Pressure Transient

Pressure transient identification of depleted appliancetrap seals: a pressure pulse techniqueDA Kelly BEng, JA Swaffield BSc PhD FCIBSE, LB Jack BEng PhD MCIBSE, DP CampbellBA PhD and M Gormley MSc MPhil PhD MCIBSE

Drainage Research Group, School of the Built Environment, Heriot-Watt University, Edinburgh, UK

The appliance trap seal plays a vital role in safeguarding occupied space from ingress of foulsewer gases driven by the barrage of pressure transients generated within the system duringnormal appliance discharge. The health risks related to depleted trap seals can be severe.In 2003, the rapid spread of the SARS virus at the Amoy Gardens housing complex inHong Kong was attributed to depleted bathroom floor-drain traps.This paper presents a technique whereby depleted trap seals can be located remotely bymonitoring the system response to an applied single pressure pulse. A Method ofCharacteristic based numerical model allows the system pressure response to be predictedwhile laboratory and site test results are shown to validate this proposed technique.Practical application: Appliance trap seal depletion poses a serious health risk byproviding a route for cross-contamination and infection spread. Implementing a routine andregular maintenance regime would help to ensure that the water level within the trap sealremains above the critical level. However, current methods rely on visual inspections whichare highly impractical in large complex buildings. A technique allowing the status of allconnected trap seals to be quickly determined would be an invaluable tool for facilitymanagers by improving operational efficiency and by indicating persistent failures, thus,highlighting areas requiring modification to ensure performance compliance.

List of symbols

A Flow cross-sectional area (m2)

c Wave propagation speed (m/s)

CJ Compliance factor

CR Boundary reflection coefficient

CT Boundary transmission coefficient

Cþ, � Characteristics in x–t plane

D Pipe diameter (m)

f Friction factor

F( ), f( ) Pressure waves

K Loss coefficient

L Pipe length (m)

mSp System response data

(mmwater gauge)

N Number of pipes, nodes or defect

p Airpressure (mmwatergauge,N/m2)

Q Flow rate (m3/s)

t Time (seconds)

T Pipe period (seconds)

�t Time step (seconds)

�x Internodal length (m)

� Density (kg/m3)

u Mean air flow (m/s)

� Poisson’s ratio

� Ratio of specific heats

Subscripts

actual Recorded data

appliance Appliance side

Address for correspondence: DA Kelly, School of theBuilt Environment, Heriot-Watt University, Edinburgh,EH14 4AS, UK.E-mail: [email protected] 1, 2, 5–7, 9 and 10 appear in colour online: http://bse.sagepub.com

Building Serv. Eng. Res. Technol. 29,2 (2008) pp. 165–181

� The Chartered Institution of Building Services Engineers 2008 10.1177/0143624408090202

atm Atmospheric conditions

local Conditions at node

m Monitoring location

piston Piston conditions

P,R, S Nodes inMoC calculation

System System side

Trap Trap conditions

D Defect

J Defect number

tþ�t, t Conditions at node at a time

1, 2,N Nodes

1 Introduction

The fundamental purpose of the buildingdrainage and vent system is to rapidly removeappliance discharge while simultaneouslyensuring that foul air from the drainage net-work is prevented from entering occupiedspace. The primary defence against cross-contamination is provided by the appliancetrap which, provided the water seal is retai-ned, prevents the ingress of sewer gases intothe building. Appliance trap seal retention hasdominated the development of building drain-age systems since the 1850s, dictating theinclusion of ventilation pipes and active con-trol devices, such as air admittance valves andvariable air volume containment devices,which aim to reduce the effects of air pressuretransients created by normal system opera-tion.1 Trap seal depletion, however, remainsa major issue and when coupled with addi-tional causes of depletion such as evapora-tion, poor maintenance and bad design, thepotential risk of cross-contamination andinfection spread becomes a serious concern.

The consequence of trap seal depletionwas realised in 2003 following the outbreakof the SARS virus which infected 8098people worldwide, resulting in 774 deaths.2

An unusually high number of cases werereported at the Amoy Gardens housingcomplex in Hong Kong where a total of

321 residents were infected. The cause of thislarge community outbreak has since beenattributed to oversized bathroom extract fansand depleted trap seals.3 The operation of theextract fan created a negative pressure withinthe bathroom capable of drawing virus-richfaecal droplets from the drainage networkinto the habitable space via the open pathcreated by the dry trap seal. Further contam-ination occurred as the infected faecal dro-plets were then discharged to atmosphere viathe bathroom extract fan, exposing the virusto adjacent apartments and neighbouringbuildings. This route of infection spread hasbeen verified by post-event forensic analysisby the Hong Kong investigative team4 andby numerical simulation of the systemoperation.5

It is vital that a depleted trap seal is quicklylocated and replenished to ensure thatcross-contamination is minimised. Currentmethods rely solely on visual system inspec-tions and are wholly impractical and effec-tively impossible to undertake in largecomplex buildings. There is, therefore, anurgent need to develop a technique wherebythe conditions of all the appliance trap sealscan be determined using a remote and non-invasive methodology.

The technique detailed in this paper usesthe transient response to an applied low-amplitude pressure pulse to detect and locatean open trap seal. As a transient wave movesalong the system it will be reflected andre-transmitted by each boundary encounteredwhether a branch to stack junction, pressurecontrol device, stack termination or appliancetrap seal. The system response to such a tran-sient wave can be analysed to decipher impor-tant system information conveyed by changesin the pressure signal. The transmission andreflection coefficients of each boundarydetermine the shape of the resultant systemresponse. Any changes in boundary condi-tion will result in a change to the systemresponse.

166 Depleted appliance trap seal identification

Figure 1 shows the transient response of asingle pipe system to an applied positive pres-sure transient and demonstrates the changein system response to an open and closed end.The pressure traces are identical up to thetime when the reflected wave arrives at themonitoring station, at which point the closedend returns a þ1 reflection and the open endreturns a �1 reflection. This normal mode oftransient propagation6,7 can be utilised tolocate a depleted appliance trap seal as theopen trap is analogous to an open end andwill return a�1 reflection. Similar techniqueshave been developed to identify leaks in largewater supply networks.8,9

1.1 Using pressure transients to identify

a depleted trap

The time, t, taken for the generatedtransient to reach a system boundary is

given by:

t ¼L

cð1Þ

where L is the pipe length from the monitor-ing point to the system boundary and c is thewave propagation speed (around 320m/s forair in a pipe at ambient temperature).The time at which the reflection arrives backat the monitoring point is known as the pipeperiod, T, and may be defined as:

T ¼2� L

cð2Þ

Taking the example shown in Figure 1 itcan be seen that the þ1 and �1 reflections arereturned at t¼ 0.31 s and, therefore, yields apipe length of 50m. If a depleted trap existsat point D Figure 1, then the time that the

00 0.10.1 0.20.2 0.30.3 0.40.4 0.50.5 0.60.6 0.70.7 0.80.8 0.90.9 1 1.11.1 1.21.2

−200

−150

−100

−50

0

50

100

150

200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Pre

ssur

e (m

m w

ater

gau

ge)

LD L

D

Time (s)

Pipe period

Positive reflectionfrom closed end

Negative reflectionfrom open end

Pressuretransientgenerator

Pressuretransducer

LT

Closed End(CR=+1) orOpen End(CR=−1)

Note subsequentalternatingpositive and negative peaks

Closed endOpen end

Figure 1 Laboratory demonstration of the þ1/�1 reflection coefficients encountered at a closed or open end termination of a singlepipe system subjected to a pressure surge

DA Kelly et al. 167

negative reflection will arrive at the monitor-ing point from the open trap will be:

TD ¼2� LD

cð3Þ

where TD and LD are the pipe period of, andthe distance to, the depleted trap respectively.Therefore, Equation (3) can be used to locatea depleted appliance trap seal (or any changein system boundary condition) provided thearrival time of the reflection is known.

2 Identification of system conditionsusing numerical analysis

A numerical method, similar to that used tolocate leaks in large scale water distributionnetworks9 will be applied to the recordedsystem response. The Compliance Factor, CJ,will be used to measure the closeness of fitbetween a system test response and that of apreviously measured or simulated database.For a system with N appliance trap seals, thedatabase can be generated by firstly measur-ing the response of the system, at location m,with no depleted traps (defect free system

denoted as 0) and then repeating for eachfailure condition by sequentially depletingeach of the traps. This will provide a full setof system responses, mSpJ¼1�N, from whichto build the database. The closeness of fitbetween any future test case, mSpactual, andthe database can be determined using a ‘leastsquares’ approach by summing the squares ofthe differences between the two:

CJ ¼Xnpointi¼1

mSpJ¼1�N �mSpactualð Þ2

ð4Þ

where npoint is the number of data points tobe compared within each trace, see alsoFigure 2. When the system test response cor-responds to a database trace, then the value ofCJ tends to zero. Thus, the matrix created byapplication of Equation (4) identifies the cor-rect system condition, whether it be defectfree or one of the failure cases, by returninga value of CJ which approaches zero.

3 Mathematical modelling

To model the propagation of low-amplitudeair pressure transients within the building

0

5

10

15

20

25

30

35

40

45

50

0 0.1 0.2 0.3 0.6 0.7 0.8 0.9 1

Pre

ssur

e (m

m w

ater

gau

ge)

Defect free (Database)Defective trap (Test set)

Time (s)

Cj=Σ(Database−Test set)2

0.4 0.5

Figure 2 Basis of the compliance factor calculation. The relative divergence of the test data from that of the database is determinedfor any particular trap seal failure


drainage and vent system, the acceptedMethod of Characteristics (MoC) solutionof the equations of continuity and momentummay be applied. The MoC solution was intro-duced by Lister,10 and was primarily appliedto large scale civil engineering ‘waterhammer’studies. Since then, this method has been fur-ther developed and has been applied to suchareas as aircraft refuelling and free surfacedrainage flows as well as to traditionalwaterhammer.11–13

The equations of continuity and momen-tum for the case of low-amplitude air pressuretransient propagation may be shown asfollows:14

Continuity: �@u

@xþ u

@p

@xþ@p

@t¼ 0 ð5Þ

Momentum:@p

@xþ �u

@u

@xþ �

@u

@tþ4fu uj j

2D¼ 0

ð6Þ

For low-amplitude air pressure transientpropagation, the density and pressure vari-ables are linked via the wave propagationspeed, c:

c ¼�p

�

� �0:5

ð7Þ

and, therefore, it is necessary to express theequations in terms of wave speed and fluidvelocity:

c2@u

@xþ

2

� � 1c@c

@tþ u

@c

@x

� �¼ 0 ð8Þ

2

� � 1ð Þc@c

@xþ

@u

@tþ u

@u

@x

� �þ4fu uj j

2D¼ 0 ð9Þ

This pair of quasi-linear hyperbolic partialdifferential equations may be solved via afinite difference solution when transformedvia the MoC into the finite difference relation-ships represented by Equations (10) to (13)that link conditions at a node one time step inthe future to current conditions at adjacentupstream and downstream nodes (Figure 3).

For the Cþ characteristics:

uP � uR þ2

� � 1cP � cRð Þ

þ 4 fRuR uRj j�t

2D¼ 0 ð10Þ

when

dx

dt¼ uþ c, ð11Þ

SRP

Boundary conditionsolved with C+

characteristic

Boundary conditionsolved with C−

characteristic

∆x

C−

∆t

C−C+ C+

Transient ReflectionEntry Exit

x +ve

Figure 3 Method of characteristics representation of air pressure transient propagation and reflection within a network branch

DA Kelly et al. 169

And for the C� characteristics:

uP � uS þ2

� � 1cP � cSð Þ

þ 4 fSuS uSj j�t

2D¼ 0 ð12Þ

when

dx

dt¼ u� c, ð13Þ

These equations are set in terms of the airmean flow velocity, u, at any section and thelocal wave speed, c, at that location. Thechoice of u and c, results from the inter-dependence of air pressure and density. As aresult it is necessary to determine pressure ateach node and each time step as:

plocal ¼patm�atm

� ��

c 2local

� �� 1= 1��ð Þ

ð14Þ

3.1 Simulating boundary conditions

Figure 3 shows the Courant Criterion,namely �t��x/(uþ c), that links internodaldistance to time step in terms of the airflowvelocity, u, and wave speed, c. It may also beseen that only one characteristic equation willexist at a pipe boundary, a Cþ at a termi-nation or a C� at an entry, introducing theneed for a boundary equation linking airflowconditions to applied water flow or othersystem parameters. Previous papers bySwaffield and Campbell14,15 established theconcept of system boundaries and introducedthe categories of active or passive to differ-entiate boundary types. Passive boundaries,e.g. pipe junctions or open and closed ends,are independent of time and the localunsteady flow regime while active boundaries,e.g. the operating characteristics of an airadmittance valve (AAV) or the displacement

of a trap seal, are based on time or anothervariable such as local pressure.

In the case of a junction of N pipes, someterminating and some originating at thejunction, there is a need for 2N equations tosolve for airflow and pressure at the first andlast nodes of these pipes. Note that pressure istaken as defined by wave speed throughEquation (14) and that initial flow velocityis assumed positive in the direction ofincreasing distance, x. In addition, continuityof flow:

XN

1Q ¼ 0 ð15Þ

and either the equivalence of pressure at thejunction, (N� 1) equations:

p1 ¼ p2 ¼ � � � pN ð16Þ

or a representation of the junction local loss:

p1 ¼ p2 þ K1�2Q21 ¼ � � � pN þ K1�NQ

21 ð17Þ

Together with the N characteristics providethe 2N equations required.

At an open termination to atmosphere theboundary condition to be solved with theavailable Cþ characteristic is represented byconstant pressure:

plocal ¼ patm ð18Þ

or some known external air pressure his-tory, e.g. wind shear over roof terminationsor pressurisation of the habitable space.Similarly, at a closed end the boundarycondition to be solved with either the availableCþ or C� characteristic is provided byputting the local airflow mean velocity to zero:

ulocal ¼ 0 ð19Þ

An AAV boundary depends upon the localair pressure at the branch to AAV interface.16


The boundary can therefore be zero velocityif the pressure is above the AAV openingpressure level. If the suction in the pipe issufficient to open the AAV, then the bound-ary equation is provided by the pressure lossthrough the valve at the flow rate and open-ing ratio, which in turn depends on local linepressure. The AAV boundary condition maythus be written as:

plocal ¼ patm � KlocalpQlocal Qlocal

�� ð20Þ

The value of the AAV loss coefficientKlocalp will vary – decreasing as the diaphragmlifts in response to greater suction pressuresuntil the valve is fully open and thereafterhaving a constant value.14

The boundary condition applicable for atrap seal is based on the application of theequation of motion to the seal water column:

plocal, tþ�t � ðpatm þ proomÞ

þ �gððHsystem �HapplianceÞ

� 0:5ðutþ�t þ utÞ�tÞ � Ltrap32�=D2trap

� �LtrapAptðutþ�t � utÞ=�t ¼ 0 ð21Þ

solved with the available Cþ (Equation (10)).This is inevitably an iterative solution as bothplocal,tþ�t and utþ�t are unknown, the veloc-ity term being defined by the Cþ character-istic (Equation (10)) coupled with the wavespeed pressure relationship (Equation (14)).Reference to Equation (21) illustrates theimportance of trap seal water retention. Themass of the trap seal water, represented inEquation (21) by the length of the watercolumn, Ltrap, is monitored at each time step.Obviously, suction in the system will result inwater loss as the system-side height, Hsystem,cannot exceed zero – water flows into thebranch depleting the trap.

Either suction or positive pressure can dis-place the water column so that an air path isformed through the trap as soon as the waterlevel on either side falls to the lowest point of

curvature of the trap. This failure condition isidentified by monitoring the trap seal lengthat each time step. Comparison with thegeometry of the trap allows the trap sealboundary condition to be modified to repre-sent a concentrated loss in either of thesecases. These cases are referred to as ‘bubblethrough’ trap seal failures and are difficult toidentify post-event as the water column willrevert to an equilibrium position as thetransient event abates.16

3.2 Transient reflection

Any change in operating system will resultin the transmission of a transient whichpropagates throughout the network at theappropriate acoustic velocity, c. Transientsare reflected at each boundary encounteredand reflections and re-transmissions occur.

Returning to the frictionless equations ofmotion and continuity allow the propagationof transients and their interaction with theflow network to be explained:

Equation of Motion

@p

@xþ �

@v

@t¼ 0 ð22Þ

Equation of Continuity

@p

@tþ �c2

@v

@x¼ 0 ð23Þ

The general solution of these equations isdue to D’Alembert and may be expressed as:

p� patm ¼ F tþx

c

� �þ f t�

x

c

� �ð24Þ

V� Vatm ¼ �1

�cF tþ

x

c

� �� f t�

x

c

� �h ið25Þ

The F() and f() functions are entirelyarbitrary and may be selected to represent

DA Kelly et al. 171

transient propagation upstream and down-stream from the site of the boundary condi-tion change. The F( ) and f ( ) functionsconform to the principle of superposition ofpressure waves and may therefore be used todevelop and explain the more complex pres-sure time histories associated with transientpropagation in flow networks. The impositionof a frictionless system excludes attenuation,however, this approach allowed Allievi tointroduce the first graphical technique fortransient prediction.

Joukowsky17 dealt with two particularboundaries that remain of fundamentalimportance: The presence of either a deadend or a fully open termination into a zoneheld at constant or known pressure.

In the first case, the local velocity remainszero provided that the pressure at that loca-tion remains above the fluid vapour ordissolved gas release pressure. Thus setting(V�Vatm)¼ 0 in Equation (25) gives F( )¼f ( ) and, therefore, the incoming pressurewave is reflected with the same magnitudeand sign – effectively doubling the local effectof the incoming pressure wave. The reflectioncoefficient may be expressed as:

CR ¼ þ1

at a dead end.In the case of a constant pressure at the

boundary, placing (p� patm)¼ 0 in Equation(24) implies that F( )¼�f ( ), and hence areflection coefficient at a constant pressurezone boundary of:

CR ¼ �1

or a reflection of the incoming wave with achange of sign.

The frictionless wave Equations, (24) and(25), may be solved at any junction boundarytogether with the equations of flow continuityand pressure equivalence across the junctionto determine values for reflection and

transmission coefficients for the junction ofn pipes (Figure 4):

Continuity of flow

Q1 ¼ Q2 þQ3 þ � � � þQn ð26Þ

Commonality of pressure at the junction

p1 ¼ p2 ¼ p3 ¼ � � � ¼ pn ð27Þ

Assuming that the incoming transient arri-ves along pipe 1, ongoing transmissions willbe generated along pipes 2! n and a reflectedtransient will propagate back along pipe 1based on pipe area and local wavespeed.Solution of Equations (24) and (25) with(26) and (27) for an incoming transient F1

in pipe 1, a transmitted wave F2!Fn inpipe 2!pipe n and a reflected wave f1 inpipe 1 yields a general expression for thereflection and transmission coefficient respec-tively for the junction:

CR ¼ðA1=cÞ � ðA2=cÞ � ðA3=cÞ � � � � � ðAn=cÞ

ðA1=cÞ þ ðA2=cÞ þ ðA3=cÞ þ � � � þ ðAn=cÞ

ð28Þ

CT ¼ð2A1=cÞ

ðA1=cÞ þ ðA2=cÞ þ ðA3=cÞ þ � � � þ ðAn=cÞ

ð29Þ

Several points emerge from these expres-sions: The transmission into each of thereceiving pipes is identical and the transmis-sion and reflection depend upon both the areaof the pipe and the wave speed within it,which in turn involves the pipe material andpipe wall thickness to diameter ratio. It will beseen that it is the sum of the (area/wave speed)that determines the coefficients, hence onepipe with a low wave speed due to its wallthickness or material can dominate the cal-culation. In the application discussed in thispaper, the wave speed in all pipes may be


assumed to be constant. As the pressuretransients are small, the system pipeworkmay be assumed rigid, simplifying the formof Equations (28) and (29) to area ratios.These expressions will become importantlater in defining the transmission of a pressuretransient through a complex network.Equation (29) will become important indetermining the effective ‘range’ of any tran-sient as it effectively determines the transientstrength after passing several junctions. Thetransient will depend upon the relative cross-sectional areas of the stack and branches.

4 Laboratory evaluation of the pressuretransient identification technique

A laboratory evaluation of the proposedtechnique was undertaken using a simulated77m high vertical drainage stack consisting of

75 and 100mm diameter pipework. Branchconnections leading to single appliance trapseals were located at 3.2m centres represent-ing typical floor levels (Figure 5). A pneuma-tically operated piston, or pressure transientgenerator (PTG), was located at the simulatedstack base which, on activation, wouldimpose a positive transient pulse into thesystem, the response of which was recordedby a pressure transducer located approxi-mately 1m from the PTG and connected to ahigh scan rate data logging system.

Initially all traps were capped off torepresent a set of full appliance trap seals –providing the defect free system for compar-ison. The system response to the appliedsingle pressure pulse was then monitored foreach failure condition by sequentially remov-ing the cap from trap 1 (T1) to trap 14 (T14),thus exposing the trap to atmosphere andsimulating a depleted appliance trap seal.

F1

F2

Fn

F3

Pipe 1

Pipe n

Pipe 3

Pipe 2

f1

Figure 4 General pipe junction with n number pipes

DA Kelly et al. 173

Figure 6 illustrates the measured systemresponse to the applied pressure transientimposed by the PTG for the defect free systemand selected defective traps at T1, T3 andT12. The pipe periods for each trap locationhave been calculated using Equation (3)

and are displayed as vertical lines along thex-axis.

The generated transient arrives at thetransducer at t¼ 1.0 s. The transient responsefor the defect free system shows that thepressure within the pipe continues to rise (toaround 100mm Water Gauge) during themotion of the PTG until a negative wave isgenerated between t¼ 1.35 and t¼ 1.4 s by theabrupt cessation of the piston motion. Duringthis period there are no negative reflectionsreturned by any of the traps, thus confirmingthat all traps are full. The introduction of adry trap at T1, however, generates a negativereflection with an arrival time of t¼ 1.057 s(pipe period of 0.057 s) which yields a trapdistance of 9m (consistent with the locationof T1, see Figure 5). The arrival time of thereflections returned from the depleted traps atT3 and T12 also show good correlation withthe predicted pipe periods.

5 Numerical modelling of thesystem response

The AIRNET computer simulation, basedupon the MoC solution of the St Venantdefining equations of unsteady flow, has beenused to model the system response of thelaboratory system. The action of the PTG atthe base of the stack is defined by theboundary equation:

u ¼ðxpiston, tþ�t � xpiston, tÞ

�tð30Þ

which may be solved with the available C�

characteristic to yield c and hence p at thepiston face. Figure 7 shows the simulatedtransient response for the defect free systemand defective traps at T1, T3 and T12. As wasshown with the measured data, the returntimes of the negative reflections generated bythe open traps correspond with those pre-dicted theoretically. This high degree of agree-ment between the measured and simulated

Opentermination

Pressure transducer

19.7m

41.6m(13×3.2m)

6.3m

0.37m

6.2m

2.8m

T10

T2

T1

100mm Ø

75mm Ø

100mm Ø

T3

T4

T7

T6

T5

T8

T9

T11

T12

T13

150mm Ø

P

Pressure transientgenerator

T14

Figure 5 Schematic of laboratory test rig


results provide confidence in the method ofcharacteristics simulation as a tool to predictsystem response and as an appraisal of thismonitoring technique.

6 Site test validation

Validation of the proposed transient analysistechnique was provided under controlled sitetest conditions using a standard single stackdrainage system in an unoccupied 17-storey

residential building in Dundee, Scotland.The system consisted of a 150mm cast ironvertical stack, with 100, 35, 42, and 54mmdiameter copper branch connections servingthe WC, WHB, bath and kitchen sink, res-pectively within each apartment. The PTGwas connected into the stack via existingaccess panels at the three test locations asindicated on Figure 8. These test locationswere chosen to investigate the practicalconsiderations of applying the transientto the top, middle and bottom of the

T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

T12

T13

T14 End

−100

−80

−60

−40

−20

0

20

40

60

80

100

120

140

Pre

ssur

e (m

m w

ater

gau

ge)

Defect at T1AIRNET

Defect at T12AIRNET

Time (s)

Negativereflectionreturnedfrom opentrap T1

Defect FreeAIRNET

Defect at T3AIRNET

0.950.95 1 1.051.05 1.11.1 1.151.15 1.21.2 1.251.25 1.31.3 1.351.35 1.41.4 1.451.45 1.51.50.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

Figure 7 AIRNET simulated pressure response of the defect free system compared with those with a depleted trap seal

End

T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

T12

T13

T14

−100

−80

−60

−40

−20

0

20

40

60

80

100

120

140P

ress

ure

(mm

wat

er g

auge

)

Defect at T12

Negative reflection returned from open trap T1

Defect at T3

Defect at T1

Defect free

Time (s)

0.950.95 1 1.051.05 1.11.1 1.151.15 1.21.2 1.251.25 1.31.3 1.351.35 1.41.4 1.451.45 1.51.50.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

Figure 6 Pressure response of the defect free system compared with those with a depleted trap seal

DA Kelly et al. 175

drainage stack. The findings are discussed inthe following sections.

The system response was recorded using anumber of calibrated pressure transducersconnected to a high scan rate data loggingPC board, collected at a 500Hz samplingfrequency. The results presented in this paperare those recorded on the connecting branchbetween the PTG and stack for Test Set 1 andTest Set 2 only. The tests performed at thebottom of the stack (Test Set 1) and the top ofthe stack (Test Set 3) differ only by the orderin which the appliance trap seals are encoun-tered by the incoming transient, T1!T17(Test Set 1) and T17!T1 (Test Set 3).

6.1 Applied pressure transient to ground floor

level (Test Set 1)

Samples of the transient response recordedat Test Set 1 are shown in Figure 9. It can beseen from Figure 9(a) that the traces aredominated by a large negative reflection,which is returned before any of the predictedtrap pipe periods, at t¼ 1.016 s; suggesting achange of boundary condition at 2.61m fromthe transducer.

Once the transient arrives at the branch-to-stack junction, ongoing transmissions willbe propagated along both the upper stacksection (toward the termination) and lowerstack section (toward the sewer) while areflected transient will be propagated backalong the incoming branch towards the PTG.At a three-pipe junction such as this, withpipes of matching diameter and wave speed,the transmission and reflection coefficients willbe 2/3 and 1/3, respectively (see Equations (28)and (29)). As the pressure transient propagatesthroughout the upper and lower stack sectionsit will be reflected and transmitted by eachboundary encountered. Therefore, the mea-sured system response is a superposition of theresponse from the three-pipe junction and thereflections from both upper and lowers sec-tions of the stack. The large negative reflectionfrom the sewer connection was removed by

WC (T2)

WHB Sink

WC (T3)

WHB Sink

WC (T4)

WHB

WC (T5)

WHB

WC (T6)

WHB

WC (T7)

WHB

WC (T8)

WHB

WC (T9)

WHB

WC (T10)

WHB

WC (T11)

WHB

WC (T12)

WHB

WC (T13)

WHB

WC (T14)

WHB

WC (T15)

WHB

WC (T16)

WHB Sink

Sink

Sink

Sink

Sink

Sink

Sink

Sink

Sink

Sink

Sink

Sink

Sink

WC (T17)

WHB

BathSink

GF

3F

4F

5F

6F

7F

8F

9F

10F

11F

12F

13F

14F

15F

16F

17F

Roof

2F

41.6m (16×2.6m)

Test set 2PTG

PTG

PTG

Pressure

To sewer

0.8m

5.8m

0.9m

Terminationopen to atmosphere

Test set 3

Bath

Bath

Bath

Bath

Bath

Bath

Bath

Bath

Bath

Bath

Bath

Bath

Bath

Bath

Bath

Test set 1 Transducer

Figure 8 The single-stack drainage system used for site testing.Note: the ground floor level is double height with accommo-dation beginning at 2nd floor


blocking the lower stack connection – effec-tively transforming the three-pipe junction intoa two-pipe junction. Figure 9(b) demonstratesthe improvement made to the magnitude ofthe propagating wave. It is now possible todistinguish a negative reflection returned fromthe open upper termination at t¼ 1.3 s fromthe defect free system trace, giving a pipeperiod of 0.3 s and a subsequent stack heightof 48m. On introduction of an open trap atT2, the negative reflection is returned att¼ 1.048 s giving a pipe period of 0.048 s anda reduced transient travel distance of 7.7m

(matching the pipe period of trap T2). Theremaining cases shown in Figure 9(b) confirmthis relationship.

The measured traces illustrated inFigure 9(b) show a more rapid natural atten-uation than those observed in the laboratorytests. This can be attributed to an increase infrictional loss due to the greater pipe wallroughness of the older cast iron pipeworkcompared with that of the new uPVC pipe-work used in the laboratory together withthe larger number of appliance junctions oneach floor which reduces wave transmission.

1.35 1.4 1.45

1.35 1.4 1.45T

2T

3T

4T

5T

6T

7T

8T

9T

10T

11T

12T

13T

14T

15T

16T

17T

OP

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

T12

T13

T14

T15

T16

T17

TO

PS

tack

(a)

(b)50

40

30

20

10

0

−10

−20

50

40

30

20

10

0

−10

−20

Pre

ssur

e (m

m w

ater

gau

ge)

Pre

ssur

e (m

m w

ater

gau

ge)

Defect at T16Defect at T7Defect at T3Defect free

Defect at T11

Defect at T6

Defect at T2

Defect free

Time (s)

Time (s)

Sewer

GF

GFLower stack

blocked

PTG

PTG

Pressuretransducer

Pressuretransducer

Bath

Bath

WHB

WHB

WC (T2)

WC (T2)

2F

2F

Sink

Sink

0.950.950.90.9 1 1.051.05 1.11.1 1.151.15 1.21.2 1.251.25 1.31.3 1.51.5

0.90.9 0.950.95 1 1.051.05 1.11.1 1.151.15 1.21.2 1.251.25 1.31.3 1.51.50.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.5

0.950.9 1 1.05 1.1 1.15 1.2 1.25 1.3 1.5

Figure 9 Site test pressure response of the defect free system compared with those with a depleted trap seal for Test Set 1 withthe: (a) sewer open, (b) sewer closed. Note: Test Set 3 results generally replicate those shown here

DA Kelly et al. 177

6.2 Imposed pressure transient applied at

mid-floor level (Test Set 2)

The initial transient response of introdu-cing the incident transient at the middle of thestack (Test Set 2) is shown in Figure 10(a).Again, a large negative reflection is returnedearlier than any of the predicted trap pipeperiods at T¼ 1.014 s. This reflection is gene-rated by the branch-to-stack three-pipe junc-tion, see Equations (28) and (29). To excludethis unwanted reflection, each upper andlower stack section may be treated sequen-tially by closing the relevant section.

A further issue requiring considerationwhen introducing the incident transient at amid-floor level is the possibility of ‘mirror’reflections being returned from defective trapson equidistantly spaced floors. For example,from Figure 10(a), it can be seen that the pipeperiod for T7 in the lower stack section issimilar to that of T11 in the upper stacksection and, therefore, both will return anegative reflection at a similar time. It is,therefore, not possible to clearly identify whichof the two traps are defective from a singlemonitoring point. Therefore, to remove this

1.2 1.25

1.2 1.25

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

T12

T13

T14

T15

T16

T17

T10

T11

T12

T13

T14

T15

T16

T17

Top

of

stac

kT

op o

fst

ack

Sew

er

(a)

(b) 50

40

30

20

10

0

−10

−20

50

40

30

20

10

0

−10

−20

−30

−30

Pre

ssur

e (m

m w

ater

gau

ge)

Pre

ssur

e (m

m w

ater

gau

ge)

Defect at T11

Defect at T13

Defect at T2

Defect free

Defect at T12

Defect at T13

Defect at T14

Defect at T15

Defect at T16

Defect at T17

Defect at T11

Defect at T10

Defect free

Time (s)

Time (s)

8F

PTG

Bath

WHB

Bath

WHB

Bath

WHB

WC (T10)

WC (T9)

WC (T8)

Sink

Sink

Sink

8F

9F

9F

PTG

Bath

WHB

Bath

WHB

Bath

WHB

WC (T10)

WC (T8)

WC (T9)

10F

10F

Sink

Sink

Sink

0.950.95 1 1.051.05 1.11.1 1.151.15 1.31.3

0.950.95 1 1.051.05 1.11.1 1.151.15 1.31.30.95 1 1.05 1.1 1.15 1.3

0.95 1 1.05 1.1 1.15 1.3

Figure 10 Site test pressure response for the defect free system compared with those with a depleted trap seal for Test Set 2:(a) both upper and lower stack sections open, (b) lower stack section blocked off


unwanted reflection both the upper and lowersections of the stack were tested separately byblocking off the corresponding opposite sec-tion. Figure 10(b) shows the results after thelower stack section was blocked off.

6.3 Application of the compliance factor

Analysis of the recorded system pressureresponse has been shown to give good visualconfirmation of the location of depleted trapseals by proving that the negative reflectionreturned from an open trap corresponds tothe theoretical pipe period for that trap. It isalso important, however, to have a numericalconfirmation of the system condition to allowautomatic recognition of the system condi-tion. The pressure compliance factor is usedto produce a quantitative value of ‘closeness-of-fit’ between a test trace and a pre-recordeddatabase trace (Equation (4)).

As an example of this numerical analysisthe pressure compliance factor has beendetermined for the test data recorded duringTest Set 1 with the sewer blocked off. Theeffectiveness of the pressure compliancefactor relies heavily on the requirement thatall pressure responses contained within thedatabase must have close correlation with therecorded test traces. Any additional systemnoise or change in operating conditions willproduce dissimilar traces causing thepressure compliance factor to be inaccurate.

Initially, a single test trace of each defectivetrap was compared with that of a singledatabase trace yielding a successful defectivetrap identification rate of only 50%. This lowsuccess rate can be attributed to a variance inthe measured transient generated by the PTGdue to occasional sticking of the piston onactivation which had the effect of increasingthe travel speed and, therefore, the pressuregenerated by the piston. Thus, to reduce thisvariation, an average pressure trace wascalculated for both the test trace and thedatabase trace, each from five single traces,greatly improving the correlation.

Table 1 shows the pressure compliancefactor matrix calculated from these averagetraces and for the first 0.3 s following the arri-val of the pressure wave (the system pipeperiod). Note that the compliance factor valuesare dependant upon the test duration beinganalysed which is itself dependant upon themaximum pipe period of the connected traps.In each case, the defective trap is correctlyidentified with the pressure compliance factorapproaching zero when compared to thematching system condition in the database.

7 Conclusion

Following the SARS epidemic at the AmoyGardens in 2003, the vital role of the

Table 1 Compliance factor matrix for Test Set 1 with sewer blocked off (first 10 traps only). The correct system status is identifiedwhen the test set matches the database trace giving Cj! 0

Test

CF DF T2 T3 T4 T5 T6 T7 T8 T9 T10

Databank DF 13 46077 42929 44135 41704 41150 42486 32767 26049 25613T2 45321 24 14740 41032 54749 59162 62614 56050 50555 50386T3 43434 14781 33 15134 37900 52529 63490 64233 61833 62338T4 41413 39460 13354 69 11607 29447 46005 55346 61663 67577T5 40262 53771 35197 11131 39 7537 21256 32074 41266 49772T6 41125 58996 49545 28549 6578 91 5986 15423 24670 32159T7 38074 58393 57808 44735 19992 4873 218 4011 11215 17225T8 32263 56374 62118 56077 31658 13910 4246 59 3570 8379T9 24559 49237 58791 62305 41079 23330 12867 3228 92 2348T10 24851 50448 61020 70317 51009 31556 19613 8439 2203 52

DA Kelly et al. 179

appliance trap seal in protecting buildinginhabitants from the potentially virus-ladenair contained within the building drainagesystem has gained much attention. Theremote and non-invasive technique detailedin this paper allows depleted appliance trapseals to be quickly identified to ensure thatthe risk from cross-contamination is mini-mised. This not only has obvious health andsafety benefits but will also prove beneficial tothe building’s facility management team bygreatly improving the effectiveness of theirmaintenance regime.

The proposed technique draws on theprinciples of pressure transient theory and inparticular uses the change in reflection coef-ficient between an open and closed boundarycondition, and the change that this has on thecharacteristic system response, to identify thelocation of a depleted appliance trap seal.It has been shown through laboratory and sitetest results, and corroborated by numericalsimulation, that a depleted appliance trap sealreturns a negative reflection when subject toan applied pressure transient. The time of thisreturning reflection, obtained from the mea-sured system response, has been shown toaccurately match that of the calculated trappipe period and when compared with that of adefect free trace allows the location of thedepleted trap to be identified.

The pressure compliance factor methodused to identify the correct system conditionhas been shown to be highly successful whencomparing a system test response with a data-base of previously measured baseline cases.This numerical analysis requires that theoperating conditions used to collect the data-base traces closely match those used in sub-sequent system testing to ensure that a goodfit is achieved. Taking multiple test traces andcalculating an average pressure-time traceimproved the correlation between the testand database traces.

The applicability of this technique requiresthat the applied pressure transient be directed

to propagate in one direction along thedrainage stack to ensure that the superposi-tion of reflected boundary condition infor-mation from equidistant pipe sections isavoided. Methods of achieving this require-ment without compromising the integrity ofthe system are currently being investigated.However, the main advantage of this tech-nique is that the whole test period is veryshort. For the 48m high building used on thesite investigations, the required testing dura-tion is within 0.3 s, as all of the physicalcharacteristics of the system can be definedwithin the first 2L/c seconds of testing, clearlya practical time limit for a technique whichis envisaged to take place during periodsof system non-use, e.g. during the night.The operation of this technique could beincorporated into the building managementsystem and programmed to perform dailysystem checks.

The next stage in the development of thistechnique will be to investigate the use of asinusoidal pressure wave as the input tran-sient and also to undertake a full set ofoperational trails within an occupiedbuilding.

References

1 Swaffield JA, Galowin LS. The engineereddesign of building drainage systems. 1992;England, Ashgate Publishing Limited.

2 World Health Organisation. Summary of SARSin the WHO European Region, CD News,Communicable Disease Report, No. 31, Oct.2003.

3 World Health Organisation. Inadequateplumbing systems likely contributed to SARStransmission. Press Release WHO/70, 26September 2003, WHO, Geneva.

4 Hung HCK, Chan DWT, Law LKC, ChanEHW, Wong ESW. Industrial experience andresearch into the causes of SARS virus trans-mission in a high-rise residential housing estate


in Hong Kong. Building Services EngineeringResearch and Technology 2006; 27(2): 91–102.

5 Jack LB. Drainage design: factors contributingto SARS transmission. Proceedings of theInstitute of Civil Engineers, ICE MunicipalEngineer 159, March 2006; Issue ME1: 43–48.

6 Wylie EB, Streeter VL. Fluid transients.New York, McGraw-Hill, 1979.

7 Swaffield JA, Boldy AP. Pressure surge in pipeand duct systems. England, Avebury TechnicalPress, 1993.

8 Brunone B. Transient test-based technique forleak detection in outfall pipes. J Water ResourPlan Manage 1999; 125(5): 302–06.

9 Stephens M, Vitkovsky J, Lambert M,Karney B, Nixon J. Transient analysis to assessvalve status and topology in pipe networks: 9thInt. Conf. Pressure Surge, BHR Group,Chester, 24–26 March 2004; 211–24.

10 Lister M. The numerical simulation of hyper-bolic partial differential equations by theMethod of Characteristics. In: Ralston andWilf (eds), Mathematical methods for digitalcomputers. New York, John Wiley, 1960;pp. 165–79.

11 Doyle TJ, Swaffield JA. An evaluation of themethod of characteristics applied to a pressuretransient analysis of the Concord refuellingsystem: Proceedings of the Institution ofMechanical Engineers, Part E, 1972; 216:133–42.

12 McDougal JA, Swaffield JA. The influence ofwater conservation on drain sizing for buildingdrainage systems. Building ServicesEngineering Research and Technology 2003;24(4): 229–43.

13 Streeter VL. Waterhammer analysis includingfluid friction. J Hyd Div ASCE 1962; 39:127–31.

14 Swaffield JA, Campbell DP. Numericalmodelling of air pressure transient propaga-tion in building drainage systems, includingthe influence of mechanical boundary condi-tions. Building and Environment 1992; 27(4):455–67.

15 Swaffield JA, Campbell DP. Air pressuretransient propagation in building drainagevent systems, an application of unsteadyflow analysis. Building and Environment 1992;27(3): 357–65.

16 Swaffield JA, Jack LB. Simulation andanalysis of airborne cross contaminationroutes due to the operation of buildingdrainage and vent systems. BuildingResearch and Information 2004; 32(6):451–67.

17 Joukowsky N. Uber den hydraulisher Stoss inWasserlietungsrohen. Memoirs de l’AcademieImperiale des Sciences de St Petersburg, 1900,translated by Simin O. ProceedingsAmerican Water Works Association, 1904; 24:341–424.

DA Kelly et al. 181

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Pressure Transient

Documents

Transcript of Pressure Transient