Ellis,J. Pressure transients in water engineering, A guide to analysis and interpretation of behaviour

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150—3600 mm with more common sizes being in the range 400—

1500 mm. At working pressures <10.5 kgf/cm

, strength is often

controlled by external load, requiring a certain minimum thickness to

guard against excessive deﬂection and collapse under vacuum pressures.

Common practice in the past has been to limit wall thickness to a

minimum of 6 mm for diameters up to 600 mm. While providing an

additional corrosion allowance, this thickness will frequently withstand

>17.6 kgf/cm

and for high-strength steel considerably higher pressures.

Advances in cathodic protection and coating technology has made

possible wall thicknesses <6 mm. For larger pipe diameters and pres-

sures >10.5 kgf/cm

, tensile strength often controls wall thickness.

Steel pipe test pressures vary according to the grade of steel. For

grades 22 to 27, pressures range from 70 kgf/cm

(700 mWG) for

smaller diameters to 20 kgf/cm

for larger diameters.

The maximum allowable deﬂection of a steel pipe should be not more

than 2% where a cement mortar lining and/or coating has been

provided. Concrete coating provides negative buoyancy for underwater

installation.

Older steel pipes in cold climates can potentially fail catastrophically.

Stainless steel pipe is also available and has the advantage of not

requiring corrosion protection. It is virtually maintenance-free and

relatively vandalproof.

1.8 Overpressure allowance

Many types of pipe are permitted, by codes of practice, to carry an over-

pressure allowance for transient or short-term events. For instance,

Table 1.5. /D as a function of pipe size

Integral pipe size Maximum % deﬂection =D

DN 100 1.6

DN 150 2.1

DN 200 2.4

DN 250 2.7

DN 300 3.0

DN 350 3.1

DN 400 3.2

DN 500 3.4

DN 600 3.6

DN 700 3.8

DN 800 and above 4.0

Pressure transients in water engineering

British Standards allow pipe materials, such as asbestos cement (AC),

ductile iron (DI) and steel, to carry peak transient pressures as high

as 115% of the maximum sustained working pressure.

1.9 Pipe linings for rigid and ﬂexible pipes

To protect pipes from corrosion a range of lining materials are available

having different advantages and disadvantages. Types of lining are:

bitumen, coal tar, coal tar epoxy, epoxy resin, cement mortar, paint

systems and polyethylene. The lining can inﬂuence the outcome of

pressure surge investigations in a number of respects. For example,

pipe lining determines to some extent the resistance to ﬂow experi-

enced and therefore the head discharge relationship for the system.

Furthermore, the strength of the lining may dictate allowable pressures,

for example where a cement mortar lining is used.

1.9.1 Bitumen

Bitumen linings comprise a mixture of 80% bitumen and 20% dry lime.

The bitumen deteriorates with age. Burstall (1997) reported ‘pufﬁng-

up’ of bitumen to give a rough tuberculated appearance. Deterioration

can also result in loss of lining in raw water pipelines.

1.9.2 Coal tar enamel

Coal tar enamel was used up until the 1960s but its use in potable water

mains was discontinued on health and water quality grounds. Because of

resistance in low pH waters it ﬁnds use in raw water lines serving wellﬁelds.

1.9.3 Coal tar epoxy lining

Coal tar epoxy lining is lighter than other lining systems and may be

used in pipe crossings where weight is a consideration. It can leach

chemicals into potable water and so its use is not preferable.

1.9.4 Cement mortar

Cement mortar is a standard lining for ductile iron and steel pipes and

for relining of cast iron mains. In some parts of the world it is perhaps

the only lining system which has a proven track record over many

years and so may be preferred over alternatives for that reason. In

Motivation for hydraulic transient analysis

treated water mains a long life can be anticipated and with correct

chlorine residuals gives a clean surface with little or no change in

carrying capacity of the main. It is a brittle material which can fail

catastrophically. Maximum pipe deﬂection (change in diameter/original

diameter) should be 2% to avoid risk of cracking. Failure of lining has

also been attributed to pressure transients.

1.9.5 Paint systems

Often found on raw water lines, for example wellﬁeld risers, paints are

applied either directly onto steel or onto an existing cement mortar

lining. The paint system may be used to inhibit corrosion of a cement

mortar lining in a low pH water environment.

1.9.6 Polyethylene lining

Heated steel pipes are dipped into a bath of powdered polyethylene thus

providing an external coating and a lining in one operation. May be

used on sewers carrying aggressive contents and also on risers of well-

ﬁelds.

1.10 Plastic pipes

Plastic pipes represent an area of growth. All plastics are corrosion

resistant, ductile and relatively impervious. Generally no protective

lining is applied either internally or externally. These materials can be

subdivided into thermoplastics and glass-ﬁbre-reinforced thermosetting

resins. Both categories are available in a range of synthetic materials,

giving a wide-range spectrum of chemical resistance.

1.10.1 Thermosetting plastics

Thermosets are hardened by heating usually in the presence of a

catalyst. The hardened state is retained under reheating.

In general, thermoset pipes have greater stiffness, lower thermal

expansion coefﬁcients and can be used at higher temperatures than

thermoplastics. Some thermoplastics may be tougher but not stronger

than thermosets which include glass-reinforced plastic (GRP), ﬁbre-

reinforced plastic (FRP) and reinforced plastic matrix (RPM).

Thermoset pipes are laminates in which a relatively brittle but

chemically resistant resin is reinforced using strong and stiff glass

Pressure transients in water engineering

ﬁbres which themselves have very poor chemical resistance in an

aqueous environment. Heterogeneous materials used to form these

ﬁbre-reinforced pipes tend to be tougher than thermoplastics and the

energy required to produce a crack is greater. While fast cracks are

possible where only short discontinuous ﬁbres are used as reinforce-

ment, failure in most cases is preceded by leakage due to cracking of

the resin between ﬁbres, producing a ﬂow path for pipe contents to

leak. To guard against this happening a 0.2% strain limit is recom-

mended.

Pipes made from thermosetting materials are usually classiﬁed in

terms of pressure rating up to around 64 bar g and ring stiffness EI=D

from 250 N/m

to 8000 N/m

1.10.2 Thermoplastics

Thermoplastics are synthetic materials softened by application of heat

and are capable of repeated softening by subsequent heating. The

principal types of thermoplastics used in the water industry are polyvinyl

chloride (PVC) and polyethylene (PE). Other materials such as acrylo-

nitride butadience styrene (ABS) and polypropylene (PP) may be used

in special circumstances.

PVC was developed by German scientists shortly before World War

II. Meanwhile in the UK, ICI scientists had discovered a means of

producing polyethylene. Being lightweight, ﬂexible and virtually free

from chemical attack made these materials contenders for pipeline

materials.

Initial poor performance of uPVC was attributed to a combination of

poor installation, interference damage and unsuitable operating condi-

tions including high transient pressures. From about 1973, when the

industry fully appreciated the limitations of the material, the failure

rate of uPVC has been below that of spun grey iron (cast iron).

Pressure pipes for water services may be obtainable in four classes as

indicated in Table 1.6.

Table 1.6. Four classes of pressure pipes

Pressure class

BCDE

Pressure, bar g 6 9 12 15

Motivation for hydraulic transient analysis

Medium-density polyethylene (MDPE) has to some extent replaced

the earlier high-density polyethylene (HDPE) and low-density poly-

ethylene (LDPE). Materials are deﬁned by density ‘’ as follows:

LDPE 0:910    0:925

MDPE 0:925    0:940

HDPE 0:940    0:965

There is also an ultra-high molecular weight, high-density polyethylene

(UHMW-HDPE). LDPE has found application in small-bore water

pipes while MDPE and HDPE may be used for water main and efﬂuent

main duties including sea outfalls. UHMW-HDPE is used in the trans-

port of abrasive slurries. Normal operating temperature range is from

408Ctoþ608C. Jointing is usually by butt-fusion welding up to

D ¼ 1600 mm and extrusion welding for D > 1600 mm.

DIN standard 8074 deﬁnes 5 series for HDPE, as shown in Table 1.7.

Other standards for polyethylene have a classiﬁcation system based

upon the diameter/wall thickness ratio D=s ¼standard dimensional

ratio (SDR) and based on continuous operation for 50 years at 208C

(Table 1.8).

For liquids other than water these pressures may be reduced by a

chemical resistance factor. At temperatures greater than 208C the

maximum continuous working pressure reduces so that by 608C,

maximum pressure is only 40% of the value at 208C.

Table 1.7. The ﬁve series for HDPE deﬁned in DIN 8074

Series

12345

Pressure, bar 2.5 3.2 4.0 6.0 10.0

Table 1.8. Classiﬁcation system for PE

Type of

material

Maximum operating pressure, bar g

Water Industrial

SDR11 SDR17 SDR11 SDR17

PE 80 12.5 8.0 10.0 6.0

PE 100 16.0 10.0 16.0 10.0

Pressure transients in water engineering

Polypropylene (PP) may be used for higher-temperature applications,

e.g. normal service temperatures up to 808C and even 1008C with a

reduced life. The same jointing techniques apply as for a polyethylene

pipe.

Speciﬁcations usually deﬁne wall thickness for a standard series of

pressure ratings, e.g. for PP (Table 1.9). ‘Alloys’ of thermoplastics

have also been used in pipe production. An example of this is the

Hepworth Industrial Plastics range of Hep3O mains which is

produced from three materials: chlorinated polyethylene (PE), poly-

vinyl chloride (uPVC) and acrylic derivatives. The objective is to

combine the tough ductile character of PE with the higher strength

of uPVC.

Composites of both thermoplastics and thermosets have been used,

such as Permastran which is made up of a PVC core overlaid with

continuous rovings of ﬁbreglass bonded with epoxy resin. The ﬁbreglass

ﬁbre provides Permastran with its hydrostatic strength while the PVC

provides a corrosion-resistant core. For a pipeline designed for

maximum working pressure of 350 psi a safety factor of 2 would be

provided and a maximum of 350 þ42 psi would be allowed for surge

pressures.

1.11 Failure modes of pipes

An understanding of pipe strength and deformation limits is necessary

to prevent premature failure. Two main forms of failure are collapse and

brittle failure. Brittle fracture is a phenomenon in which a long, fast

brittle crack runs along the pipeline in a characteristically wavy

manner. Susceptibility of thermoplastics to this is dependent upon

material and principally hoop stress. Brittle fracture in uPVC follows

the slow growth of a crack from a defect or region of different mechan-

ical properties. A conservative 0.5% hoop strain limit will avoid brittle

fracture over a 50-year life.

Table 1.9. Wall thickness and pressure ratings for PP

Class

AB CDE

Pressure, bar 3 6 9 12 15

Motivation for hydraulic transient analysis

1.12 Maximum pressure and allowable amplitude of surge in

plastic pipes

Unlike other materials, plastic pipes generally have no overpressure

allowance and the maximum sustained allowable pressure is also the

peak transient pressure. In addition some thermoplastic pipes have a

restriction placed upon the amplitude of pressure change experienced

during a transient event where this can be considered detrimental to

the life expectancy of the pipe. Typically for PVC and PE this amplitude

restriction has been set at half maximum sustained working pressure.

Since thermoplastic pipe materials have a lower strength than other

materials such as DI and steel, thicker walls are used to compensate.

The diameter of pipe available at higher pressure will also be more

limited. The typical life of these pipes has been set at 50 years by manu-

facturers although this is conservative.

1.13 Minimum pressures

As far as low or underpressures are concerned matters can be more

complicated. First there is the matter of possible damage to the pipe

to be considered. Thin-walled pipes, especially those having a relatively

small deformation modulus, may be at risk of collapse due to buckling as

a consequence of a lower pressure within the conduit than that external

to the pipe.

Fatigue damage may also occur and ovalization of a ﬂexible pipe can

also cause high stresses in the pipe wall. For ﬂexible conduits the shape

of cross-section may deviate from an original circular form. This process

of ovalization can increase over time and with falling pressure resulting

in reduced pipe stiffness. This aspect is considered in more detail in

Chapter 22.

Under sub-atmospheric conditions gas can evolve from solution with

potentially adverse consequences. Collapse of gas- or vapour-ﬁlled

cavities may possibly result in overpressures. It has also been reported

by Glass (1980) that evolution of certain gases from solution in

contaminated water could be responsible for promoting attack by

sulphate-reducing bacteria on the interior of a bitumen-lined steel

pipe in the same way as anaerobic corrosion is known to affect the

exterior of pipes.

A second consideration relates to the nature of the liquid being

conveyed. Codes of practice recommend that where treated water is

being carried then positive pressures should be maintained within the

pipeline system to avoid risk of contamination. Piezometric level

Pressure transients in water engineering

within the pipeline should be above possible groundwater levels and

also above the operating levels of any air valves which may be

present. By maintaining internal pipeline pressure at or above these

levels any leakage will be from inside the system to outside, thus

avoiding the possibility of contamination by groundwater. By keeping

minimum piezometric height above the operating level of any air

valve, the possibility of ingress of contaminants via the valve is also

avoided. A minimum pressure head of around þ2 m water gauge

(mWG) measured from the crown of the pipe may be an appropriate

minimum to adopt in many circumstances. Where the pipe is deeply

buried, this minimum may be raised, again to ensure that internal

pressure always exceeds external pressure from groundwater.

1.14 When is analysis necessary?

The questions are sometimes asked, ‘under what circumstances is an

analysis required and is there a convenient checklist which can be

applied?’ Each pipeline system is typically unique, having its own

characteristics deﬁned by topography, ﬂows and other factors. It is not

possible to be deﬁnite in saying that a speciﬁc scheme does not require

any ana lysi s. Caution would suggest that some form of study be car ried

out, even if not a detailed computer analysis. In the past, guidelines

have been laid down to identify these pipeline systems at risk and in

need of detailed examination. One such is the ASCE (19 75) two-stage

checklist. Looking through the categories of pipeline included one might

get the impression that the large majorit y of systems require investigation.

Rather than essentially duplicating the list provided by the American

Society of Civil Engineers, some comments will be made. The increased

availability of programs and their ease of use, allow a pipeline to be

studied quite quickly.

Only for very straightforward systems can an analysis be avoided. For

instance, a short, simple line operating under low head and with rela-

tively low velocities might be exempt from an initial study, except

where the issue of sub-atmospheric pressures could be problematic,

i.e. risk of pipe collapse. During commissioning there is an opportunity

to measure transient pressures and introduce any protection which may

be required. Increasing concern over water quality and the avoidance of

vacuum pressures has made it necessary to study pipeline systems where

simply pipe strength considerations might have made the need for

analysis less important. The earlier checklist did not include liquid

quality considerations.

Motivation for hydraulic transient analysis

Longer pipelines, parallel lines of differing characteristics, branching

and looped systems should all be studied. Pipelines containing inter-

mediate features such as valves, booster pumps and tanks require

investigation. Particular attention should be paid to higher head

systems or schemes where velocities are large. Where air valve opera-

tion is possible or fast-acting valves are present, study of behaviour is

essential. Where water quality is a factor, analysis is also considered

necessary.

Pressure transients in water engineering

Derivation of basic equations

Two basic methods of analysis have been used extensively in the inves-

tigation of unsteady ﬂows in pressure conduit networks. The simplest of

these has the assumption that the ﬂowing liquid is incompressible and

that the conduit walls are rigid or inelastic. This method is sometimes

known as the rigid-column analogy and has been widely employed in

the analysis of longer-period oscillations such as occur in low-pressure

tunnels of hydropower networks.

The second approach considers the liquid to be compressible and the

conduit walls to be deformable resulting in a variation of ﬂow along the

pipeline or tunnel at any instant. This ‘elastic’ approach coupled with

the large computing power and memory of modern desktop computers

has the potential to reproduce both high-frequency and longer-period

aspects of hydraulic transients in a way that was hitherto not possible.

2.1 The rigid-column approach

In this approach, as generally with the elastic analysis, it is assumed that

the head loss relationships that apply under steady ﬂow conditions are

also valid during a transient event. Resistance laws for pipe ﬂow can

thus be used to represent head loss along a main. Representing a

liquid-ﬁlled pipeline as a rigid body means that any change in velocity

imposed at one end of the line is instantaneously experienced

throughout the main.

An equation describing the relationship between ﬂow and head can

be obtained by considering the elementary system of Fig. 2.1. A simple

pipeline is shown of diameter D, cross-sectional area A and length L.

Liquid of density  ﬂows into the pipeline from an upstream reservoir

passing through a valve at the downstream end of the main. Consider