Flow Measurement and Instrumentation 18 (2007) 175–182

Flow Measurementand Instrumentation

www.elsevier.com/locate/flowmeasinst

An examination of BS3680 4C (ISO/DIS 4369) on the measurement ofliquid flow in open channels — flumes

Hoi Yeung∗

Department of Process and Systems Engineering, Cranfield University, Cranfield, Bedfordshire MK43 0AL, United Kingdom

Received 19 June 2006; received in revised form 29 December 2006; accepted 15 January 2007

Abstract

The Environment Agency (EA) of England and Wales requires consent holders to install flow-monitoring equipment to measure the flow ofsewage or trade effluent where it exceeds 50 m3/day. The daily totalized discharge has to be recorded to +/−8%.

The open channel measurement standard on rectangular throated flumes has been reviewed. There were very little experimental verificationsof the theoretical discharge equation and predicted uncertainty. The assumed flow behaviour in the throat is not consistent with observation andcomputational fluid dynamics analysis. Tests were carried out in the laboratory using a flume with a throat width of 100 mm. The experimentalevidence suggested that the operation limits imposed by the standard could be too conservative.c© 2007 Elsevier Ltd. All rights reserved.

Keywords: Measurement structure; Flume; Standards; BS3680

1. Introduction

The stated objective of the Urban Waste Water TreatmentDirectives (91/271/EEC) [1], and its subsequent amendments,Directive 98/15/EEC [2], is to ‘protect the environment fromthe adverse effects of discharges of urban waste water andof waste water from industrial sectors of agro-food industry’.Essentially, this requires member states of the EuropeanUnion to put into place regulations for achieving minimumtreatment standards and treatment works effluent quality. Flowmeasurement is not mentioned explicitly in the Directive but isrequired by implication in order to ensure that sampling regimesfor the quality parameters are appropriate and can be correctlyinterpreted and the total pollutant loads into the receiving watercan be calculated.

The Environment Agency (EA), implements and enforcesthe Directive in England and Wales. Under the newregulations, consent will be against actual flows and henceflow measurement is needed now to assess compliance. R&DTechnical Report P150 [3], outlines their requirements asregards to flow measurement. For discharges >50 m3/day

∗ Tel.: +44 0 1234 750111.E-mail address: h.yeung@cranfield.ac.uk.

0955-5986/$ - see front matter c© 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.flowmeasinst.2007.01.002

(or >250 p.e. (population equivalent)), permanent continuousmeasurement of flow rates and daily cumulative totals arerequired. Report P150 defined the performance criterion isthat the flowmeter installed shall achieve a total uncertaintybetter than +/−8% for a daily totalized flow. Total uncertaintyincludes all equipment up to the creation of the data filetransmitted to the Agency. The regulatory requirement isdetailed in ‘Minimum Requirements for the Self-Monitoring ofEffluent Flow’ [4].

By far most of effluent discharges are measured by openchannel flow structures. These structures have to comply withBS3680. Anglian Water reported [5], back in 1998, that for 450site with a population equivalent of higher than one thousand

• 4% of primary structures were incorrectly installed;• 30% weirs and 10% flumes were distorted;• 180 flumes were operating above their design limits;• a significant proportion was directly influence by the

upstream and downstream conditions;• 90% of secondary devices (level sensors) had incorrect

datum;• 23% secondary devices were incorrectly located with respect

to the gauging structure.

It was believed that this was not atypical and such problemsand were similar across the whole of the UK industry. It must

176 H. Yeung / Flow Measurement and Instrumentation 18 (2007) 175–182

Notation

A channel cross-sectional area;b width of the throat;B width of the channel upstream of the flume;CV velocity coefficient;CD discharge coefficient;d depth of water in the channel:E exit transition length;g acceleration due to gravity;h water head (m);H total specific energy;L length of the throat;P height of the invert (=0 for the experimental

flume);Re Reynolds number based on throat length and

velocity in the throat;V local velocity;V̄ average (superficial) velocity;w channel width;α coefficient to take into account the non-

uniformity of the velocity distribution;β coefficient dependent on the mean curvature of

the streamline;δ∗ displacement boundary thickness;XC combined uncertainty of CV × CD;u uncertainty (%).

Subscripts

b throat;c critical flow condition;e equivalent condition (to account for real fluid

effects);max maximum;up upstream;d downstream.

be mentioned that a lot of improvement had been made sincethen.

The general consensus of industry was that many structuresoperate outside the limit and their designs are out of the limit ofBS3680. It is also recognized that the tolerances in the standardare not generally achievable in the field. In response to the latter,EA [4] relaxes the design limits. It is made clear that theseconcessions are ‘collective wisdom of the experts’ and theireffects are not known.

The overall uncertainty has the following constituents, seeFig. 1:

• Primary device — the flume;• Secondary device — the level measuring device, flow

computer;• Transmission;• Data acquisition;• Storage;• Reporting.

In response to the industrial need, the National MeasurementDirectorate (NMD) of the United Kingdom sponsored a project(Project FEOC02) to have a closer look sewage measurementin practice and relationship with the standards. This paper isa result of the project, it is concerned with the primary devicethough it is recognized that the contribution of measurementuncertainty from the secondary device cannot be ignored andcould be dominant especially at the low flows. It is also targetedat rectangular flumes as they are extensively used in the UKboth at the inlet to treatment works and at the exit before thetreated effluent is discharged. The development of the dischargeequation as presented in BS3680 Part 4C [6] is first reviewedbelow. It was found that there is very little experimentalverification to back up the theoretical the discharge coefficient.The standard also includes an equation to allow the uncertaintyof the discharge coefficient to be calculation. However, it isquestionable as to how good the equation is. The paper alsodescribes some experiments carried out in the laboratory. Thisnew data suggests that the operation limits imposed could betoo restrictive.

2. The discharge equation

Fig. 2 shows a typical flume as defined in BS3680, part4C [6].

The specific energy, H , of flow in an open channel is givenby:

H = βd + αV̄ 2

2g(1)

where V̄ = the average velocityα =

∫ A0

v3dAV̄ 3 A

, coefficient to take into account of the non-uniformity of the velocity distribution in the channel

β = coefficient dependent on the mean curvature of thestreamline

d = depth of water in the channelg = acceleration due to gravityA = channel cross sectional areav = local velocity.It is assumed that both α and β are equal to unity and the

flow is critical (i.e. Froude number = 1), we have:

Q =

√g A3

c/wc (2)

where the subscript c denotes critical flow condition and w thechannel width.

Also, by substituting (2) into (1), we have:

Hc = dc +Ac

2wc. (3)

Eq. (2) can also be written as

Q =

(23

)3/2√

gwc H3/2c .

For an ideal fluid, with no energy losses, the energy at thethroat of the flume (or more precisely the at the position where

H. Yeung / Flow Measurement and Instrumentation 18 (2007) 175–182 177

Fig. 1. Open channel measurement system (courtesy of anglian water).

Fig. 2. Rectangular throated flume [6].

the flow is critical) will be equal to the specific energy, H , inthe upstream channel, i.e.

H = Hc.

The discharge through the flume is thus given by:

Q =

(23

)3/2√

gbH3/2 (4)

where b = the width of the throat.To take into account real fluid effects, the Eq. (4) is replaced

by:

Q =

(23

)3/2√

gbe H3/2e (5)

where be = effective throat widthHe = effective total head.Moreover, as it is not possible to have a direct measurement

of He, the height of water above the invert, h, is used instead.Additional coefficients are thus included.

Q =

(23

)3/2√

gCV CDbh3/2 (6)

where CV = velocity coefficient (to take account of the velocityhead in the approach channel);

CD = discharge coefficient (to take account of the energylosses).

In BS3860, the values of CV and CD are determined by thecalculating the ‘effective’ area and water depth in the throat.Ackers et al. [9] commented that the discharge coefficient couldalso be estimated by calculating the energy loss through theflume and such approach gave similar results to the boundarylayer approach.

CV =

(He

he

)3/2

=

(H − δ∗

h − δ∗

)3/2

(7)

and

CD =

(be

b

) (he

h

)3/2

=

(1 − 2

δ∗

b

) (1 −

δ∗

h

)3/2

(8)

where he = the effective head gauged upstream of the structure;δ∗

= the boundary layer displacement thickness at the endof the throat.

Fig. 3 shows the relationship of the displacement boundarylayer thickness, δ∗, with respect to the surface roughness, k andReynolds number, Re (Reynolds number based on the throatlength, L and velocity in the throat). The calculation is basedon the boundary layer development over a flat plate (Ackersand Harrison [7], Harrison [8]).

178 H. Yeung / Flow Measurement and Instrumentation 18 (2007) 175–182

Fig. 3. Relative displacement boundary layer thickness (BS3680 Part 4C [6]).

The standard also recommends that, for most installationswith a good surface finish, the value of δ∗/L will, in practice, liein the range of 0.002–0.004. Provided that 105 > L/k > 4000and Re > 2 × 105, δ∗/L is approximated to 0.003.

The discharge coefficient becomes:

CD =

(1 − 2

0.006Lb

) (1 −

0.003Lh

)3/2

. (9)

This is the equation generally used by practitioners and inflow computers to calculate discharge from a flume.

Experimental data to verify the discharge equation is limited.Ackers et al. [9] reported some comparisons with experimentaldata for a flume of b = 121 mm, and L = 508 mm byEngel [10]. Ackers et al. [9] also claimed that the experimentaldischarge coefficient agreed with the calculated value to within+/−2%. It was suggested that it should applied to flumes withthroat length exceeding twice the specific energy, i.e. L >

2.0H . The effects of flow curvature could become large whenL < 1.5H . The authors commented on the difficulties ofusing experimental data to verify the theoretical calculationdue to the high accuracy required from the experiment data.They asserted that to evaluate the friction assessment to anaccuracy of +/−1%, it would be necessary to measure thedischarge to an accuracy of +/−0.1% and such accuracy werenot attainable in the experimental studies they reviewed. Thesituation is better nowadays due to the advancement in flowmeters e.g. electromagnetic flow meter, if well maintained,could achieve uncertainties of +/−0.2% (for a very wellmaintained system). Thus confidence in future experimentallydetermined discharge coefficients from reputable researchersshould be much higher than those reviewed by Arckers et al.

BS3680 stated that with reasonable skill and care in theconstruction of the flume, the basic equation and coefficientsare expected to have an uncertainty approaching 1% infavourable circumstances. This suggestion seems to be at odd

Table 1Limits of application, BS3680

Limits Explanation

h > max (0.05 m, 0.05L) Due to the influence of fluidproperties and boundary layer.

h/L < 0.5 h/L may be allowed to rise to0.67 with an additionaluncertainty of 2%.

bhB(h+p)

< 0.7 The ratio of the area oftheapproach channel to the throat toensure the inlet Froude number isbelow 0.5 (p, the height of invertof the flume above the channel).

b > 0.10 mh/b < 0.3h < 2 m

with information that the standard was based on, as could beseen from the discussion above. Favourable circumstances aredefined as when CD and CV are not far from unity. The standardalso gives the following equation to estimate the combineduncertainty, XC , of CV × CD

XC = ± [1 + 20 (CV − CD)] %. (10)

The origin of this equation is unknown but is thought to bethe collective view of the experts of the technical committeewhen the standard was drafted.

The standard gives the operational limits within which thedischarge equation is applicable. The Table 1 summarizes theseconditions.

The standard also specifies geometrical tolerances which areacceptable. These are listed in Table 2.

The discharge equation only holds when the flow in thethroat is critical. The standard recommends that the total headupstream is at least 1.25 times that downstream (assumingsubcritical flow exists downstream). Critical condition in the

H. Yeung / Flow Measurement and Instrumentation 18 (2007) 175–182 179

Table 2Geometrical tolerances, BS3680

Limits Explanation

Throat width variation +/−0.2% with an absolute maximum of 10 mmThroat transverse level variation +/−0.1% slope from horizontalThroat longitudinal level variation +/−0.1% slope from horizontalApproach level variation +/−0.1% slope from horizontal (no more than +/−1% for a distance 10 times hmax)Longitudinal level variation +/−0.1% slope from horizontalCentrality of flume (amount off centre) Must be centralStaggered flume cheeks +/−0.1% of LVertical skew deviation from plane of other vertical surfaces +/−1%Horizontal skew Deviation from plane of other vertical surfaces +/−1%Curvature of entrance transition R >= 2(B − b) with deviation of +/−0.1% of Ldeviation of level variation in the exit transition +/−0.3% slope

throat can be maintained when the total energy is sufficient toovercome the energy losses in the expansion and the energyrequirement to convey the flow downstream. Thus the ratio ofupstream to downstream total head should be a function ofthe expansion after the throat. The ratio of 1.25 is appropriatefor an expansion rate (at each side wall) of 1 in 6. For lowerexpansion rate, the ratio of upstream and downstream total headis reduced, e.g. for an expansion rate of 1 in 10, the ratio is 1.20(see Table 8.3 of Ackers et al. [9]).

3. Comments on the discharge equation

The formation of the discharge equation assumes:a. The boundary layer originated at the leading edge of the

prismatic portion of the throat.b. The velocity in the throat is uniform and constant with

Froude number = 1.c. Transition from laminar to turbulent boundary layer takes

place at Re = 3 × 105.d. The control section is presumed to be at the downstream

end of the prismatic throat section.The effect of a contraction (the transition from channel

width to throat width) is that the velocity profile becomesmore uniform. The approach in the standard, however, makesno distinction between flumes with a level invert and thosewith raised invert. For the former, there is no contractionin the vertical plane. Obviously, the assumption of boundarylayer development only starts at the beginning of the prismaticportion of the throat is only an approximation. Fig. 4shows velocity development of a flume computed using acomputational fluid dynamics, CFD, package (CFX 6.1), Yeungand Turnbull [11]. As the flow passes through the transition intothe throat, the flow accelerates and the liquid level drops. Thevelocity continues to increase in the throat and does not remainconstant as assumed. It is also important to note, contrast tothe assumption, the flow becomes critical not at the end of thethroat but near the beginning. This casts doubts to the validityof using the boundary layer at the end of the throat approach.

More problematic is the issue of transition from laminar toturbulent boundary layer. The non-dimensional displacementthickness is dependent on Reynolds number (based on throatlength) see Fig. 3. For large flumes, throat width above 0.5 m,Reynolds number would be above 106 for normal operation

range and δ∗/L more or less constant. However, for smallerflumes (e.g. 100–300 mm throat width) the Reynolds numberis in the laminar and the transition region. It is thus debatableas to how accurate is the predicted δ∗/L and the uncertainty ofcorresponding discharge coefficient.

With the issues highlighted above, it is suggested thatexperimental verification of the discharge equations is urgentlyneeded especially on smaller flumes. Eq. (10), used to estimatethe combined uncertainty and the operation limits should alsobe reviewed in light of new experimental evidence.

4. Experimental studies

To gain a better understanding of the standard, limited testswere carried out in the laboratory of the Department of Processand Systems Engineering, Cranfield University. Fig. 5 showsa photograph of the test rig and its essential constituents. Theexperimental channel was 406 mm wide, 300 mm deep and4 m long. A full length partition could be installed to vary thechannel width allowing different size flumes to be tested. Forthe 101 mm throat flume tested, the upstream channel was setto 203 mm wide. Water from an open top water tank entered thechannel via a ‘three sided’ bell mouth inlet. The water from theflume is collected in another tank and pumped back to the inlettank. The return water was distributed across the bottom of theinlet tank using a manifold. Flow conditioning perforated plateswere also installed in the tank to break down large eddies andto ensure that the approach to the bellmouth was smooth. Thewalls of the channel were made of Perspex. Pressure tappingswere located at the bottom of the channel. They were connectedto stilling wells which were equipped with point gauges tomeasure the liquid level in the approach channel and throughthe flume. The point gauges could measure to +/−0.1 mm. Thewater level in the channel was controlled by altering the heightof the ‘weir’ plate at the end of the channel. The position of thisweir was fixed during each test series.

The water flow rate was measured by a 50 mm electromag-netic meter (ABB Magmaster, serial no. G/10243/1/1). The me-ter was calibrated a month before the tests by a UKAS approvedlaboratory. The performance is within ± 0.2%. Major dimen-sions of the flumes are listed below.

Channel width (mm), B 203 ± 0.5Throat width (mm), b 101 ± 0.5

180 H. Yeung / Flow Measurement and Instrumentation 18 (2007) 175–182

(a) Horizontal plane 10 cm from bottom.

(b) Vertical plane.

Fig. 4. Flow development in a flume, b = 0.5 m, Q = 121 l/s.

Throat length (mm), L 300Exit transition 1:5.9Exit transition length (mm), E 300Wall material ABS plasticFig. 6 shows the value of CvCd versus flow rate for different

downstream weir levels for all the tests. When the flow issufficiently high, CvCd is more or less constant. As the flowdecreases, CvCd value also decreases. This is due, possibly, tothe ratio of upstream to downstream level at low flows couldnot ensure that the flow in the flume is modular (critical).The minimum permissible flow through the flume is dependenton the downstream water level which is dependent on the

configuration between the flume and the next critical flowsection. Thus designers of flow measurement flume, operatorsand inspectors need to consider the plant hydraulics to ensurethe flume is modular over the whole operating range of thetreatment works.

Fig. 7 shows all the experimental data for the ratio ofupstream and downstream level hup/hd ≥ 1.1. The averageCvCd is 1.019 with a standard deviation of 0.006. The limitingoperating conditions of minimum upstream level of 50 mm andh/L of 0.5 are also shown. For the flume tested, to ensuremodularity of the experimental flume the ratio of upstream todownstream total head, Hup/Hd > 1.25. It appears that this

H. Yeung / Flow Measurement and Instrumentation 18 (2007) 175–182 181

Fig. 5. Test rig.

Fig. 6. CvCd all data, b = 101 mm.

Fig. 7. CvCd for hup/hd > 1.1, b = 101 mm.

182 H. Yeung / Flow Measurement and Instrumentation 18 (2007) 175–182

ratio could be relaxed base on result of the current investigation.(Note: the ratio of level rather than total energy is used as thisparameter can be determined much easier in the field.) TheFig. 7 also shows that the minimum flow rate tested of 2 l/s.This coincides with the standard’s recommendation that theminimum upstream water level should be above 50 mm.

The calculated CvCd values, by using method of BS3680,are also shown in Fig. 7. The curve was generated by assumingδ∗/L = 0.0035, a reasonable average given the relativelysmooth surface of the test flume and low Reynolds numbers.The Reynolds number was only Re = 1.7×105 when the waterlevel, h = 0.05 m and Re = 3 × 105 when the water level,h = 0.15 m, the minimum and maximum limits recommendby the standard. This suggests that the flume is operated in thelaminar and transition (boundary layer) region.

The calculated uncertainty, using Eq. (10) is also included.Over the range of test data, the uncertainty ranges between+/−2.8% to +/−3.4% from high to low flows. It can be seenall the experimental data fit comfortably within the uncertaintyband. It is not necessary to increase the uncertainty by 2% whenh/L > 0.5 as suggested by the standard.

The value of δ∗/L , is a function of flow rates. For the flumetested, the difference in the CvCd value in comparison with afixed δ∗/L = 0.003 was around 1% at high flow and 2% at lowflows. This demonstrates that, for smaller flumes at least, thevariation of δ∗/L over the operating range of the flume shouldto be included. The use of Eq. (10) may not be appropriate, notwithstanding the validity of the approach.

5. Conclusions

To protect the environment, the quality and quantity of thedischarge from treatment works have to be determined. Policiesare in place specifying the flow measurement requirements.The work described in the paper highlighted some ofthe deficiencies of the present channel flow measurementstandards. The uncertainties of quantity of flow dischargedto the environment could not be ascertained. The followingconclusions and recommendations are listed below.

• The discharge equation is based on theoretical calculation ofdisplacement boundary thickness on a flat plate. Some of theassumptions used are inconsistent with the flow developmentin the flume.

• There is very little experimental verification of the dischargeequation and the combined uncertainty of the CvCd;

• The results of the experiments on a 101 mm wide throatflume suggest that some of the operational limits could berelaxed without compromising the uncertainty of discharge;

• Quality experimental data are urgently needed to verifythe discharge equation and clarify the operation limit anddimension tolerance. The use of energy loss calculationshould also be revisited and compared with the boundarylayer approach. New correlation or model should bedeveloped if necessary.

Acknowledgements

The author wishes to thank Dr J. Turnbull for carrying outthe CFD simulation and Dr Riadh for the experimental work.Financial support of from NMSD for project FEOC02 is muchappreciated.

References

[1] Council directive 91/271/EEC of 21 May 1991 concerning urbanwaste water treatment. http://europa.eu.int/comm/environment/water/water-urbanwaste/directiv.html.

[2] Commission directive 98/15/EEC of 27 February 1998 amendingcouncil directive 91/271/EEC of 21 May 1991. http://europa.eu.int/comm/environment/water/water-urbanwaste/amendment.html.

[3] Hamilton I. Flow monitoring of discharges: An audit manual R&Dtechnical report P150. Environment agency; 1998.

[4] Minimum requirements for the self-monitoring of effluent flow. Environ-ment agency; version 1: April 2003. http://www.environment-agency.gov.uk/commondata/105385/min requirements 0403 422583.pdf.

[5] Turner D, Cherry P, Ward A. A benchmark for flowmeter accuracy. Waterand Waste Treatment 1998;14–5.

[6] BS 3680 – 4C: Methods of measurement of liquid flow in open channels— Part 4: Weir and flumes — Part 4C: Flumes. BSI. 1981.

[7] Ackers P, Harrison AJM. Critical depth flumes for flow measurement inopen channels. Hydraulic research paper no. 5. HMSO. London. 1962.

[8] Harrison AJM. Boundary layer displacement thickness on a flat plate.Proc ASCE J Hyd Divn 1967;93(HY4).

[9] Ackers P, White WR, Perkins JA, Harrison AJM. Weirs and flumes forflow measurement. John Wiley & Sons.

[10] Engel FVAE. The venturi flume. The Engineer 1934;158:104, 131–3.[11] Yeung H, Turnbull J. Computation simulation of rectangular long throated

flumes paper accepted for FLOMEKO 2005 13th international flowmeasurement conference. 2005.