contamination sources, where continuing consumption or leakage
can pull contaminated water into the depressurized main.
Recent studies have confirmed that soil and water samples collected immediately
adjacent to water mains can contain various levels of microorganisms, an indicator
of fecal pollution (fecal coliforms, E. coli, Clostridium perfringens, coliphages) and in
some cases enteric viruses (Besner et al. 2008; Karim et al. 2003; Kirmeyer et al.
TRANSIENT ANALYSIS 175
2001). This is especially significant in systems with leaking pipes below the water
table. Problems with low or negative pressure transients have been reported in the
literature (Walski and Lutes 1994; LeChevallier et al. 2003). Gullick et al. (2004)
studied transient pressure occurrences in actual distribution systems and observed 15
surge events that resulted in a negative pressure. Hooper et al. (2006) and Besner et
al. (2007) also reported such events in full-scale systems.
The most often identified cause for the events reported in the literature was the
sudden shutdown of pumps, either unintentional (power failure) or intentional (pump
tests). Using a pilot-scale test rig, Friedman et al. (2004) confirmed that negative
pressure transients can occur in the distribution system and that the intruded water
can travel downstream from the site of entry. Locations with the highest potential for
intrusion were identified as sites experiencing leaks and breaks, areas of high water
table, and flooded air-vacuum valve vaults. Preliminary results by Besner et al. (2007)
showed that significant concentrations of indicator microorganisms could be detected
in the water found in flooded air-vacuum valve vaults. In the event of a large intrusion
of pathogens, the chlorine residual normally sustained in drinking water distribution
systems may be insufficient to disinfect contaminated water, which could lead to dam-
aging health effects. A recent case study in Kenya (Ndambuki 2006) showed that in
the event of a 0.1 percent raw sewage contamination, the available residual chlorine
within the distribution network would not render the water safe.
Transient events that can allow intrusion to occur are caused by sudden changes
in the water velocity due to loss of power, sudden valve or hydrant closure or opening,
a main break, fire flow, or an uncontrolled change in on/off pump status (Boyd et al.
2004). Transient-induced intrusions can be minimized by knowing the causes of pres-
sure surges, defining the system’s response to surges, and estimating the system’s
susceptibility to contamination when surges occur (Friedman et al. 2004). Therefore,
water utilities should never overlook the effect of pressure surges in their distribution
systems. Even some common transient protection strategies, such as relief valves or
air chambers, if not properly designed and maintained, may permit pathogens or other
contaminants to find a “backdoor” route into the potable water distribution system.
Any optimized design that fails to properly account for pressure surge effects is likely
to be, at best, suboptimal, and at worst completely inadequate.
Pressure transients in water distribution systems are inevitable and will nor-
mally be most severe at pump stations and control valves, in high-elevation areas, in
locations with low static pressures, and in remote locations that are distanced from
overhead storage (Fleming et al. 2006; Friedman et al. 2004). All systems will, at some
time, start up, switch off, undergo unexpected flow changes, and will likely experience
the effects of human errors, equipment breakdowns, earthquakes, or other risky dis-
turbances. Although transient conditions can result in many abnormal situations and
breaches in system integrity, the engineer is most concerned with those that might
endanger the safety of a plant and its personnel, that have the potential to cause
equipment or device damage, or that result in operational difficulties or pose a risk to
the public health.
Transient pressures are difficult to predict and are system dependent, including
specific system layout, configuration, design, and operation. Engineers must carefully
consider all potential dangers for their pipe designs and estimate and eliminate the
weak spots. They should then perform a detailed transient analysis to make informed
decisions on how best to strengthen their systems and ensure safe, reliable operations
(McInnis and Karney 1995; Karney and McInnis 1990).
Figure 8-1 Example steady-state transition after a period of rapid transients
8.3. CAUSES OF TRANSIENTS ________________________________

Transient events are disturbances in the water flow caused during a change in opera-
tion, typically from one steady-state or equilibrium condition to another (Figure 8-1).
The principal components of the disturbances are pressure and flow changes at a
point that cause propagation of pressure waves throughout the distribution system.
The pressure waves travel with the velocity of sound (acoustic or sonic speed), which
depends on the elasticity of the water and that of the pipe walls. As these waves propa-
gate, they create transient pressure and flow conditions. Over time, damping actions
and friction reduce the waves until the system stabilizes at a new steady state. Nor-
mally, only extremely slow flow regulation can result in smooth transitions from one
steady state to another without large fluctuations in pressure or flow.
8.3.1. Basics—Rapid Changes in Velocity

In general, any disturbance of the flow of water generated during a change in mean
flow conditions will initiate a sequence of transient pressures (waves) in the pipe sys-
tem. Disturbances will normally originate from changes or actions that affect fluid
devices or boundary conditions. Typical events that require transient considerations
include:
s Pump shutdown or pump trip (loss of power)
s Pump startup
s Valve opening or closing (variation in cross-sectional flow area)
s Changes in boundary pressures (e.g., losing overhead storage tank, adjust-
ments in the water level at reservoirs, pressure changes in tanks, etc.)
s Rapid changes in demand conditions (e.g., hydrant flushing)
s Changes in transmission conditions (e.g., main break)
s Pipe filling or draining—air release from pipes
s Check valve or regulator valve action
In municipal water systems, most surge problems occur as a result of closing (or
opening) valves too rapidly or when pumps trip due to an unplanned power failure.
Both high and low surge pressures may cause problems. If special precautions are not
taken, the magnitude of the resulting transient pressures can be sufficient to cause
severe damage. Figures 8-2 to 8-5 describe four typical hydraulic transient problems.
The problem of shutting down a pump is illustrated in Figure 8-2. When the pump is
suddenly shut down, the pressure at the discharge side of the pump rapidly decreases
and a negative pressure wave (which reduces pressure) begins to propagate down the
pipeline toward the downstream reservoir causing low pressures at the pump and else-
where in the system. When the negative pressure wave reaches the high point (which
already has a relatively low pressure due to the higher elevation) in the pipe, the pres-
sure can drop below atmospheric to reach vapor pressure. At this pressure, gas within
the water is gradually released and the water starts to vaporize (water-column separa-
tion). On subsequent cycles of the transient when the pressure recovers, the cavity can
collapse generating a large pressure surge spike. On the suction side of the pump, the
solid sloping line represents the initial hydraulic grade and the dashed straight line
depicts the final hydraulic grade, while startup transients are not shown.
It should be noted that when the pipeline velocity reverses and the water column
returns toward the pump, it is suddenly stopped by the check valve on the discharge
side of the pump causing very high pressures. If no check valve exists, the pump can
spin backward, perhaps reaching speeds that can be damaging to the equipment. Dur-
ing normal pump operation, transients can typically be controlled by using slow clos-
ing and slow opening pump control valves, or with variable frequency drives (VFDs)
and soft start/stop controllers on the pump motors.
The problem of pump startup transient is illustrated in Figure 8-3. When a pump
is started, the pressure at the discharge side of the pump rises, sending a positive
pressure wave (which increases pressure) down the pipeline toward the downstream
reservoir. The resulting peak pressure can cause the pipe to collapse if the pressure
rating of the pipe is less than the maximum surge pressure. When the initial positive
pressure wave reaches the downstream reservoir, it is converted into a negative pres-
sure wave that propagates back to the pump and may induce cavitation. On the suction
side of the pump, the solid straight line represents the initial hydraulic grade and the
dashed sloping line depicts the final hydraulic grade, while shutdown transients are
not shown.
Figure 8-2 Transient caused by pump shutdown
Figure 8-3 Transient caused by pump startup
Pipe filling is especially vulnerable to pressure transients when the pipeline

is empty and large amounts of air are expelled during startup. Pump startup tran-
sients in pressurized pipelines are not commonly a problem, because the pumps can be
started against a closed pump control valve, and then the valve can be slowly opened,
or variable frequency drives can be used on the pump motors.
Opening a valve and closing a valve too fast can also result in severe hydraulic
transients and are illustrated in Figures 8-4 and 8-5, respectively. When the valve in
Figure 8-4 is rapidly opened, a negative pressure wave is initiated at the valve and
propagates upstream toward the reservoir decreasing the pressure in the pipe. Simi-
lar to the pump shutdown scenario, the initial negative surge can drop to vapor pres-
sure causing cavitation in the pipe. In the second example (Figure 8-5), rapidly closing
the downstream valve generates a positive pressure wave at the valve that propagates
toward the upstream reservoir increasing the pressure in the pipe.
In municipal systems, opening and closing of hydrants too quickly will sometimes
cause unacceptable transients. In Puerto Rico, the testing of a 60-in. (152 cm) but-
terfly valve caused the 72-in. (183 cm) pipeline to rupture due to a rapid valve closure
(Figure 8-6a). Walski (2009) showed that increasing hydrant-closing time can make a
dramatic difference in pressure surges in the distribution system, greatly decreasing
the impacts of hydrant closure.
Sudden and complete failure of a single pipe may also cause other unacceptable
pressures elsewhere in the water system. A pipeline rupture sends low pressure waves
propagating in both directions from the break. This can produce negative pressures
and cavitation at higher elevations. Sometimes a pipe rupture on thin-walled pipeline
will cause a pipe collapse elsewhere in the pipeline. The low pressure waves will get
reflected from nearby tanks and reservoirs as positive pressure waves that in turn can
also damage pipes in other locations. Other real life examples of catastrophic failures
due to surge pressures are shown in Figures 8-6b and 8-6c.
Pipe systems must be designed to handle both normal and abnormal operating
conditions. If an analysis indicates that severe transients may exist, the main solu-
tion techniques generally used to mitigate transient conditions are (Boulos et al. 2006;
Wood et al. 2005a; Walski et al. 2003) as follows:
s Installation of stronger (higher pressure class) pipes
s Rerouting of pipes
s Improvement in valve and pump control/operation procedures
Figure 8-4 Transient caused by rapid valve opening
Figure 8-5 Transient caused by rapid valve closure
Figure 8-6a Rupture caused by valve closure (Superaqueduct of Puerto Rico)
Figure 8-6b Damaged pump bowl
Figure 8-6c Broken air admission valve
s Limiting the pipeline velocity

s Reducing the wave speed (e.g., different pipe material)
s Increasing pump inertia (e.g., fitting a flywheel between the pump and motor)
s Design and installation of surge protection devices
8.3.2. Contributing Factors

The severity of and potential for surge problems depend on contributing factors such as
the length of pipeline, the shape of the pipeline profile, the location of pipeline “knees,”
the static head, and the initial or steady-state velocities. Figure 8-7 compares varying
pipeline profiles, showing the best profile with the least potential for surge problems
compared to pipeline profile shapes that have increasingly higher potential for surge
problems.
(A) Best pipeline profile (surge pressures will be lower for this type of pipeline profile)
(B) Fair pipeline profile (some potential for surge problems due to varying terrain)
(C) Worst pipeline profile (knees and high points cause more severe surge problems)
Figure 8-7 Varying pipeline profiles
8.3.3. Rules of Thumb for Identifying Vulnerable Systems

The following rules of thumb are intended as an aid in identifying one or more possible
conditions that tend to cause surge problems in a water distribution system:
s Pipelines without demands or water takeoffs with lengths greater than 1,000
ft (305 m)
s Static head greater than 40 ft (12 m)
s Steady-state velocities greater than 2 ft/sec (0.6 m/sec)
s Pipeline profiles with “knees” and high points
s In-line booster pump stations with long suction lines
s Some air valves, float operated, allowing rapid discharge of air during power
failure
Systems with high velocities (> 5 ft/sec or 1.5 m/sec) can also be vulnerable even
with much shorter pipelines. It should be noted that exceeding any one of the gen-
eral rules of thumb indicates a potential for surge problems, and that prudent design
should include a detailed surge analysis. Jung et al. (2007a) studied the need for com-
prehensive transient analysis of water distribution systems and concluded that only
systematic and informed surge analysis can be expected to resolve the complex tran-
sient characterizations and adequately protect water distribution systems from the
vagaries and challenges of rapid transient events.
8.3.4. Dead-End Pipelines

Dead-end pipelines are generally needed to feed into new developments. Although ini-
tial velocities are relatively low, these dead ends can sometimes be a source of severe
transients as hydrants are opened and closed for flushing. Dead ends, which may also
be caused by closure of check valves, lock pressure waves into the system in a cumula-
tive fashion, and wave reflections will double both positive and negative pressures. For
example, when a surge wave of approximately 300 ft (91 m) reaches a dead end, that
dead end will cause a positive pressure wave reflection of 300 ft (91 m). Because the
incoming and outgoing waves are additive, the dead end experiences the doubling of
the surge pressure or 600 ft (183 m). Therefore, dead ends constitute some of the most
vulnerable locations for objectionable pressures and should be carefully considered in
a surge analysis. Additionally, if the ground elevation of the dead end is sufficiently
high, cavitation can occur under a transient event. Figures 8-8 and 8-9 illustrate this
situation. The system shown in Figure 8-8 has a varying terrain with very low flow
rates and long lengths of dead-end pipes. There are approximately 15,000 ft (4,572 m)
between the pumping station and the hydrant, with 364 ft (111 m) of static head. All
pumps in the pump station have quick-closing check valves on their discharge sides.
Without any surge control, a normal pump shutdown can cause column separation,
vapor pressures, and unacceptable pressure fluctuations as shown in Figure 8-9. The
effects of dead ends on surge analysis were studied in detail by Jung et al. (2007b).
Figure 8-8 Network schematic
8.4. BASIC PRESSURE WAVE RELATIONS ______________________

8.4.1. Wave Action in Pipes
The relationship between pressure change (∆P) and flow change (∆Q), which is associ-
ated with the passage of a pressure wave, defines the transient response of the pipe
system and forms the basis for the development of the required mathematical expres-
sions (Boulos et al. 2006; Wood et al. 2005a; Walski et al. 2003; Wylie and Streeter
1993; Chaudhry 1979). Figure 8-10 shows flow and pressure conditions, which exist a
short time ∆t apart, as a pressure wave of magnitude ∆P propagates a distance ∆x in
a liquid filled line.
Figure 8-9 Pressure surge fluctuations (field measurements) following routine pump shutdown
Figure 8-10 Pressure wave propagation in a pipe
During the short time ∆t, the pressure on the left side of the wave front is P + ∆P
while the right side of the wave front is P. This unbalanced pressure causes the fluid
to accelerate. The momentum principle is:
ǻQ (8-1)
( P+ǻ P−P) A = ȡǻ x
ǻt
where A is the pipe cross-sectional area; and R is the liquid density. Canceling and
rearranging give:
P = Q xA t (8-2)
The term ∆x ⁄∆t is the propagation speed of the pressure wave. The wave speed
is equal to the sonic velocity (c) in the system if the mean velocity of the liquid in the
line is neglected. Because the mean velocity of the liquid is usually several orders of
magnitude smaller than the sonic velocity, this is acceptable. Thus:
ȡ cǻ Q
ǻP= (8-3)
A
or in terms of pressure head:
H = cQgA (8-4)
or in a more general form
c V
H= ± g (8-5)
where g is the acceleration of gravity. The resulting head rise equation is called the
Joukowsky relation, sometimes called the fundamental equation of water hammer. The
equation is derived with the assumption that head losses due to friction are negligible
and no interaction takes place between pressure waves and boundary conditions at
the end points of the pipe. The negative sign in this equation is applicable for a dis-
turbance propagating upstream and the positive sign for one moving downstream.
Because values of wave speed in many pipelines are in the range of 3,000–4,000 ft/sec
(915–1,220 m/sec), typical values of c/g in Eq. 8-5 are large, often 100 or more. Thus,
this relationship predicts large values of head rise that highlights the importance of
transient analysis. For example, if an initial velocity of 3 ft/sec (0.9 m/sec) is suddenly
arrested at the downstream end of pipeline and c/g equals 100 m/sec, a head rise of
300 ft (91 m) will result.
8.4.2. Wave Speed

The wave speed c for a liquid flowing within a line is influenced by the elasticity of the
line wall. For a pipe system with some degree of axial restraint a good approximation
for the wave propagation speed is obtained using (Thorley 1991):
c = Ef / (1+K r E f D/ Ec t l ) (8-6)
where Ef and Ec are the elastic modulus of the fluid and conduit, respectively; D is
the pipe diameter; tl is the pipe thickness; and Kr is the coefficient of restraint for
longitudinal pipe movement. Typically, three types of pipeline support are considered
for restraint. These are
Case a: The pipeline is restrained at the upstream end only.
(8-7)
Kr = 1− µ p / 2
Case b: The pipeline is restrained throughout.
(8-8)
K r = 1 − µ P2
Case c: The pipeline is unrestrained (has expansion joints throughout).
(8-9)
Kr =1
where MP is the Poisson’s ratio for the pipe material. Table 8-1 lists physical properties
of common pipe materials.
8.4.3. Wave Action at Pipe Junctions

In a piping system, junction nodes have a significant impact on the direction and move-
ment of pressure waves in the system. The effects of a pipe junction on pressure waves
can be evaluated using conservation of mass and energy at the junction. Energy losses
at the junction usually cause only minor effects and are neglected.
A wave of magnitude $H impinging on one of the junction legs, jin, is transmit-
ted equally to each adjoining leg (Figure 8-11). The magnitude of the waves is Tjin$H
where the transmission coefficient, Tjin, is given by:
g A
2 jin jin
c
Tjin =
jin
gA (8-10)
jcj j
where the summation j refers to all pipes connecting at the junctions (incoming and
outgoing). A reflection back in pipe jin occurs and is of magnitude Rjin$H where:
Rjin = Tjin −1 (8-11)
Table 8-1 Physical properties of common pipe materials

Young’s Modulus—
Young’s Modulus Ec (psi) × 106 Poisson’s Ratio
Material Ec (GPa) (Typical Values) μp
Asbestos Cement 23–24 3 0.2
Cast Iron 80–170 15 0.25–0.27
Concrete 14–30 3 0.1–0.15
Reinforced Concrete 30–60 6 —
Ductile Iron 172 24 0.3
PVC 2.4–3.5 0.4 0.46
Steel 200–207 30 0.30
High-Density Polyethylene 0.9–1.1 0.13 0.4
For the simultaneous impingement of waves arriving in more than one leg the
effects are superimposed.
Eq. 8-10 provides the basis for evaluating the effect of wave action at two special
junction cases: dead end junctions and open ends or connections to reservoirs. A dead
end is represented as a two pipe junction with A2 equal to zero. With A2 equal to zero,
Tjin equals 2 and Rjin is 1, which indicates that the wave is reflected positively from the
dead end. This condition implies that the effects of pressure waves on dead ends can
be of significant importance in transient consideration. If the pressure wave reaching
the dead end is positive, the wave is reflected with twice the pressure head of the inci-
dent wave. If the pressure wave reaching the dead end is negative, the wave reflection
will cause a further decrease in pressure that can lead to the formation and collapse of
vapor cavity. For a reservoir connection, A2 is infinite so Tjin is zero and Rjin equals −1,
which indicates that a negative reflection occurs at a reservoir.
8.4.4. Wave Action at Control Elements

A general analysis of pressure wave action at a control element (e.g., pump, valve, ori-
fice) in a pipe system is described below (Boulos et al. 2006; Wood et al. 2005a). This
analysis provides relations to account for a variety of situations.
Figure 8-12 shows a general situation at a control element where pressure waves
∆H1 and ∆H2 are impinging. At the same time the characteristics of the control ele-
ment may be changing. It is assumed that the relationship between flow through the
control element, Q, and the pressure head change across the control element, ∆H,
always satisfies a head-flow equation for the control element having the general form:
Figure 8-11 Effect of a pipe junction on a pressure wave
Copyright © 2012 American Water Works Association. All Rights Reserved.

Figure 8-12 Condition at a control element before and after action
H = A(t) + B(t)Q + C(t) Q Q (8-12)
The terms A, B, and C represent the coefficients for a general representation of

the control element head-flow equation. These coefficients may be time dependent but
will be known (or can be determined) at all times. The absolute value of Q is employed
to make the resistance term dependent on the flow direction. This representation
applies to both passive resistance elements such as valves, orifices, fittings, and fric-
tion elements and active elements such as pumps.
For passive resistance elements, however, only the coefficient C representing the
effect of irreversible loss is not zero. This coefficient represents the ratio of the head
loss to the square of the flow through the control element. For hydraulic consider-
ations, this type of square law relationship is appropriate. The sign of the pressure
head change is dependent on the direction of flow through the control element that
necessitates the use of the absolute value of the flow rate as presented in Eq. 8-12.
In Figure 8-12, subscripts 1 and 2 denote conditions on the left and right side of
the control element before the impinging waves arrive, while the subscripts 3 and 4
designate these conditions at the control element after the wave action. Here, Qb and
Qa are the flows before and after the wave action, respectively.
The basic transient flow relationship for pressure-flow changes is applied to
incoming and outgoing waves to yield the following for the outgoing waves:
H3 = H1 + 1 (Qb − Qa ) (8-13)
H4 = H2 + 2 (Qa − Qb ) (8-14)
Where:
c1 c2
1 = and 2 = (8-15)
gA1 gA2
Pressure heads after the action are given by:
H3 = H1 + H1 + H3 (8-16)
and
H4 = H2 + H2 + H4 (8-17)
The characteristic equation relating the pressure head change across and the
flow through the control element after the action is:
H4 − H3 = A(t) + B(t)Qa + C(t) Qa Qa (8-18)
The coefficients of the characteristic equation, A(t), B(t) and C(t), represent the
values at the time of the wave action and may vary with time.
Substituting Eqs. 8-16 and 8-17 into Eq. 8-18 and rearranging results in a qua-
dratic relationship for Qa or:
C(t) Qa Qa + ( B(t) − 1 − 2 ) Qa
(8-19)
( )t + H1 + 2 H1 − H2 −2 H
+A ( 1 + )2 Qb = 0
2 +
Eq. 8-19 can be solved directly for Qa using the quadratic formula or iteratively
using the Newton-Raphson method. Eqs. 8-13 and 8-14 are then solved to give the
magnitude of the pressure waves produced by the action, and Eqs. 8-16 and 8-17 yield
the pressure head after the action takes place.
This general analysis represents a wide variety of control elements that can be
subject to a range of conditions.
8.4.4.1. Control Element Characteristics. The coefficients of the control ele-
ment characteristic equation (8-12) are determined using head-flow operating data
for the control element. Some control elements such as pumps will use all three coef-
ficients to represent the head-flow variation. In some cases, the characteristic equa-
tion will be based on data, which represents the head-flow relationship for a relatively
small range of operation. For these applications, the coefficients used for the control
element analysis will be based on data valid for the operation in the vicinity of the
operating point and will be recalculated as the operating point changes. This is true
for the analysis of variable speed pumps and for pumps using data representing a wide
range of operating conditions, including abnormal situations such as flow reversal.
Many control elements, such as valves, can be modeled using only the C coeffi-
cient. These are referred to as resistive control elements where the head-flow relation
is adequately described by a single resistive term. For this application, the coefficient
C(t) is defined as the control element resistance. The term resistance is defined as the
head drop divided by the square of the flow (∆H⁄Q2). Here, the head drop is in feet
(meters), and the flow is in ft3 /sec (m3 /sec).
The control element resistance is directly related to other resistive parameters
such as minor loss (K M), valve flow coefficient (Cv), sprinkler constant (Ks), and others,
which characterize the head-flow characteristic of a resistive control element.
8.4.4.2. Wave Propagation With Friction. Because all pipeline systems con-
tain friction, the pressure wave is attenuated as it travels down a line. Line loss can
be simulated by concentrating the losses in length L at an orifice as shown in Figure
8-13. This orifice will then partially transmit and reflect pressure waves and account
for the effect of wall shear. The friction orifice will therefore attenuate a pressure wave
in a manner similar to the total attenuation that will occur as the wave travels the
length L in the pipe.
Figure 8-13 Wave propagation in a pipe section considering friction
In this representation, the loss at the orifice is:

fL 2
H = H2 − H1 = − 2
Q = CQ2 (8-20)
2gDA
where f is the friction factor; g is the acceleration of gravity; D is the pipe diameter;
and A is the pipe area.
In this case, the coefficients of the characteristic equation (Eq. 8-12) for the line
friction orifice are:
A(t) = B(t) = 0 (8-21)
and
fL
C(t) = − (8-22)
2gDA2
The friction factor can be determined using the flow rate through the orifice prior
to the wave action. Although it is true that some approximation errors will be intro-
duced if excessively long reaches are used, these errors are generally very small and
can be minimized or eliminated using shorter pipe reaches. Ramalingam et al. (2009)
developed sound guidelines in the form of error study for selecting the optimal number
of friction orifices to ensure accurate results.
8.5. GOVERNING EQUATIONS _______________________________

The fundamental equations describing hydraulic transients in liquid pipeline systems
are developed from the basic conservation relationships of physics or fluid mechanics.
They can be fully described by Newton’s second law (equation of motion) and conserva-
tion of mass (kinematic relation). These equations can incorporate typical hydraulic
devices and their interactions with the wave conditions in the pipes.
Applying these basic laws to an elementary control volume, a set of nonlinear
hyperbolic partial differential equations can be derived. If x is the distance along the
pipe centerline, t is the time, and partial derivatives are represented as subscripts,
then the governing equations for transient flow can be written as:
Continuity
c2
Ht + Qx = 0 (8-23)
gA
Momentum (Dynamic)
1
Hx + Qt − f (Q) = 0 (8-24)
gA
where f(Q) is a pipe resistance (nonlinear) term that is a function of flow rate.
The preceding equations are first-order hyperbolic partial differential equations

in two independent variables (space and time) and two dependent variables (head and
flow). The solution of these equations with appropriate initial and boundary conditions
will give head and flow values in both spatial and temporal coordinates for any tran-
sient analysis problem.
Unfortunately, no exact analytical solution exists for these equations except for
simple applications that neglect or greatly simplify the boundary conditions and the
pipe resistance term. When pipe junctions, pumps, surge tanks, air vessels, and other
hydraulic components are included, the basic equations are further complicated. As a
result, numerical methods are used to integrate or solve the transient flow equations
(Wylie and Streeter 1993; Tullis 1989; Chaudhry 1979).
8.6. NUMERICAL SOLUTIONS OF TRANSIENTS _________________

Several approaches have been taken to numerically model pressure transients in water
distribution systems (Boulos et al. 2006; Wood et al. 2005a–b; Walski et al. 2003). The
two most widely used and accepted methods are the Lagrangian Wave Characteristic
Method (WCM) and the Eulerian Fixed-grid Method of Characteristics (MOC). Each
method assumes that a steady-state hydraulic solution is available that gives initial
flow and pressure distributions throughout the system. The main difference between
the two numerical methods is in the way pressure waves are tracked between the
pipe boundaries (e.g., reservoirs, tanks, dead ends, partially opened valves, pumps,
junctions, surge control devices, vapor cavities, etc.). The MOC tracks a disturbance
in the time-space grid using a numerical method based on characteristics, while the
WCM tracks the disturbance based on wave propagation mechanics. Both methods
have been well documented in the literature (Ramalingam et al. 2009; Jung et al.
2007; Boulos et al. 2005–2006; Wood et al. 1966, 2005a–b; Walski et al. 2003; Wylie
and Streeter 1993) and have been implemented in various computer programs for pipe
system transient analysis. The methods will mostly produce the same results at the
network nodes when using the same data and model to the same accuracy. A brief
description of each method follows.
8.6.1. Method of Characteristics (MOC)

In MOC, the governing partial differential equations are converted to ordinary dif-
ferential equations and then to a difference form for solution by a numerical method.
Solution space comprises two equations called the characteristic equations along with
two compatibility equations for any point in a space-time grid. The method divides the
entire pipeline into a fixed number of segments, writes the characteristic and compat-
ibility equations for every grid location, and then solves these equations for head and
flow at all grid locations. The line friction of the entire pipeline is distributed in each of
these segments. The various boundary conditions are handled by combining the appro-
priate characteristic equation with the equations defining the boundary.
8.6.2. Wave Characteristic Method (WCM)

The WCM is based on the concept that transient pipe flow results from generation and
propagation of pressure waves that occur as a result of a disturbance in the pipe sys-
tem. The method essentially tracks the movement of pressure waves as they propagate
throughout the system and computes new conditions at either fixed time intervals or
only at times when a change actually occurs. It requires the calculation of the effects of
these pressure waves impinging on the network junctions and control elements along
with the appropriate boundary conditions. The entire line friction is modeled as an
equivalent orifice situated at the midpoint of a pipeline or multiple orifices distrib-

uted uniformly throughout the pipeline (i.e., distributed friction profile). Pressure and
velocity or flow rate time histories are computed for any point in the network by sum-
ming with time the contributions of incremental waves.
8.7. METHODS OF CONTROLLING TRANSIENTS ________________

The means of controlling pressure transients in water distribution systems will gener-
ally depend on whether the initiating event results in an upsurge (e.g., a high pressure
event caused by a shutdown of a downstream pump or valve) or a downsurge (e.g., a
low pressure event caused by the shutdown of an upstream pump or valve). Downsurge
events can lead to the undesirable occurrence of water-column separation (cavitation)
that can result in severe pressure surges following the collapse of a vapor cavity or
intrusion of contaminated water through a leak or other opening.
A number of surge protection devices are commonly used to help control high and
low pressure transients in water distribution pipe systems. Small systems are just as
vulnerable as large systems. No two systems are completely identical; hence the ulti-
mate choice of surge protection devices and operating strategies will usually differ.
Of course, it is always best whenever possible to avoid rapid flow changes. A transient
analysis should be carried out to predict the effect of each individually selected device.
As a result of the complex nature of transient behavior, a device intended to suppress
or fix a transient condition could result in a worsening of the condition if the device is
not properly selected or located in the system. Designers must evaluate the relative
merits and shortcomings of all the protection devices that they may select. A combina-
tion of devices may prove to be the most desirable and economical. A brief overview of
various commonly used surge protection devices and their functions is provided in the
following discussions. Additional details are available in Boulos et al. (2005, 2006),
Wood et al. (2005a), Walski et al. (2003), and Thorley (1991).
8.7.1. Devices and Systems

8.7.1.1. Simple Surge Tank (Open). Open surge tanks or stand-pipes can be
an excellent solution to both upsurge and downsurge problems. These tanks can be
installed only at locations where normal static pressure heads are small (or tall tanks
are acceptable). They serve two main purposes: (1) to prevent high pressures during
pump startup conditions or valve shutdown conditions by accepting water; or (2) to
prevent cavitation during pump shutdown by providing water to a low-pressure region.
8.7.1.2. Surge Vessel (Air Chamber—Closed Surge Tank—Bladder
Tank—Hybrid Tank). Surge vessels (or air chambers), which are pressure vessels
partly full of air, have the advantage that they can be installed anywhere along a line
regardless of normal pressure head. It should be noted that under very low static con-
ditions or downhill pumping, special care will be required to keep the surge tank from
completely draining. These vessels are normally positioned at pump stations (down-
stream of the pump delivery valve) to provide protection against a loss of power to the
pump. They serve the same function as an open surge tank but respond faster and
allow a wider range of pressure fluctuation. Their effect depends primarily on their
location, vessel size, entrance resistance, and initial gas volume and pressure. Closed
surge vessels are normally equipped with an air compressor to control the initial gas
volume and to supply make-up gas, which is absorbed by the water. Some closed surge
tanks are equipped with a precharged pressurized bladder (bladder surge tanks) that
eliminates the need for an air compressor. Hybrid tanks are equipped with an air vent
that admits air when the pressure goes below atmospheric pressure.
8.7.1.3. Feed Tank (One-Way Surge Tank). The purpose of feed tanks is to
prevent initial low pressures and potential water-column separation by admitting
water into the pipe subsequent to a downsurge. They can be either open or closed, will
have a check valve to allow flow only into the pipe system, and can be installed any-
where on the line.
8.7.1.4. Pressure Relief Valve. A pressure relief valve ejects water out of a side
orifice to prevent excessive high-pressure surges. It is activated when the line pressure
at a specified location (not necessarily at the valve) reaches a preset value. The valve
opens and closes at prescribed rates over which the designer often has some degree of
control. It can eject water into the atmosphere or a pressurized region, or into an open
or closed surge tank.
8.7.1.5. Surge Anticipation Valve. A surge anticipation valve is much like a
pressure relief valve, but it gets triggered to open on a downsurge in pressure (sensed
at a specified location) in anticipation of an upsurge to follow. This valve, when acti-
vated, follows and completes a cycle of opening and closing based on valve opening and
closing rates. For systems where water-column separation will not occur, the surge
anticipation valve can solve the problem of upsurge at the pump due to reverse flow or
wave reflection. However, this valve must always be used with caution for it can make
low pressure conditions in a line worse than they would be without the valve.
8.7.1.6. Air Release/Vacuum Valve. Air release/vacuum breaking valves are
installed at high points in a pipeline to prevent low pressure (cavitation) by admitting
air into the pipe when the line pressure drops below atmospheric conditions. The air
is then expelled (ideally at a lower rate) when the line pressure exceeds atmospheric
pressure. Two-stage air valves release the air through a smaller orifice to prevent
the “air slam” that occurs when all the air is released and the water column rejoins.
A three-stage air valve can be designed to release the air through a second (smaller)
orifice to further reduce the air slam.
8.7.1.7. Check Valve. A check valve allows flow only in one direction and closes
when flow reversal is impending. For transient control, check valves are usually
installed with other devices such as a pump bypass line as described below. Pumps are
often equipped with a check valve to prevent flow reversal. Because check valves do
not close instantaneously, it is possible that a substantial backflow may occur before
closure that can produce additional and sometimes large surges in the system. Check
valve modeling includes a time delay between check valve activation and complete clo-
sure of the check valve. The check valve is often treated as a valve closing in a linear
fashion that is activated by flow reversal and closes completely over the delay period.
Check valves can also be used to isolate high pressure waves from reaching a section
of a pipeline. One of the great advantages of a check valve is that it can prevent pipes
from draining, and keeping the pipe full of fluid tends to reduce startup transients.
8.7.1.8. Pump Bypass Line. In low-head pumping systems that have a positive
suction head, a bypass line around the pumps can be installed to allow water to be
drawn into the discharge line following power failure and a downsurge. Bypass lines
are generally short line segments equipped with a check valve (nonreturn valve) pre-
venting back flow (from the pump discharge to the suction side) and installed parallel
to the pump in the normal flow direction. They are activated when the pump suc-
tion head exceeds the discharge head. They help prevent high-pressure buildup on the
pump suction side and cavitation on the pump discharge side.
8.7.1.9. Flywheel. Increasing the pump rotational inertia by attaching a fly-
wheel (Figure 8-14), a large-diameter steel plate, to the pump motor is sometimes a
useful surge control device, especially for sewage pumping systems, because the fly-
wheel is not in contact with the foul water. When power fails, the rotational energy
provided by the flywheel will reduce pump speed gradually, allowing the pumping
Figure 8-14 Flywheels to be installed in a large pump station
system to slowly come to rest, thus avoiding unacceptable transient pressures. Three
problems accompany flywheel installations:
s They must be large and heavy enough to provide additional rotating inertia
to be effective. Pump and motor bearings and supports must then be designed
to accommodate the extra weight, and additional space is required.
s Pump startup requires extra power to overcome the inertia of flywheels.
s Pump startup must be gradual to keep the motors from burning out.
Nonetheless, flywheels are useful type of surge control and can be found in many
pumping installations.
8.7.1.10. In-Line Pump Control Valve. For large pumping systems with large-
diameter headers and high flows, in-line pump control valves are a viable option. In-
line pump control can be operated similarly to surge anticipator valves, which open
when line pressure drops below a specified set point, remain open for a preset period
of time, and then close in a manner that prevents high pressures resulting from rapid
valve closure. Properly installed, these valves prevent high pressures at pump sta-
tions, but the valve movements must be set with care; otherwise, more severe problems
can occur. Four quadrant pump curves have to be analyzed in conjunction with the
other transient parameters to develop a solution. Of course, these valves have no abil-
ity to prevent low pressures and column separation from occurring in the downstream
pipe lines.
8.7.2. Choice of Surge Protection Strategy

A number of techniques can be used for controlling/suppressing transients in munici-
pal water distribution systems. Some involve system design and operation while others
are related to the proper selection of surge protection devices. For example pressure
relief valves, surge anticipation valves, surge vessels, surge tanks, pump bypass lines,
or any combination of them can be used to control high pressures. Low pressures can
be controlled by increasing pump inertia or by adding surge vessels, surge tanks, air
release/vacuum valves, pump bypass lines, or any combination of that group. The over-
riding objective is to reduce the rate at which changes to the flow occur.
Surge protection devices are normally installed at or near the point where the
disturbance is initiated such as at the pump discharge or by the closing valve (with
the exception of air relief/vacuum breaking valves and feed tanks). Figure 8-15 illus-
trates typical locations for the various surge protection devices in a water distribution
system. A comprehensive transient flowchart for considering the transient protection
of the system is shown in Figure 8-16. This flowchart is discussed in detail by Boulos
et al. (2005, 2006). When developing a protection strategy, it must be recognized that
no two systems are hydraulically the same; hence, no general rules or universally
applicable guidelines are available to eliminate unacceptable pressures in a water
distribution system. Any surge protection devices and/or operating strategies must be
chosen accordingly (Boulos et al. 2005, 2006; Wood et al. 2005a; Walski et al. 2003;
Thorley 1991).
The final choice will be based on the initial cause and location of the transient
disturbance(s), the system itself, the consequences if remedial action is not taken, and
the cost of the protection measures themselves. A combination of devices may prove
to be the most effective and most economical. Final checking of the adequacy and
efficacy of the proposed solution should be conducted and validated using a detailed
transient analysis.
8.7.2.1. Pump Station and Downstream Pipeline Protection. Because
pump stations are aboveground, surge failures and remedial solutions can be readily
observed. However, failures to buried downstream pipelines are sometimes undetected
and become subject to unseen and overlooked failures. It is important to recognize that
some surge control solutions protect only the pump station but do not necessarily pro-
tect the downstream pipelines from column separation and negative pressures. Both
the pump station and the downstream pipelines should be protected.
8.7.2.2. Float-Operated Air Valves Versus Surge Resistant Air Valves. A
number of vacuum relief valves are often needed for filling and draining pipelines.
Also, additional air valves may be required to protect the pipelines from extreme low
pressures due to surge transients. The total number of air valves depends on pipeline
profile and initial pipeline velocities. Of course, the number of air valves should be
limited and carefully considered, because adding large volumes of air to pipelines can
create other types of operational problems, such as air binding. If pipeline profiles are
too steep and the initial velocities are too high, numerous air valves would be required.
In that case, other types of surge control devices should be considered instead.
Because float-operated air valves require water to close the float, some pipe sys-
tems with high static head require surge resistant air valves to prevent damaging the
float. Damage to the air valve and high pressures occur when water column slams the
float closed, pushing the low density air out around the float.
A safer air valve solution would be the so called surge-resistant air valves that
trap the air inside the air valve body, using it as a cushion, and then slowly releasing
the air to prevent high pressures and damage to the valves.
8.7.2.3. Normal Pump Operation Protection Versus Power Failure Pro-
tection. Normal pump operation for a surge-vulnerable system can include slow clos-
ing and slow opening pump control valves or variable frequency drives on the pump
motors to eliminate undesirable surges during day-to-day operation.
Power failure on surge-vulnerable systems requires the surge-control devices.
Backup power and generators do not come on-line quickly enough to prevent transients
from occurring. It should be noted that the use of surge chambers requires quick-
closing check valves immediately downstream of the pumps. The quick-closing check
valves prevent the surge chamber from spilling water back through the pumps during
Figure 8-15 Typical locations for various surge protection devices
pump shutdown. Slow-closing pump control valves would not be used in conjunction
with a surge chamber. If a surge chamber is required for surge control, it would also
be used for normal pump shutdown and startup and pump control valves would not be
required.
This section focused on pumps. There are other control strategies such as educa-
tion of operators to slowly open/close valves, adjusting speed of mechanically operated
valves, and not operating tanks such that the altitude valve closes and cannot absorb
the transient.
8.8. TRANSIENT MODELING CONSIDERATIONS ________________

Transient analysis is essentially based on equations governing the movement of pres-
sure waves throughout the municipal water system. This type of network analysis
requires a significant number of calculations and is an extremely demanding com-
putational exercise. This is usually carried out using transient modeling software.
Although the system should be described in full, some simplifications and assumptions
will be needed for its model representation. This is necessary to reduce the network
model complexity and computational run times, and also because some of the basic
transient flow data required will not be available (Thorley 1991).
Having considered some of the detail of transient analysis and protection, it is
perhaps helpful to include some tips or guidelines that would assist in preparing com-
puter simulation files. In essence, the good news is that transient modeling uses much
of the same data required for steady-state modeling. A steady-state analysis of the ini-
tial conditions for the transient analysis is required. There are, however, a number of
additional considerations for developing a transient analysis model.
s The location (including elevation) of hydraulic devices (pumps, control valves,
check valves, regulating valves, etc.) is required for the model.
s A transient model should carry out calculations at all local high and low
points because the pressure extremes often occur at these locations.
s Cavitation must be modeled for transient analysis. If cavitation occurs at any
location in the distribution system, it can greatly affect the transient analysis
results (Jung et al. 2009b).
Figure 8-16 Flowchart for surge control in water distribution systems
s Skeletonization guidelines are significantly different than those for steady-

state analysis. Dead-end pipes, for example, will have a very significant effect
on a transient analysis while having no effect on the steady-state analysis.
Jung et al. (2007) performed a detailed study of the issues associated with
water distribution model skeletonization for surge analysis. They concluded
that skeletonization can introduce some significant error in estimating pres-
sure extremes and can overlook water-column separation and subsequent col-
lapse at vulnerable locations in the distribution system.
s Series and parallel pumps with similar characteristics may be modeled as a

single equivalent pump if none of the individual pumps to be combined are
subjected to a pump trip, startup, or a speed change.
s Pressure (positive or negative) surges can drastically alter the local pressure
and affect the demand magnitude that can be extracted at any given node in
the system. Pressure-sensitive demands versus fixed (constant or pressure
independent) nodal outflows should be used to assess the impact of pressure
changes and produce more accurate transient results (Jung et al. 2009a).
s It is good practice to allow a transient model to operate initially at steady-
state for a short period before the transient is initiated. This provides addi-
tional assurance that the transient model is operating correctly.
s For transient analysis it is necessary to use a computational time interval
such that the pressure wave travel times for all pipe segments will be a mul-
tiple of this time increment and this integer multiple will be calculated for
each line segment. Some adjustment is required to obtain a time interval
that is not unreasonably small. This will amount to actually analyzing a
model of the piping system with pipe lengths (or wave speeds) different than
the actual values and a sensitivity check should be made to assure that the
time interval chosen is acceptable. The time interval required for accurate
transient analysis may be quite small (0.01 to 0.001 seconds). For example if
the wave speed is 4,000 ft/sec (1,220 m/sec), a time increment of 0.01 seconds
represents a travel distance (and therefore, length accuracy) of 40 ft (12.2 m)
for the model. A time increment of 0.001 seconds represents a travel distance
(and length accuracy) of 4 ft (1.2 m) for the model. The length accuracy of the
model (maximum difference between actual and model pipe lengths) must be
sufficient to generate an accurate solution. However, increasing the accuracy
will require a longer computational time. It should be noted that the shortest
pipe in the network model plays a dominant role in determining the compu-
tational time interval. Consideration should be given to merging very short
pipes into longer pipe segments or simply removing them from the network
model but only when their resulting effect on the system transient behavior
is negligible.
8.9. DATA REQUIREMENTS __________________________________

The data requirements for surge analysis include all data necessary to do a steady-
state analysis. A steady-state analysis for the starting conditions is required. Initial
conditions of flow in all pipe segments and static pressure head (or pressure) at all
junctions and components must be calculated before initiating the transient analysis.
Note that the required initial pressure head (or pressure) conditions are static heads
(P/G) and not total heads or hydraulic grade lines (elevation + P/G). The static pressure
is the pressure that a pressure gage attached to the line at that position would read.
This requirement is necessary to address cavitation during transient conditions.
In addition to the usual pipe data (length, diameter, and roughness), the wave
speed must be calculated for each pipe. This requires the wall thickness of each pipe,
material, Poisson’s ratio and elastic (Young’s) modulus, and the bulk modulus and
density of the fluid. In addition, information on the degree of restraint of the pipes is
required. Because many of these parameters may not be directly available, estimates
for typical pipe materials are often used.
Characteristic data (or an equation) that relate the pressure change and flow to
the operating point must be used for all hydraulic components and for the full range
of operating conditions during the transient analysis. All system components (pumps,
valves, etc.) should be initially in a balanced state (the initial pressure change across
the component and flow through the component should be compatible with the charac-
teristic relationship for that component). The characteristic data for a component must
account for changes in the set point of the component (valve opening, pump speed,
etc.) that occur during the transient analysis. Normally, the steady-state character-
istics are used. Figure 8-17 shows typical valve closure characteristics for a linear
stem movement for several types of valves (Boulos et al. 2006; Wood et al. 2005a). It
is assumed that the valves will operate on these curves during transient conditions.
Pump steady-state head-flow-speed curves are often used to model pump opera-
tion. However, if during the transient the pump operates in abnormal zones (turbining,
etc.), it is necessary to use more detailed four quadrant pump operating characteristics
(i.e., ± speed and ± flow). Of the many methods developed for this purpose, the Suter
curve is the most widely used (Thorley 1991; Suter 1966). A typical four quadrant
pump characteristic curve is shown in Figure 8-18. In this figure, the x-axis repre-
sents the four quadrants of pump operation, and the y-axis represents the correspond-
ing head and torque characteristics. These data are normally not provided by pump
manufacturers. However, many of these four quadrant curves are available for a range
of pump specific speeds. Typically, one of these curves is selected by matching the spe-
cific speed of the pump to the available curves. The additional pump data required for
transient analysis include the efficiency and the total inertia (pump and motor).
A characteristic equation that relates the pressure change and flow to the operat-
ing point of all hydraulic surge control devices along with their locations must also be
available. All such devices (surge tanks, air valves, etc.) should be initially in a bal-
anced state (the initial pressure change across the component and flow through the
component should be compatible with the initial characteristic relationship for that
component). The characteristic equation for a surge control device must account for
changes in the set point of the device (relief valve, nonslam air valve, etc.) that occur
during the transient analysis.
Figure 8-17 Representative valve closure characteristics
Figure 8-18 Typical pump four quadrant characteristics (Suter curve)
Finally, the exact nature of the disturbance and its intended timescale must be
specified. The disturbance can be either a change in the open area ratio for a valve,
the speed ratio for a pump, or any other change in operation (check valve closing, pipe
rupture, etc.) that results in a change in flow.
8.10. SUMMARY ___________________________________________

Hydraulic transient, also called pressure surge or water hammer, is the means by which
a change in steady-state flow and pressure is achieved. When flow conditions in the
water pipeline system are changed, such as by closing a pump or a valve or by starting
a pump, a series of pressure waves is generated. These disturbances propagate with
the velocity of sound within the medium until dissipated down to the level of the new
steady-state by the action of some form of damping or friction. In the case of flow in a
water distribution network, these transients produce velocity and pressure changes.
When sudden changes take place, however, the results can be dramatic because pres-
sure waves of considerable magnitude can occur and are quite capable of destroying
equipment and pipelines. Only if flow regulation occurs very slowly is it possible to go
smoothly from one steady-state to another without large fluctuations in pressure head
or flow velocity.
Clearly, flow control actions can be extremely important, and these actions have
implications not only for the design of the hydraulic system but also for other aspects
of system operation and protection. Problems such as selecting the pipe layout and
profile, locating control elements within the system, and formulating operating rules
as well as the ongoing challenges of system management are all influenced by the
details of the control system. A rational and economic operation requires accurate
data, carefully calibrated (static- or extended-period simulation) models, ongoing pre-
dictions of future demands and the response of the system to transient loadings,
and correct selection of both individual components and remedial strategies. These
design decisions cannot be considered an after-thought to be appended to a nearly

complete design. Transient analysis is a fundamental and challenging part of ratio-
nal system design.
Transient analysis is essential to good design and operation of piping systems.
Transient modeling provides the most effective and viable means of predicting poten-
tially negative impacts of hydraulic transients under a number of worst-case scenar-
ios, identifying weak spots, and evaluating how they may possibly be avoided and
controlled. The basis of surge modeling is the numerical solution of conservation of
mass and linear momentum equations. A number of widely used computer codes based
on Eulerian (MOC) and Lagrangian (WCM) numerical solution schemes are currently
available and have been successfully validated against field data and exact analytical
solutions. However, surge analysis computer models can only be effective and reliable
when used in conjunction with properly constructed and well-calibrated hydraulic net-
work models. Poorly defined and calibrated hydraulic network models may result in
poor prediction of pressure surges and locations of vapor cavity formation and, thus,
defeat the whole purpose of the surge modeling process.
Looped water distribution systems comprising short lengths of pipes may be less
vulnerable to problems associated with hydraulic transient than a single long pipe
system. This is because wave reflections (e.g., at tanks, reservoirs, junctions) will tend
to limit further changes in pressure and counteract the initial transient effects. For
networks with long pipelines and irrespective of whichever numerical basis is used, a
good transient model will have nodes along those pipes defining the important high
and low points to ensure accurate calculations are made at those critical locations. An
important consideration is dead ends (which may be caused by closure of control or
check valves) that lock pressure waves into the system in a cumulative fashion (wave
reflections will double both positive and negative surge pressures). As a result, the
effects of dead ends need to be carefully evaluated in transient analysis.
Proper selection of components for surge control and suppression in water dis-
tribution systems requires a detailed surge analysis to be effective and reliable. In
addition, good maintenance, pressure management, and routine monitoring programs
are essential components of transient protection. With these capabilities, water util-
ity engineers can greatly enhance their ability to better understand and estimate the
effects of hydraulic transients and to conceive and evaluate efficient and reliable water
supply management strategies, safeguard their systems and public health with maxi-
mum effectiveness, and forge closer ties to their customers. It is understanding com-
plexity through simplicity.
8.11. GLOSSARY OF NOTATIONS _____________________________

A cross-sectional area [L2 ]
A, B, C coefficients of control element characteristic equation
c sonic wave speed [L T-1]
D pipe diameter [L]
Ec elastic modulus of the pipe [M L -1T-2 ]
Ef elastic modulus of the fluid [M L -1T-2 ]
f pipe friction factor
f(Q) pipe resistance (nonlinear) term that is a function of flow rate [L]
g acceleration of gravity [L T-2 ]
H head [L]
Kr coefficient of restraint for longitudinal pipe movement

L pipe length [L]
P pressure [M L -1 T-2 ]
Q volumetric flow rate [L3 T-1]
R surge wave reflection coefficient at pipe junction
T time [T]
T surge wave transmission coefficient at pipe junction
tl pipe thickness [L]
V flow velocity [L T-1]
$t time interval [T]
$x spatial grid size [L]
MP Poisson’s ratio for the pipe material
R liquid density [M L -3 ]
8.12. REFERENCES
Besner, M.C., Lavoie, J., Morissette, C., and Chaudhry, M.H. 1979. Applied Hydraulic
Prevost, M. 2008. Effect of Water Main Transients. New York: Van Nostrand
Repairs on Water Quality. Jour. AWWA, Reinhold Co.
100(7):95–109. Fleming, K.K., Gullick, R.W., Dugandzic,
Besner, M.C., Lavoie, J., Payment, P., and J.P., and LeChevallier, M.W. 2006. Sus-
Prevost, M. 2007. Assessment of Tran- ceptibility of Distribution Systems to
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What are some of the causes of hydraulic transients?

What are some of the causes of hydraulic transients?

What effects can hydraulic transients have on piping systems?

What effects can hydraulic transients have on piping systems?

AWWA MANUAL M32

8.1. SYNOPSIS _____________________________________________

8.2. INTRODUCTION _______________________________________

Figure 8-1 Example steady-state transition after a period of rapid transients

8.3. CAUSES OF TRANSIENTS ________________________________

8.3.1. Basics—Rapid Changes in Velocity

Figure 8-2 Transient caused by pump shutdown

Figure 8-3 Transient caused by pump startup

Pipe filling is especially vulnerable to pressure transients when the pipeline

Figure 8-4 Transient caused by rapid valve opening

Figure 8-5 Transient caused by rapid valve closure

Figure 8-6a Rupture caused by valve closure (Superaqueduct of Puerto Rico)

Figure 8-6b Damaged pump bowl

Figure 8-6c Broken air admission valve

s Limiting the pipeline velocity

8.3.2. Contributing Factors

Figure 8-7 Varying pipeline profiles

8.3.3. Rules of Thumb for Identifying Vulnerable Systems

8.3.4. Dead-End Pipelines

Figure 8-8 Network schematic

8.4. BASIC PRESSURE WAVE RELATIONS ______________________

Figure 8-10 Pressure wave propagation in a pipe

or in terms of pressure head:

or in a more general form

8.4.2. Wave Speed

Case a: The pipeline is restrained at the upstream end only.

Case b: The pipeline is restrained throughout.

Case c: The pipeline is unrestrained (has expansion joints throughout).

8.4.3. Wave Action at Pipe Junctions

Rjin = Tjin −1 (8-11)

Table 8-1 Physical properties of common pipe materials

8.4.4. Wave Action at Control Elements

Figure 8-11 Effect of a pipe junction on a pressure wave

Copyright © 2012 American Water Works Association. All Rights Reserved.

Figure 8-12 Condition at a control element before and after action

H = A(t) + B(t)Q + C(t) Q Q (8-12)

The terms A, B, and C represent the coefficients for a general representation of

Pressure heads after the action are given by:

H4 − H3 = A(t) + B(t)Qa + C(t) Qa Qa (8-18)

Figure 8-13 Wave propagation in a pipe section considering friction

In this representation, the loss at the orifice is:

A(t) = B(t) = 0 (8-21)

8.5. GOVERNING EQUATIONS _______________________________

The preceding equations are first-order hyperbolic partial differential equations

8.6. NUMERICAL SOLUTIONS OF TRANSIENTS _________________

8.6.1. Method of Characteristics (MOC)

8.6.2. Wave Characteristic Method (WCM)

equivalent orifice situated at the midpoint of a pipeline or multiple orifices distrib-

8.7. METHODS OF CONTROLLING TRANSIENTS ________________

8.7.1. Devices and Systems

Figure 8-14 Flywheels to be installed in a large pump station

8.7.2. Choice of Surge Protection Strategy

Figure 8-15 Typical locations for various surge protection devices

8.8. TRANSIENT MODELING CONSIDERATIONS ________________

Figure 8-16 Flowchart for surge control in water distribution systems