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

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272

600 mm square pipe

support block

25 mm grout

under baseplate

75 mm thick grade

C25 concrete as

blinding

900

500

390 mm high

value support

block

1600

800 mm

810 mm high pipe

support block

Visqueen D.P.M.

H. wheel

Wall thickening around

puddle pipe

300

54.600

54.300

49.430

48.129 IL

T.O.C.

54.725

C.L. 51.900

50.200 m

For details of access

platform see Record

DRG. No. 7

54.600

51.330

53.435

54.775

53.527

Fall

Soffit 54.400

Item 6

1000

49.200

48.239

T.O.C.

Fall

54.400

400

550 600 280

333

1118

2621

TWL 53.400

(See detail)

Item C

Open

Varies (45.630–48.480)

1600

400 mm valve

support block

48.854

49/915

T.O.C.

D13.

D18.

D24

300

500

D14.

D11.

D15.

Fig. 15.11. Elevation of feeder tank

273

Fig. 15.12. Feeder tank chamber under construction

Fig. 15.13. Inlet to feeder tank under construction

Feeder tanks or volumetric tanks

274

Predicted level

Observed level

Time (s)

Level (mAOD)

53.6

53.4

53.2

53.0

52.8

52.6

52.4

52.2

52.0

0.335

31.825

63.315

94.805

126.295

157.785

189.276

220.767

252.257

283.747

315.236

346.725

378.214

409.703

441.193

472.682

504.171

535.662

567.154

598.646

630.138

661.631

693.123

724.615

756.107

787.599

819.091

850.583

882.075

913.567

945.059

Fig. 15.14. Feeder tank water level after pump trip

1 m

Trip of two pumps

Trip of three pumps

1 min.

Fig. 15.15. Unsatisfactory feeder tank behaviour after pump trip

Pressure transients in water engineering

check valve closure occurred relatively abruptly, causing a sudden

reduction of ﬂow into the tank as ﬂow was then forced through the

smaller ﬁlling connection. This sudden ﬂow deceleration would produce

additional surge effects in the pipeline.

Feeder tanks, by their nature, are located some distance from pump-

ing stations but still require regular inspection and maintenance if they

are to fulﬁl their function. When work is being carried out on a feeder

tank, the isolating valve will be closed and hydraulic transient investi-

gations should be carried out to establish a safe pumping rate while the

tank is out of service.

A further notable effect of the feeder tanks in this installation was to

inﬂuence the peak heads at the pumping station. Figure 15.17 shows

predicted piezometric level at the pumping station after pumps were

tripped. The ﬁrst upsurge after ﬂow reversal as the vessels reﬁll is

quite modest. At this stage the feeder tanks are supplying water to

the vessels, and head at this end of the pipeline system is largely

275

Short-term level change in feeder

before NRV closure

Short-term level change in

feeder before NRV closure

Trip of three pumps

Trip of two pumps

Fig. 15.16. Detail of feeder tank water level at commencement of reﬁlling

Feeder tanks or volumetric tanks

controlled by the water level in the feeder and by the inertia of the

relatively short length of main between the pumping station and the

feeder tanks. During the second and much higher upsurge, the feeder

tanks are reﬁlling and the head at their connections is much greater.

Also the inertia of the entire length of main is involved, leading to

the much greater head rise.

15.6 Aspects of feeder behaviour to consider

It is important that any simulation be of sufﬁcient duration that the

complete picture of transient behaviour is established.

The capacity of feeder tank necessary can be quite sensitive to the

pipeline route and it may be worthwhile to consider some alternative

pipeline proﬁles in order to reduce the required capacity of feeder.

One of the examples discussed considered alternative alignments and

the resulting effects upon volumetric tank volume.

Reﬁlling of the feeder is usually accomplished through reversed ﬂow

in the pipeline system downstream of the tank although on occasion it

may be necessary to rely upon restarting of pumping to complete the

reﬁlling process. Filling is accomplished through a smaller-diameter

connection usually ﬁtted with a valve which closes in response to

rising water level in the tank. The check valve on the outﬂow connec-

tion closes as ﬂow starts to re-enter the tank, forcing water through the

more constricted ﬁlling connection which discharges above top water

276

Second upsurge while

the feeder is re-filling

Elevation (mOD)

Time (min.)

1 2 3 4 5 6 7 8

Steady pumping level

First upsurge

controlled by feeder

Fig. 15.17. Head variations at pumpi ng station following pumping failure

Pressure transients in water engineering

level. Flow resistance acts to throttle inﬂow thus limiting magnitude of

reversed ﬂow and assisting to prevent secondary pressure transient

effects developing when inﬂow ceases. The inlet valve shuts progres-

sively as tank water level rises, with ﬂow decelerating gradually to

avoid occurrence of secondary transients. Figure 15.14 shows a record

of correct feeder tank water level behaviour during both outﬂow and

inﬂow.

Feeder tanks are usually installed at some distance from a pumping

station and not subject to daily inspection. A prolonged interval

between inspections carries the risk of malfunction. Figure 15.15

shows a recording of water level in a malfunctioning feeder tank

during outﬂow and inﬂow. Surface waves were recorded at the start

of outﬂow and when ﬂow began to re-enter the tank. These waves

were the consequence of a delay in response of the outﬂow check valve.

15.7 Preliminary estimation of feeder tank volume

There are two aspects to establishing an initial estimate of the required

chamber volume. Continued ﬂow into a downstream pipeline when the

feeder has come into operation will draw water from the tank. If an

upstream pumping station is equipped with a pressure vessel for

instance then this vessel will require to be reﬁlled following the down-

surge which results from a pumping failure. Vessel reﬁlling occurs after

ﬂow reversal in the pipeline between the pumping station and the

feeder tank. Depending upon relative rates of deceleration of ﬂow

within the pipelines upstream and downstream of the feeder tank,

vessel reﬁlling may commence while the feeder is still supplying water

to the downstream pipeline or alternatively vessel reﬁlling may not

start until ﬂow reversal has taken place in the downstream pipeline.

In the ﬁrst instance the feeder is required to supply water both to the

upstream and downstream pipelines. Vessel reﬁlling water comes from

the feeder in this case. If ﬂow has reversed in the downstream pipeline

before the vessel starts to reﬁll then reﬁlling water comes from the

downstream pipeline to some extent.

Equation (17.9a), developed for estimation of buffer tank volume,

may also be used to estimate the volume of a feeder tank.

Vol

max

=Vol

¼ D=ðfLÞlnf1 þ hf=zgð17:9bÞ

In this case Vol

max

is the volume of feeder tank water supplied to the

downstream pipeline and Vol

is volume of the downstream pipeline.

D, L and f are respectively the diameter, length and overall friction

277

Feeder tanks or volumetric tanks

factor of the downstream pipeline. The friction factor includes an

allowance for losses in the outﬂow connection of the feeder. hf is

the pipeline resistance loss during steady ﬂow along the downstream

pipeline and z is the level difference between the feeder tank and the

discharge level downstream.

When it is considered necessary to include vessel reﬁlling volume,

the equations derived in the Appendix to Chapter 12 could be used

or alternatively any of the graphical methods. As an example, equation

(A12.5a) might be used. For simplicity, this equation ignores the effect

of pipeline resistance.

Vol

=Vol

¼ V

=ð2gÞ=fzð1  h

=zÞþh

lnðh

=zÞg ðA12:5aÞ

In this equation Vol

is the maximum expanded gas volume in the

vessel, Vol

is the volume of pipeline upstream of the feeder tank,

=ð2gÞ is the kinetic energy of ﬂow, z is the head difference between

the vessel and the feeder and h

is the absolute minimum head in the

vessel. Subtracting from Vol

an estimate of minimum volume during

the return upsurge will yield the required volume of reﬁlling water.

Minimum volume during the reﬁlling upsurge cannot be deﬁned with

any precision. For instance, in Fig. 15.17 two reﬁlling phases are

shown. The ﬁrst more modest upsurge occurs while outﬂow was still

occurring from feeder tanks and with the head at the pumping station

strongly inﬂuenced by the feeder tank water level. The second and

larger upsurge takes place when the feeders are reﬁlling and so is not

relevant as far as estimating volumes abstracted from the feeder

tanks. An estimate of peak pressure during the ﬁrst upsurge could be

used to establish a minimum gas volume at this point and this would

then be subtracted from maximum expanded gas volume to obtain a

required reﬁlling volume.

278

Pressure transients in water engineering

Discharge conditions

The discharge arrangement of outlets from a pressure pipeline system

can have a signiﬁcant bearing upon the behaviour of pressure transi-

ents, especially during later stages of an event when ﬂow has reversed

in parts of the network. While not necessarily inﬂuencing an initial

downsurge following pumping failure for instance, subsequent events

can be materially affected. One example concerns the ability of the

downstream limits of a pipeline to provide liquid for expelling air

from the pipeline or to reﬁll an upstream pressure vessel. Some typical

examples of outfall conﬁgurations are given together with a description

of their inﬂuence on events elsewhere in a system. Examples of time-

dependent behaviour are provided in some cases.

16.1 Vertical bellmouth

A simple and common conﬁguration at the downstream end of a pumping

main is shown in Fig. 16.1. Normally ﬂow enters the receiving reservoir via

the vertical bellmouth exiting at or above top water level (TWL) in the

tank. When water level in the chamber is below the discharge elevation

of the bellmouth it cannot inﬂuence static head of the pipeline system,

but rather system head is dictated by the bellmouth elevation.

Suppose ﬂow reverses during a transient event with TWL below the

bellmouth exit elevation. The relatively small diameter and storage

capacity of the vertical pipe extending to the bellmouth will permit

head to fall quite rapidly within the pipe. Changing water level and

piezometric level H in the ﬁlling connection will be governed by

equations (16.1) and (16.2):

dH=dt ¼ AV and V þ g=aH ¼ Jþð16:1Þ

279

where A

is area of the air—water interface in the connection and A is

the rising main cross-sectional area. If water level reaches the rising

main level then:

¼ A=sin ðÞð16:2Þ

Depending upon the magnitude of a reversed velocity and its duration,

the vertical pipe may empty of water and air will start to enter the

upstream pipeline. Where the reversing ﬂow is being used to expel sub-

stantial air pockets at upstream air valves or to reﬁll a pressure vessel or

volumetric tank, the volumes required may be substantial. This can

lead to correspondingly large air volumes within the pipeline upstream

of the outfall and reduced piezometric level over downstream parts of

the system. A case study illustrating this aspect of behaviour may be

found in section 16.5 of this chapter. Such low pressures are undesirable

from a water quality standpoint as ingress of groundwater is a possibility.

If little or no reﬁlling water is required then it is likely that the

duration of reversed ﬂows will be modest and emptying of the vertical

pipe may not occur.

16.2 A tank or chamber of ﬁnite area

The case of a large reservoir effectively with surface area ¼1has been

considered in Chapter 6 on boundary conditions. When surface area is

280

Common horizontal datum

Piezometric level during filling

TWL

BWL or LDO

Drawoff

Piezometric levels

during reversed flow

Fig. 16.1. Vertical bellmouth ﬁlling arrangement

Pressure transients in water engineering

more modest, as where a tank is being ﬁlled or where ﬂow is entering a

discharge chamber (Fig. 16.2), variations in level are more important.

In both of these cases the changing liquid surface level in the tank or

chamber has a direct inﬂuence upon the prevailing static head

operating. This boundary can be represented by the equation:

dH=dt ¼ VA

 Q

out

ð16:3Þ

where A

is the surface area of the chamber, A

is the cross-sectional

area of the inlet pipe and Q

out

is the outﬂow (if any) from the tank.

If H > sewer invert then Q

out

¼ fnðHÞ and if H < sewer invert

out

¼ 0:0. In addition there is the quasi-invariant value reaching

the tank at the time of interest along a Cþ characteristic, thus:

V þ g=aH ¼ Jþ

Setting H=t ¼ dH=dt and averaging over the time increment t

then:

H=t ¼ðV þ V

ÞA

=2  Q

out

281

out

Common horizontal datum

Rising main

Minimum level

Manhole or

discharge chamber

While filling

or emptying

During steady

flow

Gravity sewer

Variable piezometric level

Fig. 16.2. Chamber connection with gravity ﬂow outlet

Discharge conditions