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

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Pump power requirements are correspondingly smoothed by this

approach. Figure 10.21(b) shows typical output from either a double-

acting single cylinder or single-acting twin cylinders. Figure 10.21(c)

shows ﬂow from a three-cylinder single-acting unit. Built-in accumula-

tors (small air cushions) are often included on suction and delivery

branches as a means of smoothing ﬂow. Behaviour of air vessels is

discussed in Chapter 12.

Using the turbine pump form of performance curves of head and

power against ﬂow for these pumps produces almost vertical gradients

and for practical use it is more convenient to use curves of ﬂow and

power as a function of head as illustrated in Fig. 10.22.

10.10.2 Pneumatic ejector

For sewage applications involving small ﬂows and requiring the

capability to pass solids of up to say 100 mm diameter it is not practical

to make a centrifugal pump capable of meeting both of these criteria.

One solution is to use a pneumatic ejector, the main components of

which are shown in Fig. 10.23. A compressor delivers air to a receiver.

Sewage ﬂows enter via gravity sewers to collect in ejector cylinders. A

ﬂoat is located in each cylinder and when this ﬂoat rises to a deﬁned

level the air inlet valve to that cylinder opens to allow air to enter

thus pressurising the contents of the cylinder. When sufﬁcient pressure

has developed to overcome pressure in the outlet pipeline system then a

non-return valve opens automatically to permit discharge of the ejector

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Power P against head H

Flow Q against head H

P and Q

Fig. 10.22. Performance curves for displacement pumps. (Performance curves of

turbine-type pumps are not convenient due to steepness of H—Q and P—Q

curves)

Pressure transients in water engineering

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Check valve

Air vent pipe

Compressed

air receiver

Inlet gravity sewer

Check valve

Air compressor

Compressed air

supply pipe

Discharge

pressure pipe

Isolating valve

Ejector cylinder

Elevation

Plan

Check valve

Isolating valve

Inlet gravity sewer

Air exhaust pipe

Air supply pipe

Discharge

pressure pipe

Fig. 10.23. Components of ejector station

Pumps

cylinder contents to the downstream pipeline system. Twin cylinders

are often provided with one ﬁlling while the other is discharging.

Usually one compressed air system supplies both cylinders. Overall efﬁ-

ciency will typically be in the range 20—50%. Ejector stations are

designed to handle ﬂows from isolated premises or groups of houses at

inﬂow rates of between 1 litre/s to 10 litres/s at delivery heads of up to

a maximum of about 30 mWG.

Each operation of an ejector cylinder will produce a transient within

the downstream pipeline system. Ejectors are normally rated according

to the size of cylinder, for example 150 litres, 250 litres. Discharge

normally will be completed in around 60 s so that corresponding

average ﬂow would be 2.5 litres/s or 4.2 litres/s. Actual discharge rate

may well exceed these values, possibly reaching twice the average, i.e.

5.0 litres/s or 8.4 litres/s, if the air supply is generous. In a DN 100

rising main this would produce a velocity change of 0.6—1.1 m/s and

a corresponding inertial pressure rise.

It is not uncommon to ﬁnd several ejector stations teed into a rising

main which also acts as a collector pipeline for these stations. Each time

an ejector operates it will induce a pressure transient within the rising

main. The ﬂow rate from the ejector will be dependent to some

extent upon the piezometric level in the rising main. Figure 10.24

illustrates this situation with ﬂow from the pumping station into the

rising main.

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Datum

u/s

dx/dt = V – a

dx/dt = V + a

d/s

Pressure waves travelling upstream and downstream

from ejector connection

Steady flow piezometric line

Pumping station

ector station connection

Collector/rising main

Fig. 10.24. Operation of an ejector station on a sewage rising main

Pressure transients in water engineering

If the discharge from the ejector is Q

then with reference to Fig. 10.24

the equations required for solution at the ejector connection are:

from characteristics

Jþ¼V

u=s

þ g=aH and J¼V

d=s

 g=aH

and from conservation of volume

u=s

A þ Q

¼ V

d=s

eliminating V

u=s

and V

d=s

then,

H ¼ðJþJþQ

=AÞ=ð2g=aÞð10:11Þ

To obtain an idea of the magnitude of the inertial pressure rise caused

by an ejector, assume that there is no time for wave reﬂections to occur

prior to the maximum discharge from the ejector being achieved. Then

if Jþ and J remain at their initial steady ﬂow values, the initial head

at the ejector connection before discharge Q

occurs will be:

¼ðJþJÞ=ð2g=aÞ

and when the maximum discharge from the ejector is Q

max

, maximum

head will be:

max

¼ H

þ Q

max

=ð2Ag=aÞ

or peak inertial head

H ¼ Q

max

=ð2Ag=aÞð10:12Þ

Suppose Q

max

¼ 5 litres/s, D ¼ 300 mm (A ¼ 0:0707 m

) and a ¼

1000 m/s. The maximum inertial head increase will be:

H ¼ 0:005=ð2  0:0707  9:81=1000:0Þ¼3:6m

In a smaller main, say D ¼ 200 mm,

H ¼ 0:005=ð2  0:0314  9:81=1000:0Þ¼8:1m

The smallest sewage rising main may have diameter D ¼ 100 mm

giving: H ¼ 0:005=ð2  0:00785  9:81=1000:0Þ¼32:4m.

In a plastic rising main these inertia head values would be reduced

proportionately for the smaller wave speed in these pipes.

10.10.3 The hydraulic ram

This pump is an example of a device which produces a hydraulic

transient for the purpose of lifting water to a higher level. The

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Pumps

principle of operation may be illustrated with reference to Fig. 10.25.

The supply pipeline has to have sufﬁcient length and diameter that a

worthwhile amount of kinetic energy is contained within the ﬂow,

typical lengths being between 5 and 20 m. The air vessel is located

from 0.5 to 3 m below the water surface in the supply reservoir and

the difference in level between the supply reservoir and the waste

valve can be up to 6 m. If the waste valve is suddenly closed the

water column in the supply line is rapidly decelerated with an atten-

dant pressure rise. This rising pressure pushes upon the non-return

delivery valve, allowing ﬂow to enter the air vessel and pressurise this

chamber, causing ﬂow to pass through the riser pipe into the elevated

storage tank. Once ﬂow in the supply line comes to rest and starts to

reverse, pressure below the delivery valve falls and this valve closes.

Falling pressure can also be used to reopen the waste valve allowing a

further cycle of operation to commence. Overall efﬁciency of the

process is around 50%.

The hydraulic ram has been described as an hydraulic transformer

converting low pressure into high pressure.

10.10.4 The jet pump

Jet pumps or injectors operate by transference of momentum from a

high-velocity jet of ‘motive’ ﬂuid to a ‘pumped’ ﬂuid medium within a

mixing tube (Fig. 10.26). A jet pump may be installed in a borehole

with a centrifugal pump at the surface providing the motive force for

the jet pump.

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Supply

reservoir

Air vessel

Supply pipeline

Fast-closin

valv

Non-return valve

Header tank

Riser

Fig. 10.25. Schematic of hydraulic ram

Pressure transients in water engineering

The performance of this unit is described using two quantities. The

relationship between pumped mass ﬂow and motive mass ﬂow is

called the ﬂow coefﬁcient q, thus:

q ¼ 

=ð

Or in the case where water comprises both motive and pumped media:

q ¼ Q

ð10:13Þ

the pressure or head relationship Z for a jet pump can be deﬁned as:

Z ¼ðH

 H

Þ=ðH

 H

Þð10:14Þ

Efﬁciency of the pump  is then:

 ¼ qZ ¼ Q

ðH

 H

Þ=½Q

ðH

 H

Þ ð10:15Þ

Performance curves for a pump of this type may have the form shown

in Fig. 10.27. In any analysis there are ﬁve unknowns: H

, H

, Q

and Q

. The equations available for solution at any time comprise three

characteristic equations, the head relationship and the ﬂow coefﬁcient

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Piezometric levels

Pumped fluid

Mixing tube

Diffuser

Motive fluid

Nozzle

Common horizontal datum

+ Q

Fig. 10.26. Principles of a jet pump

Pumps

relationship. These are sufﬁcient to yield values of the dependent

variables after each time increment.

When the jet pump is without moving parts it will merely act to

partially transmit and reﬂect transients developed elsewhere in the

pipeline system and does not of itself initiate any pressure transient

effects. Some jet pumps are ﬁtted with a control valve, usually in the

form of a needle valve, which can be used for discharge regulation.

Should the valve setting be adjusted then the jet pump will initiate a

transient event.

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Z–q

h–q

h, Z

Fig. 10.27. Performance curves for a jet pump

Pressure transients in water engineering

Flywheels

The concept of a reservoir of energy, however modest, being stored in

the rotating elements of a pumpset was established in the previous

chapter. The present section develops this idea as a means of surge

suppression by considering how the amount of energy, contained

within the rotating pump system, may be enhanced to improve the

ability to control rates of ﬂow and pressure change at the pump after

it is tripped.

The rate of change of velocity at a pump determines the severity of

the hydraulic transient developed when the pump is started or

stopped. During start-up the changes in velocity will be controlled by

the mode of starting and to some extent any surge problems associated

with pump start can be designed out by an appropriate choice of starting

method. For instance, if rates of velocity increase produce unacceptable

surges then a ﬂow control valve may be a possible remedy. This valve

can be used to regulate the way in which ﬂow rate is allowed to

develop. During a ‘normal’ pump shutdown under either automatic or

operator control, the rate of deceleration of ﬂow can again be

controlled. In the event of a power failure, on the other hand, the

pump speed and also pump discharge will reduce in a manner controlled

by the characteristics of the pumpset, liquid and pipeline system. The

only source of energy remaining to allow pumping to continue is that

stored within the rotating elements of pump, shafting and motor.

11.1 Moment of inertia

The stored energy E ¼

in the rotating elements of a centrifugal

pump installation is dependent on the moment of inertia I ðkg:m

for a given speed of rotation ! (rad/s). As the pump decelerates

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following a pumping failure, energy is transferred to the water from this

store of energy. Increasing the moment of inertia is an obvious way in

which the amount of stored energy can be increased. After a pump is

tripped, this additional energy in the rotating elements can be used

to prolong pumping thus reducing rate of ﬂow deceleration dV=dt

and with it the severity of pressure transient effects. This increase of

moment of inertia can be achieved by adding a ﬂywheel to each

pump/motor shaft. Shearing of the shaft between ﬂywheel and pump

impeller will render the ﬂywheel ineffective.

11.2 Flywheels

The ﬂywheel consists of one or more metal disks rotating on the same

shaft as the pump and motor and with the same speed. Figure 11.1

shows a typical installation for a vertical pump.

On the delivery side of a pumping station after pump failure, the rate

at which head decreases and ﬂow decelerates is reduced by adding

additional inertia. In the case of a booster station, on the suction side

of the station, rate of head rise and rate of ﬂow deceleration are also

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Shaft to electric motor

Upper bearing

Flywheel assembl

Lower bearing

Coupling

Shaft extending

downwards to pump

Fig. 11.1. Flywheel installation

Pressure transients in water engineering

reduced by adding a ﬂywheel. After ﬂow has ceased and the check valve

on each pump delivery branch has closed, the pump/ﬂywheel arrange-

ment plays no further part in the transient event in a rising main. The

ﬂywheel may have been added for the purpose of controlling either

minimum or maximum transient pressures in the main. Where peak

pressures are to be controlled then these will arise as a consequence of

deceleration of a reversed ﬂow which has occurred subsequent to the

initial downsurge following pumping failure. The only way in which the

ﬂywheel can limit such maximum pressures is by previously controlling

these initial minimum piezometric levels. The adverse hydraulic gradient

producing ﬂow deceleration and accelerating ﬂow in the reversed

direction in the main is thus limited. So it is only by limiting the

initial downsurge that the subsequent upsurge is controlled.

The ﬂywheel forms an integral part of the pumpset assemblage and it

is speed change of the machine that initiates the transient event. By

adding the ﬂywheel the rates of speed change are reduced and the

pressure transient is controlled at its source. The entire system beneﬁts

from the ﬂywheel solution. This contrasts with some other forms of

surge alleviation in which the hydraulic transient is allowed to

develop and its subsequent spread through the majority of a pumping

system is restricted by additional surge equipment. Reducing rates of

velocity change at the pump itself gives check valves time to respond

thus reducing potential for valve slam. The same applies during pump

start if the ﬂywheel means that a slower acceleration of pump occurs.

The check valve will not then be thrown open.

This form of hydraulic transient suppression also has the advantage of

ease of maintenance.

Where a gearbox is included, relative speeds of pump and motor

require to be considered (Miller, 1978). Resultant inertia is expressed

in terms of pump speed so that

I ¼ I

imp

þ I

shaft

þ I

motor

pump

11.3 Limitations on ﬂywheel size

Sometimes the size of ﬂywheel which can be added is limited by one or

more factors. The extent to which inertia can be increased is usually

determined by capability of the motor and starting equipment. Limita-

tions on the power of motor that can be operated using direct-start

means have already been mentioned in Chapter 10. To illustrate the

potential limitation of the ﬂywheel solution, in one Middle East

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Flywheels