IS 14869 (2000): Liquid Flow Measurement in Open Channels ... · The flow conditions considered are...

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है”ह”ह

IS 14869 (2000): Liquid Flow Measurement in Open Channels -Rectangular, Trapezoidal and U-Shaped Flumes [WRD 1:Hydrometry]

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IS 14869:2000

ISO 4359:1983

Indian Standard

LIQUID FLOW MEASUREMENT IN OPENCHANNELS — RECTANGULAR, TRAPEZOIDAL

AND U-SHAPED FLUMES

“Its 17.120.20

0 BIS 2000

BUREAU OF INDIAN STANDARDSMANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

OctOber 2000 Price Group ILI

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Fluid Flow Measurement Sectional Committee, WRD 01

NATIONAL FOREWORD

This Indian Standard which is identical with ISO 4359:1983 ‘Liquid flow measurement in open channels— Rectangular, trapezoidal and U-shaped flumes’ issued by the International Organization forStandardization (ISO) was adopted by the Bureau of Indian Standards on the recommendations of theFluid Flow Measurement Sectional Committee (WRD 01 ) and approval of the Water Resources DivisionCouncil. In the adopted standard, certain conventions are, however not identical to those used in IndianStandards. Attention is especially drawn to the following:

a) Wherever the words ‘International Standard’ appear referring to this standard, they should beread as ‘Indian Standard.

b) Comma (,) has been used as a decimal marker while in Indian Standards, the current practiceis to use a point (.) as the decimal marker.

Technical Corrigendum 1 to the above International Standard has been incorporated.

CROSS REFERENCES

In this ado~ted standard, the followina International Standards have been referred to. Read in theirrespective places, the foliowing indian”Standards:

/international .Standard

ISO 748 Liquid flow measure-ment in open channels —Velocity-area methods

ISO 772 Liquid flow measure-ment in open channels —Vocabulary and symbols

1S0 1438 Liquid flow measure-ment in open channels usingthin-plate weirs and venturiflumes

Corresponding Indian Standard

IS 1192:1981 Velocity areamethods for measurement offlow of water in open channels(first revision)

IS1191 :1971 Glossary of termsand symbols used in connectionwith the measurement of liquidflow with a free surface (firstrevision)

IS 9108:1979 Liquid flow mea-surement in open channelsusing thin plate weirs

Dearee ofEquTva/ence

Identical with elucidation inIndian Standard (/S 1192:1981is under revision basedon ISO748:1997 ‘Measurement ofliquid flow in open channels —Ve/ocity-area methods?

Technically equivalent (/S 1191:1971 is under revision based onISO 772:1996 ‘Hydrometric de-terminations — Vocabu/aryandsyrnbok~

Technically equivalent to ISO1438-1:1980 ‘Water flow mea-surement in open channelsusing weirs and venturi flumes:Part 1 Thin plate weirs

REFERENCES TO ERRORS AND CLARIFICATIONS IN TEXT

The Technical Committee while adopting the text of this international Standard identified certain textualerrors to the

ClauseReference

9.4.1

10.1.5

10.4.1

10.6.1

11 .7.5(c)

D-4.8

Fig. 2

following clauses and felt necessary to correct these in the Indian context:

Corrections

Replace ‘total head’ by ‘effective total head’ in the first sentence.

Replace ‘pent’ by ‘point’ in the last line.

Line before equation (24) rrtay be changed as ‘Substitute (22) and (23) into (21)’,

Replace ‘of ‘ by ‘is’ in the tast sentence.

Replace ‘wherever the water surface lies’ by ~atall water levels’ in the last line.

Replace by ‘Compute discharge for the given head from equation (44)’.

Read the title as ‘Geometry of Rectangular Throated Flume’.

IS 14869:2000ISO 4359:1983

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ContentsPage

1 Scope and field ofapplicetion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

3 Definitions andsymbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

4 Units ofmeesurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

5 Selection of the type of flume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

6 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

6.1 Selection of site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

6.2 Installation condkions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

6.3 Flume structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . 3

6.4 Downstream conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

7 Maintenance – General requirements.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

8 Measurement of heed . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . 3

8.1 General requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

8.2 Gauge well . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

8.3 Zerosetting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

9 Determination of discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

9.1 General equationsfordischarge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

9.2 Celoulationof diechargefromobserved heed . . . . . . . . . . . . . . . . . . . . . . 5

9.3 Calculation of stage-discharge relationships . . . . . . . . . . . . . . . . . . . . . . . 5

9.4 Approach velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Rectangular throated flume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2 Locetion ofheedmessurement aection . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3 Provision formodular flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.4 Evaluation of discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.5 Computation of stage-discharge relationship . . . . . . . . . . . . . . . . . . . . . .

10.6 Limits ofappiication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.7 Uncertein~ of measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

6

6

7

7

7

8

8

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LS 14869:2000

ISO 4359:1983

11 Trapezoidal fhroated flumes .,....,, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

11.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

11.2 Location ofhead measurement section . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

11.3 Provision formodular flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

11.4 Evaluation of discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

11.5 Computation of stage-discharge relationship . . . . . . . . . . . . . . . . . . . . 10

11.6 Graphical approach todesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

11.7 Limits of application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

11.8 Uncertainty of measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

12 U-throated (round-bottomed) flumes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

12.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

12,2 Location ofhead measurement section . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

12.3 Provision formodular flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

12,4 Evaluation of discharge.......,.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

12.5 Computation of stage-discharge relationship . . . . . . . . . . . . . . . . . . . . . . 14

12.6 Limits of application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

12.7 Uncertainty of measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

13 Errors in flowmeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

13.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

13.2 Sources of error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

13,3 Kinds of error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

13.4 Errors in coefficient values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

13,5 Errors in measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

13.6 Combination of uncertainties to give overall uncertainty on discharge 17

Annexes

A Guide for the selection of weirs and flumes Ior the measurement

of the discharge of water in open channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

B Symbols andunits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~

C Velocity distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...22

D Computation of discharge using boundary Isyer theory . . . . . . . . . . . . . . . . . . . . 23

E Examples illustrating methods for the computation of discharge . . . . . . . . . . . . 26

F Example of the computation of the overall uncertainty of dischargemeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~

G Determination of height of hump – Rectangular throated flumes . . . . . . . . . . . 31

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IS 14869:2000

ISO 4359:1983

Indian Standard

LIQUID FLOW MEASUREMENT IN OPENCHANNELS — RECTANGULAR, TRAPEZOIDAL

AND U-SHAPED FLUMES

1 Scope and field of application

This International Standard deals with the measurement offlow in rivers and artificial channels under steady or slowly vary-ing flow conditions, using certain types of standing-wave (or

critical depth) flumes. A wide variety of flumes has beendesigned but only those which have received general accep-tance after adequate research and field testing, and whichtherefore do not require in-situ calibration are considered.Three types of flumes, covering a wide range of applicationsare recommended as follows :

a) Rectangular-throated (see figure 1).

b) Trapezoidal-throated (see figure 4).

c) U-throated, i.e. round-bottomed (see figure 5).

The flow conditions considered are uniquely dependent on theupstream head, i.e. subcritical flow must exist upstream of theflume, after which the flow accelerates through the contractionand passes through its critical depth, and the water levelbeyond the structuce is low enough to have no influence uponits performance.

Annex A gives the guidelines for the selection of weirs andflumes for the measurement of the discharge of water in openchannels.

2 References

ISO 748, Liquid flow measurement in open channels –Velocity-area methods.

ISO 772, Liquid flow measurement in open channels –Vocabulary and symbols.

ISO 1438, Liquid flow measurement in open channels usingthin-plate weirs and venturi flumes.

3 Definitions and symbols

For the purpose of this International Standard, the definitionsgiven in ISO 772 apply. A full list of symbols with the cor-responding units of measurement, is given in annex B.

4 Units of measurement

The units of measurement used in this International Standard

are SI units.

5 Selection of the type of flume

5.1 The type of flume that should be used depends uponseveral factors, such as the range of discharge to be measured,the accuracy required, the head available and whether or notthe flow carries sediment.

5.2 The rectangular-throated flume is simpler to construct.To achieve proportionality, i.e. to avoid either pending or draw-down in the approach channel when the discharge is variable,

provision of a hump in the bed becomes necessary withdischarges bigger or smaller than the design discharge (seefigure 2).

5.3 The trapezoidal-throated flume is more appropriatewhere a wide range of discharge is to be measured with consis-tent accuracy. This shape of throat is particularly suitablewhere it is necessary to work to a given stage-dischargerelationship.

5.4 The LJ-throated flume is useful for installation in aU-shaped channel or where discharge is from a circular-sectionconduit. It has found particular application in sewers and -atsewage works.

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IS 14869:2000ISO 4359:1983

6 Installation 6.2 Installation conditions

6.1 -Selection of site 6.2.1 General requirements

6.1.1 The flume shall be located in a straight section of chan-nel, avoiding local obstructions, roughness or unevenness of

the bed.

6.1.2 A preliminary study shall be made of the physical andhydraulic features of the proposed site, to check that it

. conforms (or can be constructed or modified so as to conform)to the requirements necessary for measurement of discharge bya flume. Particular attention should be paid to the followingfeatures in selecting the site :

a) The adequacy of the length of channel of regular cross-section available.

b) The uniformity of the existing velocity distribution (seeannex C).

6.2.1.1 The complete measuring installation shall consist ofan approach channel, a flume structure and a downstreamchannel. The condition of each of these three componentsaffects the overall accuracy of the measurements. Installationrequirements include such features as the surface finish of theflume, the cross-sectional shape of the channel, channelroughness and the influence of control devices upstream ordownstream of the gauging structure.

6.2.1.2 The distribution and direction of velocity may have anim~ortant influence on the performance of a flume (see 6.2.2and’’ennex C).

6.2.1.3 Once a flume has been installed, any changes in thesystem which affect the basis of the design will change thedischarge characteristics.

c) The avoidance of a stee~ channel (but see 6.2.2).

6.2.2 Approach channeld) The effects of any inc[eased upstream water levels dueto the measuring structure.

e) The conditions downstream (including such influencesas tides, confluences with other streams, sluice gates, mil[dams and other controlling features, including s,easonalweed growth, which might cause drowning).

f) The impermeability of the ground on which the struc-ture is to be founded and the necessity for piling, grouting

or other means of controlling seepage.

g) The necessity for flood banks, to confine the maximumdischarge to the channel.

h) The stability of the banks, and the necessity for trimm-ing and/or revetmant.

j) Uniformity of the section of the approach channel.

k) Effect of wind, which can have a considerable effect onthe flow over a river, weir or flume, especially when theseare wide and the head is small and when the prevailing windis in a transverse direction.

m) Aquatic weed growth.

n) Sediment transportation.

6.1.3 If the site does not possess the characteristics necessaryfor satisfactory measurements, or if an inspection of the streamshows that the velocity distribution in the approach channeldeviates appreciably from the examples shown in annex C, thesite should not be used unless suitable improvements are prac-ticable. Alternatively, the performance of the installationshould be checked by independent flow measurement.

6.2.2.1 If the flow in the approach channel is disturbed byirregularities in the boundary, for example large boulders orrock outcrops, or by a bend, sluice gate or other feature whichcauses asymmetry of discharge across the channel, the ac-curacy of gauging may be affected. The flow in the approach

channel should have a symmetrical velocity distribution (seeannex C) and this can most readily be achieved by providing along straight approach channel of uniform cross-section.

6.2.2.2 A length of approach channel five times the water-surface width at maximum flow will usually suffice, providedflow does not enter the approach channel with high velocity viaa sharp bend or angled sluice gate. However, a greater lengthof uniform approach channel is desirable if it can be readily pro-vided,

6.2.2.3 The length of uniform approach channel suggestedin 6.2.2.2 refers to the distance upstream of the head measur-

ing position. However, in a natural channel it would beuneconomic to line the bed and banks with concrete for thisdistance, and it would be necessary to provide a contraction inplan if the width of the lined approach to the flume throat is lessthan the width of the natural channel. The unlined channelupstream of the contraction shall nevertheless comply with therequirements of 6.2.2.1 and 6.2.2.2.

6.2.2.4 Wing walls to effect a contraction in plan shall besymmetrically disposed with respect to the centre line of thechannel and should preferably be curved with a radius not lessthan 2HmaX. The downstream tangent point shall be at least

H~ax upstream of the head measurement section, and the linedsection of approach channel from the end of the curved wingwalls to the entrance transition of the flume shall be ofprismatic section.

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IS 14869:2000

ISO 4359:1983

6.2.2.5 Inachannel where the flow is free from floating andsuspended debris, good approach conditions can also be pro-vided by suitably placed baffles formed of vertical laths, but nobaffle should be nearer to the point at which head is measuredthan 10IfmaX.

6.2.2.6 Under certain conditionsa hydraulic jump may occurupstream of the measuring structure, for example if theapproach channel is steep. Provid~d the hydraulic jump is atadistance upstream of not less than about 3017maX, flowmeasurement will be feasible, subject to confirmation that an

even velocity distribution exists at the gauging section.

6.2.2.7 Conditions intheapproach channel can beverifiedbyinspection or measurement for which several methods areavailable such as floats, velocity rods, or concentrations of dye,the last being useful in checking conditions at the bottom of the

channel. A complete and quantitative assessment ofvelocity distribution may be made by means of a current meter.The velocity distribution should then be assessed by referenceto annex C.

6.3 Flume structure

6.3.1 The structure shall be rigid and watertight and capableof withstanding flood flow conditions without damage fromoutflanking or from downstream erosion. The axis shall be inline with the direction of flow of the upstream channel, and the

gebmetry shall conform to the dimensions given in the relevantclauses.

6.3.2 The surfaces of the flume throat and the immediate ap-proach channel shall be smooth : they can be constructed inconcrete with a smooth cement finish or surfaced with asmooth non-corrodible material. In laboratory installations, thefinish shall be equivalent to rolled sheet metal w planed,sanded and painted timber. The surface finish is of particularimportance within the prismatic part of the throat but can berelaxed a distance along the profile 0,5HmaX upstream and

downstream of the throat proper.

6.3.3 In order to minimise uncertainty in the discharge, thefollowing tolerances are acceptable :

a) On the bottom width of the throat, 0,2 % of this widthwith an absolute maximum of 0,01 m.

b) On deviation from a plane of the plane surfaces in thethroat, 0,1 % of L..

c) On the width between vertical surfaces in the throat,0,2 ‘A of this width with a maximum of 0,01 m.

d) On the average longitudinal and transverse slopes ofthe base of the throat 0,1 YO.

e) On a slope of inclined surfaces in the throat, 0,1 %.

f) On a length of the throat, 1 % of L-.

g) On deviation from a cylindrical or a conical surfaca in

the entrance transition to the throat, 0,1 % of L.

h) On deviation from a plane of the plane surfaces in theentrance transition to the throat, 0,1 YO of L.

j) On deviation from a plane of the. plane surfaces in theexit transition from the throat, 0,3 YO of L.

k) On other vertical or inclined surfaces, deviation from aplane or curve, 1 Y..

m) On deviation from a plane of the bed of the linedapproach channel, 0,1 YO of L.

—The structure shall be measured on completion, and averagevalues of relevant dimensions and their standard deviations at95 YO confidence limits computed. The former shall be used forcomputation of discharge and the latter shall be used to obtainthe overall uncertainty in the determination of discharge (see13.5).

6.4 Downstream conditions

The flow conditions downstream of the structure are importantin that they control the tail water level which may influence the

operation of the flume. The flume shall be so designed that itcannot become drowned under the operating conditions (see10.3.1, 11.3.2 and 12.3.2). Construction of a flume in a river or

stream may alter flow conditions and cause scouringdownstream of the structure. This may result in accumulation

of river bed material further downstream which, in time, mayraise the normal water level sufficiently to drown the flume,particularly at low rates of flow. Any such accumulation ofmaterial shall be removed before it becomes excessive.

7 Maintenance – General requirements

Maintenance of the measuring structure and the approachchannel is important to secure accurate continuous

measurements.

It is essential that the approach channel to flumes shall be keptclean and free from silt and vegetation as far as practicable forat least the distance specified in 6.2.2.2: The float-well, and theentry from the approach channel shall also be kept clean andfree from deposits.

The throat and the curved entry to a flume shall be kept cleanand free from algal growths.

8 Measurement of head

8.3 General requirements

8.1.1 Where spot measurements are required, the headupstream of the flume throat can be measured by a vertical orinclined gauge, a hook, point, wire or tape gauge. Where a

continuous record is required, a recording gauge shall be used.The location of the head measurement section is dealt with in10.2, 11.2 and 12.2.

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IS 14869:2000

ISO 43~9 :1983

8.1.2 As the size of the flume and thehead on it reduces,small errors in construction and in thezero setting and readingof the head measuring device become of greater relative impor-tance.

100mm diameter pipe is usually suitable fora fiow measure-mentinthe fieid. Adiameterof3 mmmaybe appropriate in thelaboratory.

8.3 Zero setting

3.2 Gauge well

8.2.1 It is usual to measure the head in a separate gauge wellto reduce the effects of water surface irregularities. When thisis done, it is also desirable to measure the head in the approachchannel asa check.

8.2.2 Thegauge well shall b.evertical andof sufficient heightand/or depth to cover the full range of water levels. In fieldinstallations it shall have a minimum margin of 0,3 m over the

maximum water level estimated to be measured. Attherecom-mended position for the measurement of head, the well shall beconnected to the approach channel by means of a pipe or slot.

8.2.3 Both the well and the connecting pipe or slot shall bewatertight, and where the well is designed for the accommoda-tion of the float of a level recorder, it shall be-of adequate size

and depth to give clearance around the float at all stages. Thefloat shall not be nearer than 0,075 m to the wall of the well.

8.2.4 The pipe or slot shall have its invert not less than 0,06 mbelow the lowest level to be gauged, and it shall terminate flushwith the boundary of the approach channel and at right anglesthereto. The approach channel boundary shall be plain andsmooth (equivalent to carefully finished concrete) within adistance of ten times the diameter of the pipe or width of slotfrom the centre line of the connection. The pipe maybe oblique

to the wall only if it is fitted with a removable cap or plate, setflush with the wall, through which a number of holes aredrilled. The edges of these holes shall not be rounded orburred.

8.2.5 Adequate additional depth shall be provided in the wellto avoid the danger of the float grounding either on the bottomor on any accumulation of silt or debris. The gauge wellarrangement may include an intermediate chamber of similarsize and proportions between it and the approach channel, toenable silt and other debris to settle out where they may be

, readily seen and removed.

8.2.6 The diameter of the connecting pipe or width of slotshall be sufficient to permit the water level in the well to followthe rise and fail of head without appreciable delay, but on theother hand it shall be as small as possible consistent with easeof maintenance, to damp out oscillations due to short periodwaves.

8.2.7 No firm rule can be laid down for determining the size ofthe connecting pipe or slot, because this is dependent on thecircumstances of the particular installation, for examplewhether the site is exposed and thus subject to waves, andwhether a large diameter well is required to house the floats ofrecorders. It is preferable to make the connection too largerather than too small, because a restriction can easily be addedlater if short period waves are not adequately damped out. A

8.3.1 Initial setting of the zero of the head-measuring deviceaccurately with reference to the level of the invert of the throat,and regular checking of this setting thereafter, is essential ifoverall accuracy is to be attained.

8.3.2 An accurate means of checking the zero shall be pro-vided. The instrument zero should be obtained by a directreference to the throat invert, and a record of the setting made

in the approach channel and in the gauge well. A zero checkbased on the water level (either when the flow ceases or justbegins) is liable to serious errors due to surface tension effectsand shall not be used.

9 Determination of discharge .

-9.1 General equations for discharge

9.1.1 Critical depth theory, augmented by experimental data,may be used to deduce the basic equations for free dischargethrough a streamlined contraction. The simple theory relates tothe frictionless flow of an ideal fluid, and an additional coeffi-cient has to be introduced in practice, either based on experi-ment or deduced by considering a modification to the simpletheory, taking account of the boundary layer development witha real fluid such as water. This International Standard describesdesk calculating methods for determining discharge but wheremany structures are being considered, computer analysis maybe more appropriate.

9.1.2 The specific energy, E, of flow in an open channel isgiven by :

E = l)d + a@12g . . . [1).. “,’.!‘!,

where .,.J,,*

d is the depth of flow;

V is the average velocity through the section;

a is the coefficient taking into account non-uniformity invelocity distribution;

~ is the coefficient dependent on the mean curvature ofthe streamlines.

The equation of continuity is :

where

Q is the total discharge;

A k the area of the flow cross-section.

. . . (2)

4

1S 14869:2000ISO 4359:1983

Hence ()Q= g & Cv be h;12 . (7)

E = ~d + czQ212gA2 . . . (3)

whereCritical flow occurs when E has its minimum value for a givendischarge Q, treating the depth d, and the area A which isrelated to it for any given cross-secrion geometry, as thevariables. It can be shown that the specific energy is a minimumwhen

Cv = (HJhJ312 . . (8)

Cv is a dimensionless coefficient allowing for the effect ofapproach velocity on the measured water level upstream of theweir. Effective heads and widths can be determined fromobserved values

&A3Q2=— . . .

aw(4) .—

a) by a simple empirical correction (see 10.4.1, 11.4.1 and12.4.1), orwhere w is the water surface width.

b) by theoretical considerations of boundary layerdevelopment (see annex D).9.1.3 Experimentally observed velocity profiles indicate that

the velocity distribution is almost uniform in the throat ofa flume, and it may be assumed therefore that a = 1. [fthe streamlines are not significantly curved, a conditionapproached if the throat is in excess of a certain minimumlength, then ~ = 1. Hence the basic equation defining critical

flow through a strtitimlined contraction is

9.2.3 Analogous relationships.can be derived for flumes withtrapezoidal throats :

()2 312&Cv C, be h:12Q= ~ . (9)

Q = (g A:/wJ1/2 . . . (5)where

the subscript c indicating critical flow.C~ is a numerical coefficient which-takes into account thenon-rectangular flow section.

9.1.4 Equation (5) is not immediately applicable to the-theoretical derivation of a stage-discharge relationship,because :

C, = f{m Hce/be) . . . (lo)

Hce is the effective total head at critical section.

a) it does not take account of the development of a boun-dary layer of slower moving fluid in the throat; Although theoretical design and calibration procedures exist

utilizing the above equations, they are cumbersome. This islargely because C~ is dependent on Hce which differssignificantly from the gauged head h. An alternative method ofcomputing discharge from equation (5) is given in 11.5.

b) it is based on the area and water surface width at thecritical section, the location of which is ‘ill-defined so that

direct measurement of the water level at that section isimpractical.

9.2.4 The corresponding relationship for U-throated flumesis :Thus the basic equation has to be transformed into a more

practical form, and adjusted to take account of the boundaryeffects. ()Q= ;3[2&C, Cu De h:12 . . . (11)

9.2 Calculation of discharge from observed head

9.2.1 For the flow of a real fluid through a streamlined rec-tangular contraction, equation (5) can-be expressed in terms ofthe effective total head as follows :

CU is a numerical constant which takes account of thenon-rectangular flow section.

Cu = f(HcJDe) . . . (12)

(6) De is the effective diameter of base of the U-shapedthroat.

where

be is the effective width of flume throat;

He is the effective total head.

9.3 Calculation of stage-discharge relationships

9.3.1 In the case of a flume with a rectangular throat equa-tion (7) has to be used to compute the stage-discharge relation-ship for the structure. However, equations (9) and (11 ) cannotconveniently be used to compute this relationship fortrapezoidal and U-throated flumes. An alternative approach canbe used.

9.2.2 Equation (6) can then be expressed in terms of he, theeffective head gauged upstream of the structure, for flumeswith rectangular throats es follows :

5

IS 14869:2000ISO 4359:1983 +

9.3.2 A theoretical calibration for a gauging structure for thewhole range of discharge can be derived by considering flowconditions in the throat of the flume and d~ducing correspon-ding heads and discharges. The principle of the method is toselect a series of values of d= the critical depth in the throat,and calculate corresponding values of Q and He using theexpressions

Q = (g /&/wc)’/2 ...

and

He=dc+~ . . .c

(13)

(14)

The effective total head, He, can be converted to total head, H,as described in 11.5 and 12.5 and total head H, can be con-verted to measured gauged head, h, as outlined in 1“1.5 and12.5.

. . . (18)

9.4.4 For a trapezoidal approach channel :

A=(h+p)[B+m#r+f2)l

where

B relates to the bed width of the approach channel;

ma is the side slope of the approach channel walls.

9.4.5 For a U-shaped approach channel :

‘4 = : D:J[M + p)/Dal . . . (19)

where Da is the diametrical width of the approach channel.

10 Rectangular throated flume

9.4 Approach velocity

10.1 Description

9.4.1 The total head is related to the gauged head by theequation :

He = he + a@g . . . (15)

where

.—Va is the mean velocity in the approach channel at thegauging section;

a is a coefficient (the kinetic energy or Coriolis coefficient)which takes account of the fact that the kinetic energy headexceeds V~/2g if the velocity distribution across the sectionis not uniform.

In applying the equations in this International Standard, a maybe taken as unity, with the tolerances given in 10.7.2, 11.8.2and 12.7.2 and the provisions of 6.2.2 and bearing in mindannex C.

9.4.2 From equations (8) and (15}, coupled withequatiorls (7), (9) and (11), a general relationship for Cv may bedefined by :

(q/3 _l)l/2 ~ 1 ~be he

—cvc~oru . . .3J3 A

(16)

where A is the cross-sectional area of the approach channelflow.

9.4.3 For a rectangular approach channel

A= B(h+p) . . . (17)

twhere

B is the width of the approach channel;

p is the height of flume invert above the invert of theapproach channel.

10,1.1 The rectangular throated flume consists of a constric-tion of rectangular cross-section symmetrically disposed withrespect to the approach channel.

This is the most common type of flume and the easiest to con-struct, but it cannot be adapted to suit non-rectangular chan-nels when loss of head is important.

10.1.2 There are three types of rectangular throated flumes :

a) with side contractions only;

b) with bottom contraction or hump only;

c) with both side and bottom contractions.

The type to be used depends on downstream conditions atvarious rates of flow, the maximum rate of flow, the permissi-ble head loss and the limitations of the h/b ratio, and whetheror not the stream carries sediment.

10.1.3 The invert of the throat shall be level throughout itswidth and length. The sides of the flume throat shall be verticaland parallel and square with the invert, so that the width of thethroat is accurate from top to bottom and end to end. The sur-faces of the throat and entrance transition shall be smooth;they may be constructed in ~oncrete with a smooth finish, orlined with a smooth non-corrodible material. The centre line of

the throat shall be in line with the centre line of the approachchannel. In the case of flumes without a hump (bottom con-traction), the floor of the approach channel shall be level, and

at no point higher than the invert of the throat, for a distance ofat least 2hmaX upstream of the haad measurement section.

10.1.4 The flume geometry shall be as shown in figure 1. Theradius of the curved transition to the bed and walls of the throat

shall beat least 4P and 2(B – b) respectively. The 1 in 6 expan-sion beyond the throat may be truncated as shown in figure 1when recovery of head is not important.

6

IS 14869:2000

ISO 4359:1983

10.1,5 When the required recovew of head is more than80 O+., the alternative flume geometry with side and bottomcontractions could be as shown In figure 2. The glacis slopedownstream of the throat shall be I In 20 for a length of 2H

(where }{ k the total head above tlw sill of the hump) beyondwhich it may be more. The length of (he side walls downstreamof throat shall be 4H and their divergence shall be 1 in 10. Forgreater recovery of heads, the side WJIIS shall be parallel up tothe toe of the glacis and then a hyperbolic expansion should begwen up to the pent where the dow[)s?rearn channel begins.

NOTE When the ratio of the depth of water downstream above thesillof the throat to depth of water upstrezimover the sillof the throat islessthan 0,5, a flumed standing wave fall (see figure 3) should be used,wth baffle platform, baffle wall, sttlling bas!n and deflectors for effi-cient dissipationof energy.

10.2 Location of head measurement section

The head on the flume shall be measured at a point far enough

upstream of the contraction to be clear of the effects of draw-.down, but close enough to ensure that the energy loss betweenthe section of measurement and the throat will be negligible. Itis recommended that tne head measurement section be locateda distance of between 3 and 4 times /rmaX upstream of theleading edge of the entrance transition.

10.3 Provision for modular flow

10.3.1 Flow is modular when it is independent of variations intail-water level, and for this to be so, the velocity has to be thecritical velocity in the throat, The invert level shall therefore beat such an ‘elevation as to produce Imodular flow for the fullrange of design discharges. The dimensions of the flume shall

be such that the total head upstream (relative to throat invert) isat least 1,25 times that downstream (assuming subcritical flowexists downstream) at all rates of flow, Nevertheless, it may bepossible to reduce this difference provided that the occurrenceof free discharge is confirmed. On the other hand, if theexpan-sion is truncated, the ratio shall be at least 1,33.

10.3.2 In artificial channels it is frequently possible to deter-mine the depth downstream at various rates of flow withreasonable accuracy, for example by means of a friction for-

mula if the channel is long enough and of constant slope or byreference to the characteristics of controlling featuresdownstream.

If the flume is to be installed in an existing channel or streamthe following information should then be obtained at the site :

a) The maximum depth recorded with an estimate of therate of flow at that depth.

b) The approximate depths at two or more intermediaterates of flow.

c) The dead water level in the stream, i.e. the level underzero flow conditions.

10.4 Evaluation of discharge

10.4.1 The basic discharge equation for rectangular throatedflumes is given in 9.2.2 and this may be rewritten as :

()2 3’2 –

Q={: xjgCv Co b h 3i2 (20)

where

.,. (21)

but

be = h -20.

he=h– J,

where 8, is the boundary layer displacement thickness.

Substituting from (22) to (23) into (21)

(22)

(23)

(24)

where L is the length of prismatic section of the contraction at

the flume,

For most installations with a good surface finish the valueof i$,/L will, in practice, lie in the range 0,002 to 0,004.Provided 105> Llk~ > 4 O(XIand Re > 2 x 105, 6+IL maybe assumed equal to 0,003.

Equation (24) then becomes :

(25)

Various values of CD derived from this equation are given intable 1 and these are the values which apply to well-constructed installations as detailed above.

10.4.2 A more sophisticated approach is given in annex Dwhich takes into account the development of the boundarylayer in the throat of the flume. This enables the user to takeinto account the variability of ti, /L and to use the more general

expression for CD given in equation (24).

10.4.3 The value of Cv can be computed from equations (16),

(17), (22) and (23), or more conveniently, can be read fromfigure 6 or extracted from table 2 to a sufficiently close approx-imation. Figure 6 is expressed in terms of be, he and A, but inpractice it will be found acceptable to use J and h in place of be

and he in entering the diagram. Table 2 implicitly makes thisassumption. In cases where the approach channel is not trulyrectangular in section where h is measured, B can be deter-mined from the expression :

~ = Cross-sectional area

h+p. . . (26)

10.4.4 The procedure indicated in 10.4.3 shall be adopted forcalibration. For preliminary design purposes, however, in thecase of the flume shown in figure 2, the discharge equation canbe expressed as :

()Q= ; 3’2&c@2 . . . (27)

7

IS 14869:2000

ISO 4359:1983

where Cis the overall coefficient and for design purposes mayreassumed tohavea value between 0,97 and 1,00.

When the structure is combined with a bridge having piers inthe throat, the term b in equation (27) can be replaced by

(b-npbp-2Ccnp H)

-where

b~ isthewidth of-pier;

rrD is the number of piers;

CC isthe coefficient of contraction

= 0,045 forpiers with round nose

= 0,040 forpiers with pointed nose.

10.5 Computation of stage-discharge

relationship

10.5.1 The stage-discharge relationship for a rectangularthroated flume is obtained by considering a series of values ofgauged head, h, andrepeating themethod given in 10.4.1 to10.4.3 for each. Corresponding gauged heads and dischargescan then be plotted toprovide thestage-discharge relationshipfor the flume.

10.6 Limits of application

10.6.1 The practical ower limit of h is related to themagnitude of the influence of fluid properties and boundaryroughness. The recommended lower limit of 0,05 m or 0,05L,whichever is the greater.

10.6.2 There is also a hmit on the ratio of the areas of theapproach channel and the throat arising from difficultiesexperienced when the Froude number in the approach channelexceeds 0,5. The recommended upper limit of

bh

B(h + p)

is 0,7.

10.6.3 Other limitations arise from inadequate experimentalconfirmation for extreme sizes or geometries :

a)

b)

c)

10.6.4

b shall be not less than 0,10 m.

h/b shall be not more than 3.

h shall be not more than 2 m.

h/L should not exceed 0.50. This limitation on h/Larises from the necessiiy to ensure parallel flow conditions atthe critical-section in the throat. h~~x/L maybe allowed to riseto 0,67, with an additional uncertainty in coefficient of 2 %.

8

10.7 Uncertainty of measurement

10.7.1 The overall uncertainty of measurement will dependon :

a) the standard of construction and finish of the flume;

b) the uncertainty of the formula for the coefficient ofdischarge;

c) the uncertainty of the velocity of approach coefficient;

d) a correct application of the installation conditions;

e) the uncertainty of the zero setting;

f) the uncertainty of measurement of the geometry of theflume;

g) the accuracy of the head gauge.

10.7.2 With reasonable skill and care in the construction ofthe flume, the coefficients are expected to have an uncertaintyapproaching 1 % in favorable circumstances, for examplewhen CD and Cv are not far from unity. An estimate of ‘the

combined percentage uncertainty (XC) on the coefficients maybe obtained from the equation :

xc = t [1 +20(CV - CD)] ...(28)

10.7.3 The method by which the uncertainty of the coeffLcients is to be combined with the uncertainties due to othersources of error is explained in ciause 13. [In applying equa-tion (28), CO is obtained from equation (25). ]

11 Trapezoidal throated flumes

11.1 Description

11.1.1 Trapez~idal throated flumes can be designed to copewith many different flow conditions, and the optimum throat

geometry (i.e. bed width and side slopes) will depend on therange of flow to be measured and on the characteristics of thestream or channel in which it is to be installed. Design methodsby which the geometry might be selected to approximate to an

existing or predetermined stage-discharge relation are outlinedin 11.6.

11.1.2 Trapezoidal throated flumes should have a geometry

generally as indicated in figure 4. In some circumstances,however, it will be appropriate to make the invert of the throatlevel with the invert of the approach channel, i.e. p = O; thiswill be the case if sediment has to be conveyed through theflume. This International Standard covers only Ihat class oftrapezoidal throated flume in which the sloping walls of thethroat extend above water level.

11.1.3 The flume shall be installed with the throat centre linein line with the centre of the approach channel. Subcritical flowshall exist in the flume approach, and the flume shall be

.-

IS 14869:2000ISO 4359:1983

installed at such an elevation as to operate with free dischargethroughout the range. The surfaces of the flume shall be of

smooth concrete, galvanized steel or other smooth non-corrodible material. The throat section is of particular impor-tance and shall have a level invert and be truly prismatic, thesloping walls being plane surfaces, symmetrically disposed andmaking a sharp intersection with the invert of the throat.

11.1.4 The entrance and exit transitions may be plane or

curved surfaces to suit convenience of construction.

11.1.5 The convergence of the entrance transition on anyplane section, if formed from plane surfaces, should not bemore than 1 in 3 at each side. If curved surfaces are used, theseshall be well-streamlined, for exampleby using the face of in-clined cylinders, or a skew cylinder, or a vertical-axis cone. Thesurfaces shall lie entirely inside (i.e. on the channel centre-lineside of) planes defining a 1 in 3 convergence on each side, andif curved shall terminate truly tangential to the planes formingthe throat.

11,1.6 The surfaces forming the exit transition shall lie entirelyinside planes defining a 1 in 3 expansion on each side. A 1 in 6

expansion gives very good recovery of head and a high modularkmit.


The head on the flume shall be measured at a point far enough

upstream of the cont~action to be clear of the effects of draw-down, but close enough to ensure that the energy loss betweenthe section .of measurement and the throat will be negligible. Itis recommended that the head measurement section shouldbelocated a distance of between 3 and 4 times /rmaXupstream of

the leading -edge of the entrance transition.

11.3.3 In artificial channels, it is frequently possible to deter-mine the depfh downstream at various rates of flow approx-imately, for example by means of a friction formula if the chan-nel is long enough and of constant slope or by reference to thecharacteristics of controlling features downstream.

11,3.4 If the flume is to be installed in an existing channel or

stream, the following information should then be obtained atthe site :




11.3 Provision for modular flowwhere

11,4 Evaluation of discharge

11.4.1 The basic discharge equation for flumes withtrapezoidal throated flumes is given in 9.2.3 and may beexpressed as :

()~=;3J2&Cv C, CDb h3J2 . . . (29)

The modular discharge coefficient, CD, is given by an expres-

sion analogous to that for a rectangular flume as given in equa-tion (24).

11.3.1 Flow is modular when it is independent of variations intail-water level, and for this to be so, the velocity shall passthrough the critical velocity in the throat. The invert level shalltherefore be at such an elevation as to produce modular flowfor the full range -of design discharges. The dimensions of theflume shall be such that the total head upstream is well inexcess of that downstream when related to the invert of thethroat (assuming subcritical flow exists downstream).

11.3.2 As the modular limit is dependent on head recoverybeyond the throat, the necessary ratio of upstream to

downstream head is dependent on the angle of expansion, asfollows :

1 in 20 each side HIH~ > 1,10

1 in 10 each side H/H~ > 1,20



where Hd is the total head just beyond the exit transition,

related to the flume invert.

q is a function of m;

m is the slope of flume sides (m horizontal to 1 vertical).

For installations with a good surface finish c$,/L can be taken as

0,003 and equation (30) reduces to

CD=0°+)0+)3’2 (31)The value of q is obtained from figure 7 and the value of themodular discharge coefficient is then obtained by substitutingknown values of q, L, b and h in equation (31).

11.4.2 Annex D describes a method of determining CD from

equation (30) taking into account the variability of d*/L.

11.4.3 The value of Cv can be computed from equations (16)and (18) making the assumptions that be = b and hp = h.Alternatively, figure 6 may be used in association with thecalculated value of A using equation (18).

9

IS 14869:2000ISO 4359:1983

11.4.4 The value offunction of In[{,.Pl!Je

(’, <o be !rs,rted in equation (29) is aand this is yven in figure 8. If it were

accurate to assume that Hce = h, thegauged head, the use of

the basic equation to evaluate discharge would be direct,Ihougll perhaps tedious. Initially it can be assumed thatII , /]. tiowever, to perforn) ~1 accurate calibration, or

accurately to deduce the dischar:y for a spot measurementof head, successive approximatic][l is necessary, using the

equ3tion :

(32)

For practical purposes it is sufficiently accurate to make the

assumption that /te = h and bc = II giving a more readilyusable exmession :

fnH nrh—-— ~ c213

be=’ = b v. . . (33)

11.4.5 The computation of discharge to the first approxima-tion for a given head acting on a trapezoidal flume of known

geometry is thus made as follows :

a) List the values of m, ma, .!J,B, p, L and g.

b) Compute the area of the approach channel cross-section using equation (17) or equation (18) orequation (19) depending on the shape of the approachchannel.

— ——.c) Calculate fl = J(I + rn2) – m, or obtain fromfigure 7,

d) Calculate C~fromequation (31) using known valuesofrl, L, band h.

e) As a first approximation, assume mHCJbe = mhlband obtain C~’rom figure 8for the given value of h.

f) Obtainthe initiai value of Cvfromfigure 6assuming thathe = hand be = band entering thediagram at C~bh/A.

g) Calculate the first approximation value of Qusingequa-tion (29) with the above values of CD, C, and Cv.

11.4.6 Following the first approximation in 11.4.5 the valuesof C=, Cv and Q need refining. CD holds its final value. The nextapproximation proceeds as follows :

a) mHcelbe is obtained from equation (33).

b) Figure 8 then provides the new value of C,.

c) C~behJA can now be worked out (assuming be = band he = h), and a new value of Cv obtained from figure 6.

d) The value of CD, together with the revised values of c.and C~ shall then be inserted in equation (29) to obtain amore accurate figure for Q.

11.4.7 The procedure carried out in 11.4.6 shall be repeateduntil sufficient precision has been obtained. An example of themethod of computation of discharge is given in annex E.


relationship

11.5.1 Select a range of values of dc the critical depth in thethroat, (a roughly logarithmic series is more convenient than an

arithmetic one) and for each value proceed as follows :

a)

b)

c)

d)

11.5,2

WC = b + 2mdc (34)

Ac = (b + mdc) de (35)

Calculate Q using equation (13)

Calculate He using equation (14)

The next stage is to calculate the head correction,H+ = H - He. For installations with a good finish 13,1Lcan betaken as 0,003 and H. can be derived but substituting this valuein the expression :

H*=% X:XL . .w=

(36)

where

P, = b + 2dc (1 + m2)’12 ,.. (37)

If the surface finish is not smooth the value of d,/L can beobtained as described in annex D. Substitution of thecalculated value of d+/L in equation (36) gives the value of H.taking into account the variability of iS,/L.

11.5.3 For each value of dc, calculate the total head,H = He + H, The values of Q and H derived in 11.5.1 and11.5.2 provide the total head discharge relationship for theflume.

11.5.4 To convert from the total head, H, to gauged head, h,the expression

~2

h=H–2%

(38)

shall be used, where iia is the mean velocity in the approachchannel at the gauging section. In applying equation (36), thegeometry of the approach channel shall be used to compute itscross-sectional area Aa. Assuming this to be of trapezoidal sec-tion, the appropriate equation is

A,={h+p) [B+m, (h+p)l . . . (39)

where

p is the height of the hump at the throat;

B is the bed width of the approach channel;

ma is its side slope (ma horizontal to 1 vertical).

“lo

IS 14869:2000

ISO 4359:1983

11.5. FJ Because /~ occurs Im[,![cl?ly he right hand side of

er~!j;!!ion (38), a method of suc ;essii,( ipproxir nation is needed

to delermine Ii

First approximation :

se! t! ]fanci hcncecalculat? 1 ,1 ‘- m equation (39), Insert

,. lr~ equation (38), wrlere v,+, (L) ! and thus obtain /1.

Se(ornd approxlrnatloll

Obtain Iaz frorr equatior) (39) 11-s:rtirlg h = hl, Hence,/ -= Q .la2 and /12 = 1/ L:2’:!L,:.

“Third approximation, etc.

Repeat procedure until h,, – h,, , is too small to have asignificant etfect on the accuracy,

11.5.6 Having thusworked outpairs ofvaIues of Qandh foraseries of values of dc, the calibration curve for the flume may beplotted to large logarithmic scales. Discharge values forintermediate yalues of h may be read off as necessary. Notethat the calibration curve is not a straight line on a log-log plot.

11.5.7 An example of the calculation of the stage-dischargerelationship for a trapezoidal flume (with and without boundarylayer corrections) is given in annex E.

11.6 Graphical approach to design

11.6.1 There is considerable flexibility in the design of atrapezoidal throated flume, and this permits the designer toselect values of m and b which will provide a close match to apredetermined relationship of head-to-discharge at two flows.For design purposes an approximate formula which effectivelyassumes CD = 1,0 is adequate.

11.6.2 A convenient graphical method has been derived, us-ing equation (29) in the form

on the assumption that H = Hc for design purposes.

(40)

11.6.3 Required values of Q and H are estimated from aknowledge or estimate of the existing stage-discharge relation-ship at the site, paying due regard to the head loss needed forfree flow, practical limitations on the height of the throat abovethe stream bed (it shall not be below “no flow” level), and otherlimitations given. The two values of

(41 )

corresponding to these boundary conditions are worked outand plotted on transparent material against H as abscissa onthe same logarithmic scales as in figure 9.

11.6,4 Vertical and horizontal guldel!nes are added to theoverlay and the Y =. 1 and I -- 1 co ordinates are marked.Move the overlay, keeping the axes parallel with figure 9, unttl

the two plotted points Ile on the curve. The intercept ot \ = 1on the overlay with the !’-ax!s of fl~ure 9 gives 1,’!~ and theintercept ot \ 1 on the overlay wtth the v-axis of figure 9gives Ij) I’]and hence )Tl

11.6,_5 An example IS shown by dotted lines for which

0,21m; corresponding to discharges of 24,8 m3/s and0,22 m3!s respectively. These requirements are met by a flumein which b = l,22m and m = 0,90.


11,7.1 The practical lower limit of h is related to the

magnitude of the influence of fluid properties and boundaryroughness. The recommended lower limit is 0,05 m or 0,05L,whichever is the greater.

11.7.2 h/L should not exceed 0,50. This limitation on h/Larises from the necessity to ensure parallel flow conditions atthe critical section in the throat. h~aX/L maybe allowed to riseto 0,67 with an additional uncertain~ in coefficient of 2 ?10.

11.7.3 The ratio of areas of the approach channel and thethroat should preferably be such that the Froude number, Fr, inthe approach channel does not exceed 0,5 at any discharge.This shall be checked at each end of the range, and atintermediate flows, using the equation

Fr, = ~/~- . . . (42)

11.7.4 It may be necessary in some situations (for examplewhere coarse sediment is being carried which would deposit inthe approach channel) to allow Fra to rise to 0,6 but, because

of surface irregularities at high Froude numbers, the measure-ment of head and performance of the flume are less certain,and an additional tolerance of 2 VO should be allowed when0;6 > Fr, > 0,5.

11.7.5 Other limitations arise from inadequate experimentalconfirmation for extreme eizes or geometries :

a) b shall be not less than 0,1 m;

b) h shall not be more than 2 m.

c) At all elevations, the width between the throat wallsshall be less than the width between the approach channelwalls at the same elevation, i.e. there shall be a contractionwherever the water surface lies.

d) The sloping walls of the throat shall continue upwardswithout change of slope far enough to contain themaximum discharge to be measured.

11

IS 14869:2000ISO 4359:1983

11.8

11.8.1on :

a)

b)

Uncertainty of measurement

The overall uncertainty of measurement will depend

the standard of construction and finish of the flume;

the uncertainty of the formula for the coefficient ofdischarge;






11.8.2 With reasonable skill and care in the construction ofthe flume the basic equation and coefficients are expected tohave an uncertainty approaching 1 % in favorablecircumstances, for example when Co and Cv are not far fromunity. An estimate of the combined percentage uncertainty XC

on the coefficients can be obtained from the equation :

xc = + [1 + 20(CV - CD)] ...(43)

11.8.3 The method by which the uncertainty in the coeffi-cients is to be combined with uncertainties due to otharsources of error is explained in clause 13. [In applying theabove equation CD is obtained from equation (31).1

12 U-throated (round-bottomed) flumes

12.1 Description

12.1.1 Flumes with their inverts in the form’ of a cylindricalsurface with a horizontal axis cannot cope with such a widevariety of situations as the trapezoidal throated flume, but they

have advantages over the rectangular throated fluma in cartaincircumstances, for example in sewerage systems where theflow enters from a circular or U-shaped conduit. The sensitivityof a U-throated flume is greater than that of a rectangularthroated flume, especially in the lower range of discharge lyingwithin the lower semi-cylinder.

12.1.2 U-throated flumes shall have a geometry generally asindicated in figure 5. Two basic types are available when the

approach channel is U-shaped also :

a) A level invert arrangement in which no rise in invertlevel occurs at the throat.

b) A raised invart level, in which the rise in invert level ishalf the difference in thediametrical widths of the approachchannel and throat.

The former has advantages where heavy sediments are carried;the latter has the advantage of a simpler transition geometry.

12

12.1.3 The flume shall be installed with the throat centre linein line with the centre of the approach channel. Subcritical flow

shall exist in the flume approach, and the flume shall be in-stalled at such an elevation as to operate with free dischargethroughout the range. The surfaces of the flume shall be ofsmooth concrete, galvanized steel or other smooth non-corrodible material. The throat section is of particular impor-tance and shall have a level invert and be truly prismatic. Thelower part shall accurately conform to the surface of a semi-cylinder, and the walls shall be plane vertical surfaces parallel tothe axis of the semi-cylinder, the distance between themaccurately matching the invert diameter.

12.1.4 The lower part of the entrance transition, if formed of apart.conical, or part of a skewed conical, surface shall generatea convergence in any plane radial to the flume axis of not morethan 1 in 3. The upper part of the entrance transition, if formedof plane surfaces, shall converge at not more than 1 in 3 ateach side. If curved surfaces are used, these shall be well-streamlinad, for example generated by circular curves, and shalllie entirely inside the alternative part-conical part-planeentrance shown by the full lines in figure 5. They shall ter-minate truly tangential to the surfaces forming the throat.

12.1.5 The surfaces forming the exit transition shall La withinsurfaces defining a 1 in 3 expansion. A 1 in 6 expansion givesvery good recovery of head and a high modular limit.


The head on the flume shail be measured .at a point far enoughupstream of the contraction to be claar of the effects of draw-down, but close enough to ensure that the energy loss betweenthe section of measurement and the throat will be negligible. Itis recommended that the head measurement section be locateda distance of betwaen 3 and 4 times hmx upstream of theleading edge of the entrance transition.

12.3 Provision for modular flow

12.3.1 Flow is modular whan it is independent of variations intail-water level, and for this to be so, the velocity must passthrough the critical velocity in the throat. The invert level shalltherefore be at such an elevation as to produce modular flowfor the full range of design discharges. The dimensions of theflume shall be such that the total head upstream is well inexcess of that downstream (related to the invert of the throat).

12.3.2 As the modular limit is dependent on head recoverybeyond the throat, the necessary ratio of upstream todownstream head is dependent on the angle of expansion asfollows :

1 in 6 each side HIH~ > 1,241 in 3 each side H/H~ > 1,35

where Hd is the total head just beyond the exit transition,

related to the flume invert.

12.3.3 In artificial channels it is frequently possible to deter-mine the depth downstream at various rates of flow with

IS 14869:2000ISO 4359:1983

reasonable accuracy, for example by means of a friction for-mula if the channel is long enough and of constant slope or byreference to the characteristics of controlling featuresdownstream.

12.3.4 If the flume is to be installed in an existing channel orstream, the following information shall then be obtained at thesite :




12.4 Evaluation of discharge

12.4.1 The basic discharge equation for U-throated flumes isgiven in 9.2.4 and thlc may be written as :

()2 3’2&C, Cu CD D h312Q= y ,..

where

(44)

For installations with a good surface finish c5,/L can betaken as0,003 and equation (45) reduces to the form

‘.=(’-%)[-=)3’2 (4)in order to compute Q for a given value of h, it is thereforenecessary to evaluate the coefficients Cv, Cu and CD.

12.4.2 The value of CD is computed using equation (“W) andknown values of L, D and h. Annex D describes a method of

determining CD from equation (45) taking into account thevariability of d,/L.

12.4.3 If it were correct to assume that Hce = h, the gaugedhead (see figure 10) which expresses the shape coefficient Cuas a function of Hce/De, would provide a value of Cu directlyfor a given head and throat diameter. Although the assumptionHce = h may be made for design purposes, or as a firstapproximation; to develop an accurate calibration, or toaccurately deduce the discharge for a spot measurement ofhead, successive approximation is required, utilizing theequation :

Hce

he =C:13 . . . (47)

For practical purposes it is su”fficiently accurate to make the

assumption that he = h. Hence :

H=, H—==h- h

= C:’3e

““. (48)

12.4.4 The value of Cv can be computed from equations (16)and (19) making the assumption that he = h and be = b.Alternatively figure 6 gives a sufficiently close approximation.In entering figure 6, the value of Cu, as a first approximation,shall be read from figure 10 assuming Hce/De = h/D.

12.4.5 The approach channel area required for the use infigure 6 is obtained from the geometry of the approach channelat the given water level. If the approach channel is U-shaped,and the water level lies within the semi-circular base portion :

Aa=~D~(O–sin Ocos O)

where

()/j=cos-l l_?LD,

for da > ~ Da,

. . . (49)

(50)

(51 )

where da = h + p, i.e. the depth of water in the approachchannel at the gauging section relative to the invert level at thatpoint.

12.4.6 The computation of discharge for a given head acting

on a U-shaped flume of known geometry thus proceeds asfollows :

a) List the values of D, L, Da, p.

b) Compute the area of the approach channel cross-section. If it is U-shaped, use equation (49) or (51).

c) As a first approximation, assume HcelDe = h/D andobtain CU from figure 10 for the given value of h.

d) Calculate Cu Dh/A and obtain a first approximation for

CV from figure 6.

e) Compute Co from equation (46).

f) Calculate H,.e from equation (46) using the above valueof c“.

12.4.7 Following the first approximation in 12.4.6 the values

of H,.e, Cv and Cu need refining. The next approximation pro-ceeds as follows :

a) Making the assumption that De = D, evaluate Hce/Deand obtain a mew value of Cu from figure 10.

b) Evaluate Cu Dh/A and obtain a new value of Cv fromfigure 6.

c) Calculate the new value of Hce using equation (48).

13

IS 14869:2000ISO 4359:1983

12.4.8 Clause 12.4.7 shall be relx~led until sufficient pre-cision has been obtained.

12.4.9 Discharge islhencompulwi from equation (44). (Seeex;~mple In annex E )


relationship

125.1 For flow condn,ons for .*J’ih d, < D/Z, select aserws of values of 0, the semi-angle :,.lbtended at the centre ofcurvature of the invert by the water jLlrfa Ce, between 0,5 andn 12 radians. For each angle, evaluate the depth, water surfacewidth and cross-sectional area from :

dc 1a) –(1 - Cose) =f, (0)

5’2. . . (52)

(53)

Ac) J=-; (0 – sin 6 cos f?) = .f~ (0) , (54)

~2

11, j2t J3 mw be taken from table 3.

12.5.2 When dcsectional area arefollows :

a) WC=D

> D/2, water surface width and cross-

calculated for a range of values of dc as

. . . (55)

b)Ac=&2+(&D)D ...{56)/

12.5.3 The calculations described in 12,5.1 and 12.5.2 provide

a series of corresponding values of dc, WCand A ~ throughoutthe full range of a U-throated flume. The discharge, Q, and theeffective upstream head, He, for each value of dc can then becalculated using equations (13) and (14) respectively.

12.5.4 The next stage is to calculate the head correction,H, = H – He. For installations with a good surface finish,

8-IL can be taken as 0,003 and H, can be derived bysubstituting this value in the expression :

(57)

where

Pc = DO . . . (58)

Oi

‘)\

Pc=~+21dc–; D . . . (59)

Equation (58) applies when dc < D/2 (0 < x/2) and equa-tion (59) applies when dc > D/2. If the surface finish is not

14

smooth, the value of J,/L can be obtained as described IVannex D. Substitution of the calculated value of d+/[. in equa-tion (57) gives the value of H+taking into account the variabilityof (). [[..

12,5.5 For each value of ~/, , calculate the total head,

H = Ife + H,. The values of Q and H derived in 12.5.3 and12.5.5 provide the total head discharge relationship for theflume,

12.5.6 To convert from total head, H, to gauged head, h, the

expression

V2—.

h=H–2k

(60)

shall be used, where Va is the mean velocity in the approachchannel at the gauging section. For applying equation (60), the

geometry of the approach channel shall be used to compute itscross-sectional area Aa. Assuming this to be of U-shape, theappropriate equations are :

A,~ (0, - sinfla COSO,) = ~~ (0,) (61)

~’

‘i’hea=arccOs(+Da-h-9wDawhen (h + p) < D,12

and

Aa=&; +(h-; Da}Da .,. (62)

when (h + p) > Da12

where @ais the semi-angle subtended at the centre of curvatureof the invert of the approach channel by the water surface, Dais the width of the approach channel and p is the height of thehump at the throat.

12.5.7 Because h occurs implicitly in the right hand side ofequation (60), a method of successive approximation is neededto work out h.

First approximation :

Set h = H and hence calculate A,, from either equation (61)or equation (62). Insert V,, in equation (60), whereVa, = Q/Aal, and thus obtain h,.

Second approximation :

Obtain Aa2 from equation (61) or (62) inserting h = hl. HenceV,2 = QlAa2 and h2 = H - G~212g.

Third approximation, etc. :

Repeat procedure until hn – hn _, is too small to have asignificant effect on the accuracy.

IS 14869:2000ISO 4359:1983

12.5.8 Having thus worked out pairs of values of Q and h for a

series of values of dc, ~he calibration curve for the flume maybeplotted to large logarithmic scales. Discharge values forintermediate values of h may be read off as necessary. Notethat the calibration curve is not a straight line on a log-log plot.

12.5.9 An example of the calculation of the stage-dischargerelationship for a U-throated flume (with and without boundarylayer corrections) is given in annex E.


12.6.1 The practical lower limit of h is related to themagnitude of the influence of fluid properties and boundaryroughness. The recommended lower limit is 0,05 m or 0,05 Lwhichever is the greater.

12.6.2 h/L should not exceed 0,50. This limitation on h/Larises from the necessity to ensure parallel flow conditions atthe critical section in the throat. h~aX/L maybe allowed to riseto 0,67, with an additional uncertainty in coefficient of 2 0/0.

12.6.3 The ratio of areas of the approach channel and thethroat should preferably be such that the Froude number, Fr, inthe approach channel does not exceed 0,5 at any dkcharge.This shall be checked at each end of the range, and atintermediate flows, using the equation :

.. . (63)

12.6.4 Itmay be necessary in some situations ( r example

%where coarse sediment is being carried which would r?posit in

the approach channel) to allow Fra to rise to 0,6 but, becauseof surface irregularities at high Froude numbers, the measure-ment of head and performance of the flume are less certain,

and an additional tolerance of 2 VO should be allowed when0,6 > Fr, > 0,5.

12.6.5 Other limitations -arise from inadequate experimentalconfirmation for extreme sizes or geometries :

a) D shall be at least 0,1 m.

b) h shall be not more than 2 m.

c) At all elevations, the width between the throat wallsshall be less than the width between the approach channelwalls at the same elevation, i.e. there shall be a contractionwherever the water surface lies.

12.7 Uncertainty of measurement

12.7,1 The overall uncertainty of measurement will dependon :

a) the standard of construction and finish of the flume;

b) the uncertainty of the formula for the coefficient ofdischarge;






12.7.2 With reasonable skill and care in the construction ofthe flume, the basic equation and coefficients are expected tohave an uncertainty approaching 1 YO in favorable

circumstances, for example when CD and Cv are not far fromunity. An estimate of the combined percentage uncertainty

(Xc) on the coefficients may be obtained from the equation :

XC=+ [1+20 (CV– CD)]% . . . (64)

12.7.3 The method by which the uncertainty of the coeffi-

cients is to be combined with the uncertainties due to othersources of uncertainty is explained in clause 13.

13 Errors in flow

13.1 General

measurement

13.1.1 The total uncertainty of any flow measurement canbe estimated if the uncertainties from various sources arecombined. The assessment of these contributions to the totaluncertainty will indicate whether the rate of flow can bemeasured with sufficient accuracy for the purpose in hand.This clause is intended to provide sufficient information for theuser of this International Standard to estimate the-uncertaintyin a measurement of discharge (see ISO 5168).

13.1.2 The error may be defined as the difference betweenthe true rate of flow and that calculated in accordance with theequations used for calibrating the flume, which is assumed tobe constructed and installed in accordance with this interna-tional Standard. The term uncertainty is here used to denotethe deviation from the true rate of flow within which themeasured flow is expected to lie some nineteen times out oftwenty (with 95 ?40 confidence limits).

13.2 Source5 of error

13.2.1 The sources of error in the discharge measurement

may be identified by considering a generalized form ofdischarge equation for flumes

()Q= :3’2 CD Cv Cs b &h3/2 . . . (65)

NOTE – For U-throated flumes C~ is raplaced by Cu, and /J = D.

(2/3) s/2 isa numerical constant not subject to error; g, the accelerationdue ,to gravity, varies from place to place, but the variation may beneglected in flow measurement.

15

IS 14869:20001S0 4359:1983

13.2.2 Theonlysources oferror which need to reconsideredfurther are :

a) The discharge coefficient CD and the velocity of

approach coefficient Cv. Numerical estimates and uncer-

tainties in the combined coefficient Cv CD are given in 10.7,11.8 and 12.7.

b) The shape coefficient, C,, for a trapezoidal throatedflume or Cu, fora U-throated flume, is assumed to beac-curately computed. The combined percentage uncertainty

XC is assumed to be covered by the uncertainties in thecoefficients CDCV. However, C~ is dependent on a

knowledge of the side slope, m, and allowance shall bemade for inaccuracy in estimating m.

c) The dimensional measurement of the structure, forexample the bed width of the flume, b, or the diameter ofthe U-throated Tlume, D.

d) The measured head, h.

13.2.3 The uncertainties in b (or D) and h have to beestimated by the user. The uncertainty in dimension will de-pend upon the accuracy to which the device as constructed canbe measured; in practice this uncertainty may proveto be in-significant in comparison with other uncertainties. The uncer-tainty in the head will depend upon the accuracy of the head-measuring device, the determination of the gauge zero, andupon the technique used. This may be small if a vernier ormicrometer instrument is used, with a zero determination ofcomparable precision.

13.3.3 A measurement may also be subject to systematicerror; the mean of very many measured values would thus stilldiffer from thetrue value of the quantity being measured. Anerror in setting the zero of a water level gauge to invert level, forexample, produces a systematic difference between the truemean measured head andthe actual value. As repetition of themeasurement does not eliminate systematic errors, the actualvalue can only be determined by an independent measurementknown to be more accurate.

13.4 Errors in coefficient values

13.4.1 All errors in this category are systematic.

13.4.2 The values of the various coefficients quoted in this in-ternational Standard are derived from theoretical considera-

tions. The limitations quoted are those necessary to restrict ap-plication to those conditions where experiment has shown that

the theory of critical flow and the assessment of boundary layerdisplacement thickness are applicable.

13.4.3 The uncertainties in the coefficients quoted in thepreceding sections of this International Standard are based on

an assessment of the uncertainties in the estimate of boundarylayer displacement thickness, in the allowance for approachvelocity and in the use of graphs for CU, C~, etc. The deviation

of experimental data from various sources from theoreticalprediction is consistent with these suggested values of uncer-

tainty.

13.5 Errors in measurement

13.3 Kinds of error

13.3.1 Errors can be classif~d as random or systematic, theformer affecting the reproducibility (precision) of measurement

and the latter affecting its twe accuracy.

13.3.2 The standard deviation of a set of n measurements of aquantity Y under steady conditions may be estimated from theequation

[11[2

; (yi - J71

SY = n–1. . .

where J is the arithmetic mean of the n measurements.

The standard deviation of the mean is then given by :

Sy.—

‘r- 6. . .

(m

(67)

and the uncertainty of the mean is twice s; (to 95 % prob-ability) 11. This uncertainty is the contribution of the observa-tions of Y to the total uncertainty.

13.5.1 Both random and systematic errors will occur inmeasurements made by the user.

13.5.2 Since neither the methods of measurement nor theway in which they are to be made are specified, no numericalvalues for uncertainties in this category can be given; they have

to be estimated by the user. For example, consideration of themethod of measuring the f Iume should permit the user to deter-mine the uncertainties in the bed width, b, the side-slope m inthe case of trapezoidal throated flumes, and the diameter D ofa U-throated flume.

13.5.3 The discharges given by the equations are volumetricfigures, and the fluid density does not affect the volumetricdischarge for a given head provided the operative head isgauged in fluid of identical density. If the gauging is carried outin a separate well, a correction for the difference in density maybe necessa~ if the temperature in the well is significantly dif-ferent from that of the flowing fluid. However, it is assumedherein that the densities are equal.

13.5.4 The uncertainty of the gauged head should be deter-mined from an assessment of the separate sources of uncer-tainty, for example the zero uncertainty, the gauge sensitivity,

~) This factor of two assumes that n is large. For n = 6 the factor should be 2,6; n = 8 requires 2,4; rr = 10 requires 2,3; n = 15 requires 2,1.

16

IS 14869:2000ISO 4359:1983

backlash in the indication mechanism, the residual randomuncertainty in the mean of a series of measurements, etc. Theuncertainty of the gauged head is the square root of the sum ofthe squares of the separate uncertainties.

13.5.5 The above component uncertainties should becalculated at the 95 ?k confidence limits but when the value ofa co,mporlent uncer~ainty is determined from only a single

measurement, it is said to be rectangularly distributed and theuncertainty may be taken, for the purpose of this InternationalStandard, to be the (plus or minus) limits within which the trueva!ue is known to lie (i.e. half the estimated maximum devia-tion),

13.6 Combination of uncertainties to give overalluncertainty on discharge

13.6.1 The total uncertainty is the resultant of several con-tributory uncertainties, which may themselves be compositeuncertainties (see 13.5.4).

13.6.2 The uncertainty of the rate of flow shall be calculatedfrom the following equation :

X=*4 (x;+yzx~+ozx:+lpx;) . .. @6)

where

Xc is the percentage uncertainty in C, CD;

Xb is the percentage uncertainty in b (or D);

Xh is the percentage uncertainty in h;

“Xm is the percentage uncertainty in m.

y, @ and v are numerical coefficients depending on the flumegeometry. In the simple case of a rectangular flume, y = 1,

@ = 1,5, and v = O (assuming the walls are truly verticai). Fora trapezoidal throated flume, y and v depend on mHc/h, andare shown in figure 11. For a U-throated flume, v == O (assum-ing the walls are truly vertical); y and q) depend on He/D andare shown in figure 11. (In using these curves, the approxima-tion Hc = h may be used. )

100 [It; + #; + . . . (2s#l’/2Xh=f ——

h

. . . (69)

. . . (70)

Cb is the uncertainty in width measurement;

lthr#h, etc.,are uncertainties in head measurement (see13.5.4);

2SE is the uncertainty of the mean if a series of readings ofthe head measurement are taken (see 13.3.2 including foot-note).

13.6.3 Itshould be realized that the uncertainty X is not a

single value for a given device, but will vary with discharge. Itmay therefore be necessary to consider the uncertainty atseveral discharges covering the required range of measure-ment.

13.6.4 An example of the calculation of the combined uncer-tainties is given in annex F.

17

IS 14869:2000ISO 4359:1983

Guide for themeasurement of

Annex A

selection of weirs and flumes for thethe discharge of water in open channels

A.1 Scope and field of application

This annex lays down guidelines for the selection of weirs andflumes for the measurement of discharge in open channels.Consideration is limited to the steady, uniform flow of water atordinary temperatures (approximately 5 to 30 ‘C).

Despite the great number of types of weirs and flumesavailable, some of which may offer advantages for specific pur-

poses, only the following types are presently standardized.Criteria for selection from among the standard types are givenin clause A.3.

A.2 Types of standard weirs and flumes

A.2. I Thin-plate weir

A weir constructed with a crest of vertical thin plate, shaped insuch a manner that the nappe springs clear of the crest, thedischarge being determined by the head on the weir and thewidth of the crest (or the angle of the notch),

The following types are included :

— rectangular full-width weir;

,— rectangular-notch weir;

triangular-notch (V-notch) w~ir.

A.2.2 Broad-crested weir

A weir with substantial. crest dimension in the direction of flowformed in such a manner that critical flow occurs on the crestof the weir within the breadth, the discharge being determinedby the head on the weir and the width of the crest.

The following types are included :

— rectangular-profile weir with sharp upstream edge;

— rectangular-profile weir with rounded upstream edge.

A.2.3 Triangular-profile weir

A weir having a triangular profile in the direction of flow, thedischarge being determined by the head over the weir and thehidth of the crest.

The following type is included :

– triangular-profile weir having 1:2 slope upstream and1:5 slope downstream.

18

A.2.4 Standing-wave flume (free flow)

A flume with side contractions with or without bottom contrac-tions, within which the flow changes from sub-critical to super-critical, the discharge being determined by the cross-sectionalarea and velocity of flow at critical depth within the throat ofthe flume.

Thefollowing types are included :

— with rectangular throat;

— with trapezoidal throat;

— with U-throat.

A.2.5 Free overfall

An abrupt drop in the floor of a rectangular chanrrel, thedischarge being determined by the depth at the brink of thedrop and the width of the channel at the brink section.

A.3 Criteria for selection of standard weirsor flumes

The essential criteria for selection from among the standardweirs and flumes are given below.

A.3.1 Available difference in water levels

Thin-plate weirs and free overfalls require a sufficient difference

between upstream and downstream water levels which ensurefree, fully ventilated flow under conditions of maximumdischarge.

Broad-crested weirs may be used with relatively smallerdifferences in water level; triangular-profile weirs and standing-wave f Iumes may be used with even smaller clifferences inwater level.

For all types of weirs and flumes included in this International

Standard, the discharge shcwld be free or independent of thedownstream water level.

A.3.2 Accuracy of measurement

The accuracy in a single determination of discharge depends

upon the estimation of the component uncertainties involvedbut approximate ranges of uncertainties for the weirs andflumes (at 95 YO confidence levels) are as follows :

— rectangular thin-plate weirs (full-width and notch) 1

to 4 ?40;

,-

IS 14869:2000ISO 4359:1983

triangular-notch weirs (notch angles between20° and100°) 1 to 2 Y.;

broad-crested weirs 3 to 5 Y.;

— triangular-profile weirs 2 to 5 ?40;

standing-wave flumes 2 to 5 ‘/o;

— free overfal15to 1070.

Deviations from standard construction, installation or use mayresult in larger measurement errors. The larger figures givenabove ace recommended conservative values for use underconditions of strict conformance with standard specifications.The smallest values can only be obtained for weirs underrigorous control, such as may be built and installed in well-

equipped laboratories. Under field conditions, thin-plate weirsare specially subject to errors caused by natural hazards.

A.3.3 Dimensions and shape of open channel

RectanWlar full-width weirs and notch weirs (both rectangular

and triangular) of large size relative to the size of the approachchannel, should be located in vertical-walled, level-flooredrectangular channels, or in weir boxes of rectangular cross-

section for a chstance extending upstream not less than tentimes the width of Ihe nappe at maximum head. For thin-plateweirs of small size relative to the size of the approach channel,especially if the velocity of approach is negligible, the size andshape of the channel is of no importance.

Broad-crested weirs are best used in rectangular channels, butthey can be used with good accuracy in non-rectangular chan-nels if a smooth, rectangular approach channel extendsupstream from the weir by a distance not less than twice themaximum head.

Flumes can be used in channels of any shape if flow conditionsin the approach channel are reasonably uniform and steady.

For weirs and flumes of all types, the size and shape of thedownstream channel are of no significance except that theymust permit free, fully ventilated flow under all conditions ofuse.

A.3.4 Flow conditions in the approach channel

For weirs of all types, flow in the approach channel shall besub-critical, uniform and steady. Ideally, especially for relativelyhigh velocities of approach, the velocity distribution shouldapproximate that in a channel of sufficient length to developnormal (resistance-controlled) flow in straight, smooth chan-nels. For relatively low velocities of approach and for flumes,flow conditions in the channel are of less importance. In shortchannels and -weir boxes, baffles and flow-straighteners may beused io establish a normal velocity distribution. Care should betaken to ensure that erosion and/or deposition upstream of theweir or flume do not significantly alter the velocity of approachor velocity distribution to the measurement structure.

Sub-critical flow is ensured when

where

E is the average velocity, in met~es per second, in the

approach channel;

g is the acceleration due to gravity, in metres per secondsquared;

A is the cross-sectional area, in square metres, of thechannel;

B. is the width of the channel, in metres, at the water sur-face.

A.3.5 Flow with sediment load

For flows with suspended load, the use of thin-plate weirs

should be avoided because the crest edge may be damaged orworn by the suspended materials.

On streams with bed load, the use of measurement structureswhich significantly reduce the stream velocity is not recom-mended as it may result in changing deposition scour depen-dent on flow regime. Flumes will generally perform better than

weirs on streams with sediment load.

A.3.6 Flow with floating debris

Broad crested weirs, triangular profile weirs, standing waveflumes and free overfall structures will normally pass floatingdebris more effectively than thin-plate weirs. The use of thetriangular-notch (V-notch) weir in particular should be avoidedunless a debris trap is installed upstream.

A.3.7 Magnitude of discharge to be measured

For reasons related to accuracy and construction, thin-plateweirs are best used for the measurement of relatively smalldischarges. Broad-crested weirs, triangular-profile weirs andflumes are best used for large discharges.

A.3.8 Range of discharge to be measured

For best overall accuracy over a wide range of small discharges,a triangular-notch (V-notch) weir should be used in preferenceto a rectangular-notch or rectangular full-width weir. Fora widerange of larger discharge, a trapezoidal-throat or U-throatflumes should be used in preference to a broad-crested weir,free overfall, rectangular-throated f Iume a a triangular-profileweir.

A.3.9 Construction

Thin-plate weirs should be constructed with precision toolsunder machine-shop conditions, Flumes, broad-crested weirs,triangular-profile weirs and free overfalls can be constructedsatisfactorily in the field. In all cases, great care must be exer-cised in making the structures conform with standard specifica-tions.

Broad-crested weirs, triangular-pcofile weirs, free overfalls and~lumes are inherently stronger and more easily maintainedunder conditions o-f high heads in large channels.

—

19

IS 14869:2000ISO 4359:1983

Annex B

Symbols and units

Units of measurement are metres (m) and seconds (s) or derivatives of these.

Symbol

A

B

b

hp

c

cc

CD

c,

c“

c“

c1

D

d

E

e

Fr

f,, J28JB, @C

g

H

H,

h

J

k,

L

Lb

L,

L2

L3

m

Quantity

area cf cross-section of flow

width of approach channel (width at bed if trapezoidal)

‘width of flume throat (width at bed if trapezoidal)

width of piers

overall coefficient of discharge (rectangular flumes)

coefficient of contraction

coefficient of discharge

shape coefficient for trapezoidal throated flumes

shape coefficient for U-shaped throated flumes

coefficient allowing for the effect of approach velocity

coefficient of dkscharge for channels

diameter of base of U-shaped throated flumes

depth of flow

specific energy

a measure of the excess of the maximum velocity in a section over the mean

FFroude number = ~

d@

geometric functions depending on 8

gravitational acceleration

total head

correction to the total head

gauged head

fraction of discharge

equivalent sand-roughness of surface, after Nikuradse

length of prismatic section of ihe contraction at a flume

length of baffle platform

length of bellmouth entrance

iength of glacis

length of stilling basin

side-slope (m horizontal to 1 vertical)

Unit ofmeasurement

mz

m

m

m

non-dimensional

non-dimensional

non-dimensional

non-dimensional

non-dimensional

non-dimensional

non-dimensional

m

m

m

non-dimensional

non-dimensional

non-dimensional

mlsz

m

m

m

non-dimensional

m

m

m

m

m

m

non-dimensional

20

IS 148 C9 :20001s0 ,359: 1C”;:3

Fn

nP

P

P

Q

R

Re

‘P

RI

v

w

x

xl,

xc

Xh

X,n

z

a

B

Y, @, w

d,

v

v

s

?

o

&h

&h

Subscripts

a

c

d

e

1

max.

Quantity

number of measurements in series

number -of piers

wetted perimeter of flow cross-section

height of flume invert above the invert of the approach channel

discharge

radius

Reynolds number

radius of hump

radius of bellmouth entrance

average velocity through a cross-section, defined by Q/A

water surface width

overall uncertainty in the determination of discharge expressed as a percentage standarddeviation at 95 Y. confidence limits

uncertainty in h (or D)

uncertainty in the combined coefficient value

uncertainty in h

uncertainty in m

index of d in formula for canal discharge

coefficient taking into account non-uniformity of velocity distribution

coefficient dependent on mean curvature of stream lines

coefficients in the error equation

boundary layer displacement thickness

a numerical coefficient

kinematic viscosity of the fluid

standard deviation

standard error of the mean

semi,angle subtended at the centre of curvature of the invert of a U-shaped flume by thewater surface

uncertainty in width measurement

uncertainty in head measurement

values in approach channel

values at critical flow

values downstream of the flume

effective values after making allowance for boundary layer effects

values assuming an ideal frictionless fluid

the maximum value

Unit ofmeasurement

non-dimensional

m

m

m3/s

m

non-dimensional

m

m

mls

rn

non-dimensional

non-dimensional

non-dimensional

non-dimensional

non-dimensional

non-dimensional

non-dimensional

non-dimensional

m

non-dimensional

m2/s

.

—

Ion-dimensional

m

m

—

IS 14869:2000ISO 4359:1983

Annex C

Veiocity distribution

C.1 An even distribution of velocity over the cross-sectionof the approach channel in the region of the gauging station isnecessary for high accuracy of measurement of discharge bymeans of weirs, notches and f Iumes. Thts is because therecommended coefficients are empirical values obtained byvarious investigators and were usually obtained under ideallaboratory conditions. These involved either the use of screensto ensure an approximately uniform velocity over the cross-section, or a long straight approach channel conducive to theestablishment of a normal distribution of velocities.

C.2 Normal velocity distribution is defined as the distributionof velocities attained in a channel over a long uniform straightreach. A characteristic feature of flow in such a channel is thatthe velocity is a maximum at about 0,6 depth above invert, withthe average velocity occurring at about 0,4 depth above invert.

and 12.7 in mind, figure 12 provides some guidance to the type.of velocity distribution and evenness thereof that are accep-table in practice. ——

C.4 In figure 12 different patterns of isovels are shown.These isovels are contours of equal velocity in the direction offlow.

C.5 The isovels plotted in figures 12d), e) and f) provideexamples of observed normal velocity distributions, which areclearly acceptable, Figure 12a) shows some skewness, butnevertheless approximates to a normal distribution.

Figures 12b) and 12c) show appreciable departure from unifor-mity, and are considered representative of the maximum accep-table departure from ideal approach conditions for the uncer-tainties given.

C.3 Any deviation from the ideal conditions of either very C.6 If approach conditions are unfavorable, strong secon-uniform velocity or a normal velocity distribution may lead to dary currents (spiral flow) may occur. Even though an isovelerrors in flow measurement, but quantitative information on diagram showing forward components may appear reasonablethe influence of velocity distribution is inadequate to define”the in such circumstances, the presence of significant cross com-acceptable limits of departure from the ideal distribution. With ponents of velocity would make such an installation unaccep-the uncertainties on discharge coefficients quoted in 10.7, 11.8 table.

22

IS 14869:2000ISO 4359:1983

Annex D

Computation of discharge using boundary layer theory

D.1 General

Boundary layer theory can be used to determine the variationsof the notional displacement of the flow boundaries, d,, andhence it is possible to use the more generalised expressions for

CD given in equations (24), (30). and (45).

D.2 Rectangular throated flume

D.2. 1 The generalised expression for CD, see equation (24),is :

CO=(l-2:XM’-:XT2(71)D .2.2 The coefficient of discharge may be evaluated byequation (71 ) using the geometrical measurements of thestructure, provided the boundary layer displacement thickness6+ can be estimated. The relative boundary layer displacementthickness J./L may be evaluated approximately from figure 13.

‘In using this figure, certain simplifying assumptions are made :

a) The boundary layer is assumed to originate at -theleading edge of the prismatic portion of the throat.

b) Transition from Iaminar to turbulent boundary layer isassumed to take place at a Reynolds numberRe = 3 x 105.

c) The control section is presumed to be at thedownstream end of the prismatic throat section.

D.2.3 The value of k., the equivalent sand grain roughnessof the throat, may be selected from table 4 for a range of con-struction materials. From this, the ratio L/k~ may be com-puted.

D.2.4 The value of c3,/L is insensitive to Re, but Re is depen-dent upon the discharge as follows :

()L gQ 113Re=— ~

v. . . (72)

Values of v, the kinematic viscosity of water, are given intable 5.

D.2.5 The computation of discharge to the first approxima-tion for a given head acting on a rectangular throated flume ofknown geometry is thus made as follows :

a) List the values of b, B, p, L, g and k~.

b) Compute the area of the approach channel crosa-section using equation (17).

c) Obtain the value of Cv from figure 6 assuming d. = Oand CV = 1,0.

d) Make an approximation to Q using equation (20) andassuming CD = 1,00.

e) Use equation (72) to obtain the Reynolds number Re.

f) Work out L/k~ and find d./L from figure 13; hence d..

g) Use equation (71) to compute CD and recompute Qusing equation (20).

D.2.6 Following the first approximation (in D.2.5) further ap-proximations use steps c) to g) of D.2.5 as follows :

c) Repeat using value of d, obtained in f) andequations (22) and (23) to determine be he.

d) Repeat using value of d. obtained in f) andequations (21 ), (22) and (23) to determine CD.

e) to g) Repeat as above.

D.3 Trapezoidal throated flumes

D.3.I The generalised expression for CD, see equation (30),is :

CD=(’-+XM’-:XT’ (73)D.3.2 The coefficient of discharge may be evaluated fromequation (73), using the geometrical measurements of the

structure. The relative boundary layer displacement 6,/L maybe estimated from figure 13 (sea D.2.2 for the simplifyingassumptions implicit m figure 13).

D.3.3 The value of k,, the equivalent aand roughness of thethroat, may be selected from table 4 for a range of constructionmaterials. From this the ratio L/k~ may be computed.

D.3.4 The value of 6,/L is not very sensitive to Re, but this isdependent on the discharge, as follows :

‘e=w’’3(t)”3 ~~~(74)

Values of v for water are given in table 5. The ratio wC/b is afunction of mHC/b, and, making the approximation h = HCforthe purpose, may be read from figure 8.

23

IS 14869:2000ISO 4359:1983

D,3.5 The computation of discharge for a given head actingon a trapezoidal throated flume of known geometry is thusmade as follows :

a) List the values of m, tna, b, B, p, L, g, v and k~.

b) Compute the area of the approach channel cross-section. If it is of trapezoidal shape, use equation (18).

c) As a first approximation, assume mHCJbe = mh/band obtain C~ from figure 8 for the given value of h.

d) Obtain a first approximation of Cv from figure 6assuming d. = O.

e) Obtain wC/b from figure 14. As a first approximation,enter the diagram at the value of nib/h.

f) Make an approximation to Q using equation (29) withtheabove values of Cv, C~andassunting co = l,W.

g) Use equation (74) toobtain the Reynolds number, Re.

h) Work out L/k~and find 6,/L iiom figure 13; hence d,.

J) q = ~(1 + m2) – m,orobtain from figure7.

k) Use equation (73) to compute Co, and recompute Q(equation 29) using this value.

D.3.6 This completes the first approximation. These valuesof C, C,,, C’Dand Qareutilized in beginning thesecondapprox-imation as follows :

a) mHCe/be k obtained from equation (32).

b) Figure 8 is used with the above to obtain a closeapproximation of C~.

c) C~ he he/A can now be worked out, and a new value ofCv obtained from figure 6.

d) The \ialue of CD, together with the revised values of Cvand C~, shall then be inserted in equation (29) to obtain amore accurate figure for Q.

D .3.7 Steps a) to d) shall be repeated until sufficient pre-cision hasbeen.obtained in the values of Cs, Cv and CD. As CDis relatively insensitik’e to Re, it is seldom necessary to gobeyond the first approximation to Re, but third or fourth ap-plications of steps a) to c) may be necessary.

D.4 U-throated (round-bottomed) flumes

D .4.1 The generalised expression for CD, see equation (45),is :

[75)

D.4.2 The coefficient of discharge Cc may be evaluated byequation (75), using the geometrical measurements of thestructure. h is first necessary to evaluate the relative boundarylayer displacement d,/L. This may be estimated from figure 13

(see D.2.2 for the simplifying assumptior,s implicit in figuFe 13)where it is expressed as a function of relative roughness L /k~and Reynolds number Re.

D.4.3 The value of k,, the,equivalent sand roughness of thethroat, may be selected from table 4 for a range of constructionmaterials. From this and the throat length, L, the ratio L/k~may be computed.

D .4.4 The value of d,/L is not very sensitive to Reynoldsnumber, but Re k dependent on the discharge, as follows :

(76)

An alternative -expression in terms of the gauged head, h, kmore convenient :

Re=kr ()

1/3$ gh (Cv CU CD)’” + . . . (77)

v- C

The first approximations to Cu and Cv obtained as suggested in12.4.3 and 12.4.4, and the assumptitm CD = 1, maybe utilizedin evaluating equation (77).

Values of wJD are shown in figure 15 against HCJL). Inreading off the value of wC/D to insert in equation (77), the ap-proximation h = HC may be made.

D.4.5 The computation of discharge for a given head actingon a U-shaped flume of known geometry thus proceeds asfollows :

a) List the values of D, L, Da, p, ic~and v.

b) Compute the area of the approach channel cros.s-section; if it is of U-shape, use equation (19).

c) As a first approximation, assume HCJDe = h/D a~dobtain Cu from figure 10 for the given value of h.

d) Obtain a first approximation of C, from figure 6,assuming d, = O.

e) Evaluate ~m”, L/v, and L!k~.

f) Obtain wJD from figure 15, again using as a first

approximation HC/D = h/D. ‘

g) Estimate Reynolds number from equation (77), assum-ing CD = 1,0.

h) Read from figure 13 the value of 6,/L corresponding tothese values of Llk~ and Re.

j) Evaluate LID and L/h and compute CD fromequation (75).

k) HCe can be estimated from equation (47) using -theavove values of h, d./L, L and Cv. De is obtained fromDe = D – 26, and he is obtained from he = h – 6.. ‘

24

IS 14869:2000ISO 4359 ;1983

D.4.6 This completes the first approximation. These values D.4.7 Steps a) toe) shall be repeated until sufficient pre-

of HC,, Cv and CD are utilized in beginning the second approxi- cision has been obtained in the values of CU and Cv. As d./L kmation, as follows : relatively insensitive to Re, it is not usually necessary to go

beyond the first approximation to Re, but third or fourtha) Evaluate HCJDe and obtain a revised value of Cu fromfigure 10.

applications of steps a) to c) may be necessary.

b) Evaluate Cu De h,/A and obtain a revised value of Cvfrom figure 6.

c) Obtain a revised estimate of HCefrom equation (47), us- D .4.8 Discharge is then computed from equation (44) for theing the revised value of Cv. given head.

——

25

IS 14869:2000ISO 4359:1983

Annex E

Examples illustrating methods for the computation

E.1 Calculation of single discharge for a trapezoidal throated flume

E.1.l m = tn. = 1,00 p = 0,15m g = 9;81 m/s2b=0,50m L=3,00m h=1,00mB=2,00m

E. 1.2 Using the method described in 11.4, the calculation proceeds as follows :

Parameter

Mea of approach channel,4 (mz)

~umerical coe~lcient, q

Coefficient of discharge, CD

mHcelbe

Shape coefficient, C~

C~ be helA

Coefficient of velocity, Cv

L“A”prOximatiOnfirst

3,966

0,4142

0,9718

2,000

2,435

0,3069

1,023

Discharge, Q (mS/s) I .72,062

second

—

2,030

2,445

0,3061

1,023

2,072

third

2,031

2,450

0,3068

1,023

2,076

of discharge

1Equationor figure

used

2Equation 18

Figure 7

Equation 31

Figure 8

Figure 8

Equation 29

E.2 Calculation of single discharge for a trapezoidal throated flume; boundary layer corrections

E.2.I

E.2.2

m=ma=l, oo p = 0,15m v = 1,141 x 10-Gm2/sb=0,50m L=3,00m k, = 0,0015 m

l?=2,00m g = 9,81 m/s2 h=1,00m

Using the method described in annex D, the calculation proceeds as follows :

Parameter

Area of approach channel,A (mz)

mHcJbe

Shape coefficient, C~

C~ be helA

Coefficient of velocity, Cv

Wclb

Discharge, Q (m3/s)

Reynolds number, Re

c$,IL

d. (m)

Numerical coefficient, v

Coefficient of discharge, CD

Discharge, Q (m3/s)

Approximation Equationor figure

first second third used

3,866 1-1- ! Equation 18

2,000 2,030 2,031

2,435 2,445 2,450 Figure 8

0,3M 9 0,3061 0,3068

1,023 1,023 1,023 Figure 8

4,1 Figure 14

2,123 2,029 2,033 Equation 29

5,69 X 106 Equation 74

0,0052 l-\- I Figure 13

0,0156 —

0,4142 Figure 7

0,9515 1-1- ] Equation 73

2,019 Equation 29

26

E.3 Calculation of stage-discharge

6-IL = 0,003

E.3.1 m = ma = 1,00 B=2,00mb=0,50m p = 0,15m

curve for trapezoidal flume

L=3,00mg = 9,81 m/s2

E.3.2 Example of calculation of stage-dischdrge curve for a trapezoidal-throated flume when d,/L = 0,003.

Variables dc Wc P= Ac Q H, H- H ~.1 h, ‘a2 hl va3 h3

Equation Equation Equation(39) (39) (391

How Equation Equation Equation Equatton Ec/uatton Equat{onEquation Equation Equatton

Input (1{.+He) andand

obtained (34) (37) (35) (13) (14) (36)(381

(“.(::.2) ‘“ :~ “’”(31

VaT= Ql~al (~ = v,, ) Va2= Q/Aa2(Val = va~l

with w!thh=H h=hl h = h2

m m m # M’/. m m m mls m mls m In/s m

., --- 9.— 0,1526 o,07b9 0,1526 0,0789 “ 0,1526

I ., .-. 0,1401 0,173 0,2778 0,0106 0,25114 0,1618 0,2871 0,1624 0,2871’ ‘“

I

0,1624 0,2871

L 0,40 \ l,3C0 1,631 0,360 0,593 0,= 5 0,0113 0,5488 0,3139 0,5448 0,316~ 0,5447 0,3168 0,5447——

1+** ‘ ‘m ‘ ‘m’‘ “’428‘ 0’0’0’‘ 0“152’‘ ‘“on—0,60 1,7CX3

Results2,197 0,660 1,288 0,7941 0,0116 0,8057 0,4560 0,7951 0,4627 0.7948 0,4629 0,7948

0,80 2,100 2,763 1,040 2,292 1,C476 ‘0,01 18 1,0594 0,5905 1,0416 0,W2 7 1,0409” 0,6032 l,c409

1,rm 2,500 3,32s 1,530 3,ti 1,3000 0,0119 1,3119 0,7190 1,28;6 0,7378 l,28d 1 0,7389——

1,2841

l,XI 3,500 4,743 3,000—_———-——

8,Wl 1,9286 0,0122 1,9408 1,0171 1,8881 1,0570 1,8839 l,c603 1,8835

2,(XI 4,Wl 6,157 5,CO0 16,508 2,5556 0,0123 2,5679 1,2875 2,4834 1,3529 2,4746 1,3600 2,4736 ‘“

E.4 Calculation of stage-discharge curve for trapezoidal throated flume; boundary layer corrections

E.4.1 m = ma = 1,00 p = 0,15 m “ = 1,141 x 10-6 m2/s

b=0,50m L=3,00m k. = 0,001513=2,00m g = 9,81 m/s2

E.4.2 Example of calculation of stage-discharge curve for a trapezoidal-throated flume with boundary layer corrections.

Variables

HOWobtained

Results

d,-

Input

m

0,21

0,80

1,001.502.CH3

w.!f’clAc]QIWl~P lV~lWIffiG!@l%

I I I I I I I I I Eauation I I EauationFigure ‘(39) “(39)

Equation Equation Equaticm Equation Equation Equation 13 EquationEquat!on

W) (37) (35) (13) (14) (74) (Llk, = (36)(H. + He) - and (38) and

‘al :if;Aa I (Va = Va,)Vaz = Q//l

20001a2

withh=H h=hl

m m d dls m m m mls m mls

o,9rM 1,C& 0,140 0,173 0,2778 3,25 X l@ 0,0050 0,0177 0,2955 0,1588 0,2942 0,1583

1,700 2,197 o,6&l 1,288 0,7941 5, ?3 x ?0s 0,0951 0,0198 0,8?39 0,4508 0,8035 0,4574--

2,500 3,328 1,5LY3 3,839 1,3CCI0 6,31; Id O,@%2 0,0208 1,3208 0,7129 1,2949 0,731 1

3,500 4,743 3,1X13 8,ES9 1,9286 762 X l@ 0,0052 0,021 1“ --1,94!3 7 1,0106 1,8976 1,8496.——. —..-. .

4,503 K157 5,003 16,R3EI 2,5556 8,68 X 11$ 0,0052 0,0213 2,576 b 1,28U 7 2,4933 1,3450

h2

Equation(28)

{~ = !/az)

m

0.2943

0,8032

1,2936

1,8936

2,4847

Eauation I

1‘[39)

Equattonand

(38)va3 @ -la3

;;a = i82)with

h=h2

3’mls m

0,1593 0,2943

0,4576 0,8032

0,7320 1,2935

1,0527 1,8s3 2

IS 14669:2000ISO 4359:1983

E.5 Calculation of single discharge for a U-throated flume; ti,/L = 0,003

E.5.1 D = 0,40 m D, = 0,60 m g = 9,81 m/s2L=1,00m p = 0,0 h = 0,25 m

E.5.2 Using the method described in 12.4, the calculation proceeds as follows :

Approximation EquationParameter or figure


Area of approach channel,A (m2) 0,1115 Equation 49

Hc.JDe 0,6250 0,6793 0,6634

Shape coefficient, Cu 0,754 0,776 0,777 Figure 10

Cu L) h{A 0,6762 0,6959 0,6968

Coefficient of velocity, Cv 1,133 1,144 1,144 Figure 6

Coefficient of discharge, Co 0,9673 Equation 46

Effective total head,

Hce (m) 0,2717 0,2734 0,2734 Equation 48

Discharge, Q (m3/s) 0,0736 Equation 44

E.6 Calculation of single discharge for a U-throated flume; boundary layer correcticms

E.6. I D = 0,40 m p = 0,0 k~=0,0006mL=l,oorn g = 9,81 m/s2 h = 0,25 mD, = 0,60 m ~ = 1,141 x 10-Gmz/s

E .6.2 Using the method described in annex D, the calculation proceedsasfollows :

Approximation Equation-Paramatar or figura


Area of approach channel,A (m2) 0,1115 Equation 19

Hce/De 0,6250 0,6625 0,6605 —

Shape coefficient, CU 0,754 0,778 .0,778 Figure 10

CU D hlA 0,6762 0,6978 0,6978

Coefficient of velocity, Cv 1,133 1,145 1,145 Figure 6

WCID 0,993 Figure 15

Reynolds number, Re 1,06 X 106 Equation 77

b~lL 0,0047 Figure 13

6. (m) 0,0047

Coefficient of discharge, CD 0,9491 — Equation 75

Effective total head,Hce (m) 0,2666 0,26s 5 0,2665 Equation 47

Discharge, Q (mS/s) — 0,07207 Equation 44

26

E.7 Calculation of stage-discharge curve for a U-shape

8*IL = 0,003

E.7.1 D = 0,40 m Da = 0,60 m g = 9,81 m/s2

L.=1,00m p = 0,0

throated flume

E.7.2 Exampleof calculationof stage-dischargecurve for a U-throated flume when d./L = 0,003

TlVariables

HOWobtained

‘throsi dc Wc Pc Ac Q He H.

I

~l%llkl K21h21z3

I Eauation ] ] Equation I I Equation(61) w (62) Equation

(61) or (62)Equat!on

(61) or (62)

(He + H.) – and (60)and

{50)and

Val = Q/Aal(~=~1)

:;2 = Q/Aa2 ~~=~ %3 = U14,3with with a2) with

Equation(52)

Equation Equation EquationInput (53) (58) (54)

Equaticm Equation Equation(or or ($5)

(13) (14) (57)or (58)

input)or (58)

Equation(W

(~ = i,a3)

h=H1

h=hl h=h2

m mls m mls m mls

=

m

0,1180

rad m m m m &/s m m

1,00 0,0819 0,3366 0,4000 0,0218 o,d174 0,1243 0,CCK36

1,30 0,1465 0,2864 0,5XI o 0,0417 0,0430 0,2W 6 0,0040

X12 O,m o 0,4C6 ; 0,6266 0,0628 0,0779 0,2785 0,0047

U,2W o 0,4000 0,7263 0,0828 0,1180 0,3533 0,0055

0,3000 O,m-o 0,8283 0,1028 0,1632 0,42s 5 0,0C62

0,4000 o,4ilo o 1,0283 0,1428 0,2672 0,5785 0,0U77

0,1279 0,3846 0,1200 0,4318 I 0,1184 /_ 0,4405

0,2046 0,5053 0,1916 0,5527 0,1890 0,5636

0,2832 0,5933 0,2653 0,6459 O,xl 9 I 0,8568 -i

0,1884

0,2612Results

=10,3316

0,4018

0,5421

0.3590 \ 0.8874 \ 0.3363 I 0.7230 I 0,3324 I 0,73381 I 1 1 i

b,4347 0,7345 0,4072 0,7934 0,4026 o,Ea)39

0,5862 0,8534 0,5491 0,9185 o,wm9K

E.8 Calculation of stage-discharge curve for a U-throated flume; boundary layer corrections

E.8.1 D = 0,40 m p = 0,0 v = 1,141 x 10-6m2/s

L=l,Ulm g = 9,81 m/s ks=0,0006mDa = 0,60 m

E.8.2 Example of calculation of stage-discharge curve for a U-throated flume with boundary layer correction.

d. I ‘c \PclAc H+lHl~l—

Illh2 %3 h3

Equation

Equation(61) or (62)

Equation(60)

and ua3=

Q/Aa3(80)

(~.r a2) (~=rwith 83)

h = hzTVariables ‘throat

HowInput

obtained

h, ‘a2

I Equation(61) or (62)

Equation(61) or (62)and ~az =

QI’4.2with

h=hl

mls

Equation(62)

Equation Equation Equation

(or(53) (58~ (54)

or (W or (69) or (58)input)

FigureEquation Equation Equation 13

(13) (14) (76) (Llk =1867)

Equation(m)

(v; = ~1)“;::” I(H, + H I ‘;,:;l=

-1” withn-k-t=- m

Ered

1,00

X12

—

— w m3h I m I I0,0174 0,1243 6,98 x lC$ 0,CQ4o

0,0779 0,2765 ll,09xl@l o,c017

0,1214 0,4251

Residts 0,2884

0,4120

0,6359

0,78240,1632I 0,42s 5 1,39 x loa 0,0350

0,2672 0,5785 11,64. loa I 0,0052 0,5500 0,9170 0,5490I

0,5556 0,W54 i

IS 14869:2000ISO 4359:1983

Annex F

Example of the computation of the overall uncertaintyof discharge measurement

F.1 The following is an example of the application of theuncertainty formula. In each case the component uncertainties

(XC; Xb; Xh and Xm) may be taken as percentage standarddeviations at the 95 % confidence level. The total uncertainty

X therefore is found with 95 % confidence. It is assumed in theexample that the head is measured by digital punched taperecorder having a resolution of 1 mm with an uncertainty of~ 3 mm (&h). The zero is measured in each case to * I mm

(e,).

It is assumed in the example that a series of readings of a cons-tant head produced a standard deviation of the mean of1,5 mm.

F.2 Rectangular throated flume with a throat width b of1,0 m, approach channel width 1? of 2,0 m, hump height p of0,25 m and a throat length f, of 3,0 m. The uncertainty in widthmay be taken as ~ 2 mm.

F.3 The overall uncertainty in discharge at a given head, say1,rX) m, is calculated as follows :

h = 1,00m

blB = 0,5h/(h + p) = ~,80Cv = 1,039, from table 2h/L = 0,33Llh = 3,0CD = 0,868, from table 1

Hence

XC = i 2,4 % using equation (28)Xh = * 0,44 Y. using equation (70)Xb = i 0,2 % using equation (69)X = + (2,42 + 0,22 + 1,52 X 0,442)1/2

= ~ 2,5 Vo

30

.

IS 14869:2000ISO 4359:1983

Annex G

Determination of height of hump – Rectangular throated flumes

G.~ -Stage-discharge relation

The stage-discharge relation of a channel or distributary isgiven by

Q=c, ~: ...(i%)

where

Q is the discharge;

Cl is a coefficient;

d is the central depth of water in the channel;

z is the index which varies between 1,5 aqd 2,0.

Values of z are summarised below :

Series I ‘Shape of channelnumber

1 Rectangular

2 Trapezoidal

3 Unlined channels with

design side slopes 1/2 top

4

I

Lined channels withslopes 1,5 to 1

z

1,5

Vsriable and increaaeswith the flatness of theside slope

l,6to 1,7

1,9 to 2,0

As comDared to the above ecwation, the discharge in the caseof a br&d crested weir is proportional to Jfl,5 aid also to hl,5where Hand h are the total and gauged heads respectively. Asthe exponent of d: is greater than the exponent of h, there willbe draw-down at low flows and pending at high flows providedthe sill of the throat is at the same level of the channel bed,Draw-down could result in scour and pending in silting. Thiscan be avoided by providing a hump in the flume throat. Theheight of hump “p” required to give proportionality i.e. rate ofchange in “da”equal to the rate of change in “h” at a particulardischarge thus ensuring absence of either draw-down orpending is worked out below.

G.1.l Proportionality for a small variation from aparticulardischarge

Q = c1d: (for channel) ,.. (79)

= CD h1,5 (for flume) ,.. (m)

Since the rate of change of discharge in the approach channel(da in channel) is equal to the rate of change over the flume Min flume)

zC1d~–l = 1,5 CD X h0,5 . . . (81 )

substituting Cl and CD from equations (79) and (w) into (81)

Q QZ—Xd:-1=l,s_xh0,5 . . .

d; hl,5(82)

. . . (&J)

simplifying

z 31

<=5XZ

hence

3dh=~x~ . . . (84)

z

Similarly any fraction of discharge say

JQ = Cl d;~ . . . (85)

JCI d: = Cl d:~ . . . (86)

-Hence

d,JIJZ = d,~ for channel . . . (87)

on the same lines

h~ = h x J213 . . . (88)

Therefore height of hump

P=dJ–hJ . . . (89)

. daJl /Z _ hJ2/3 . . . (90)

Substituting value of h from equation (84) into equation (90)

Height of hump :

dp = daJ1/Z – ? x ~

22x J213

(p=da J1/Z–~x?

22 )

. . . (91 )

. . . (92)

Figure 16 gives tha height of hump required to give propor-

tionality at a particular value of J.

G.1.2 For bulk proportionality

Where channels are run with fluctuating discharge, the propor-tionality is not obtainable for the whole range and it is then

desirable to dasign the hump such that error over the range of-discharges chosen will be minimum. This is called the’ “bulk

31

—

IS 14869:2000ISO 4359:1983

proportionality” and in this case the height of hump required to

obtain bulk proportionality for Q, to Qz is evaluated -as givenbelow

Height of hump :

p=da2–h2. . (100)

QI = c, d:, = CD h~,5 . . . (93)

and-Substituting value of h2 from equation (99)

Height of hump :Q2= JQl = Cl d:2 = CD h;5.,. (94)

Therefore

H(- )1

dJ1/: ‘:

az

()

1–1

F

‘al= ~xda2andhl=~xh2J213 . . . (95)

For bulk proportionality

.—P= da2 –

H(- )1–1J1/Z

=da2 1-———————

(- )

1–1

J213

d,, – d,2 = h, _ h2. .. (96)

Hence

1—-xda2–J1/z

da2. &xh2_h2. ~ . (97)

Therefore

. . (101)

Substituting da2 by da, and J, from equation (95)

Height of hump :

‘4”-) ‘(’+2 ...(98)

[

()1-—— 1

P = da, J1’Z 1 –J1~Z

( ).

1–1

G

Hence

da2()

~ –1hz =

J1/Z

(- )

1-1

J213

. . . (102)

. .. (89)Figure 17 gives the height of hump required for various valuesof z and fluctuations in discharges i.e. J.

32

IS 14869:2000ISO 4359:1983

Table 1 – Discharge coefficients for ~ectangular throated flumes

CD= ( -*)(1 -%)3’2\ /. ,

Lh

Iz

0,70 0,65 , 0,60 0,55 0,50 0,45 0,40 0,35 0,30 0,25 0,20 0,15 0,10 0,05

),2 0,9924 0,9819 0,9913 0,9906 0,8698 0,8668 0,9876 0,8660 0,9839 0,9609 0,9764 0,8691) 0,9542 0,9103

1,4 0,9912 0,9807 0,8801 0,9684 0,8666 -0,8676 0,8664 0,9648 0,8627 0,9797 0,9752 0,8678 0,9530 0,9092),6 0,8800 0,9695 0,8669 0,9663 0,8675 0,9665 0,9652 0,9636 0,8615 0,9785 0,9741 0,8667 0,9519 0,8081

),8 0,8668 0,9663 0,9678 0,9871 0,8663 0,8653 0,8340 ‘2 9625 0,9603 0,9774 0,9729 0,9655 0,9532 (),907 o1,0 0,9676 0,9872 0,9666 0,9859 0,8651 0,!%4 1 (),862 9 09813 0,9792 0,9762 0,9717 0,9644 0,9496 r),go5 9

1,2 0,8665 0,9660 0,8654 0,9647 0,8639 0,8629 0,8617 0,9601 0,9780 (3,975o 0,9706 (l,g632 l),g461j o,w 81,4 0,8653 0,9648 0,9642 0,9835 0,8627 0,8618 0,9605 0,9789 0,976.8 r3,9739 0,8694 (3,962(J (3,9474 0,913381,6 0,8641 0,9636 0,9831 0,8624 0,9816 0,!3606 0,9793 0,9778 0,9757 0,9727 l),g& 3 (),860 9 0,9462 0,80271,8 0,8629 0,8624 0,!%1 9 0,8612 0,9604 (),979 4 0,9782 0,9766 0,9745 (),971 5 0,9671 o,w 8 0,9451 o,~l 6

2,0 0,9618 0,8813 0,9607 0,8600 0,9792 0,9782 0,977r) 0,9754 0,9733 0,9704 (),866 0 0,9566 o,g441) r),81yJ5

2,2 0,8606 0,9601 0,9795 0,9789 0,9781 0,9771 0,9758 0,9743 0,9722 O,gag2 0,8648 13,9575 0,9429 o,&)g 5

2,4 089794 0,9787 0,9784 0,9777 0,9769 0,9759 0,9747 0,9731 0,9710 (),866 1 0,8637 r3,9563 O,gtll 7 O,m 4

2,6 0,9783 0,9778 0,9772 0,9765 0,9757 0,9748 0,9735 0,9720 (),869 9 0,8(!89 0,9625 (),955 2 0,8406 1333973

2,8 0,9771 0,9766 0,9761 0,9754 0,9746 0,9736 0,9724 0r97r38 r),g667 13,9658 (),g61 4 0,9541 0,9395 0,6863

3,0 0,9759 0,9755 0,9749 0,9742 0,9734 0,9724 0,9717. 0,9696 0,9676 0,8646 0,9602 0,9529 13,9364 (),695 2

3,2 0,9748 0,9743 0,9733 0,9731 0,9723 0,9713 0,9701 0,$)865 (),W 4 r),g635 0,9591 0,9518 ‘0,9373 (),684 13,4 0,9736 0,973.1 0,9726 0,9719 0,9711 (),970 1 0,9669 0,9673 0,9653 (),962 3 0,956 c1 0,8507 0,9362 0,69313,6 0,9725 0,9720 0,9714 0,9708 0,9700 0,8690 0,9678 (),866 2 l),g&l 1 (),g61 2 or~ 8 o,g4g 5 r),935 () 0,69203,8 0,9713 0,9708 0,9703 0,8696 0,8668 0,9678 0,9666 0,9651 (),g63 o o,g60 1 0,9557 0,8464 (),933 9 o,~ 94,0 0,9702 0,9687 0,8681 0,8665 0,9677 0,8667 0,9655 (J,g639 o,%l 8 0,9539 o,~ 6 0,9473 o,~ 8 l),= 9

4,2 0,8690 0,8665 0,8660 0,9673 ()#g665 0,9656 (),g643 o,~ 8 0,8607 0,9578 (),953 4 (),g462 0,9317 o,@684,4 0,8679 0,9674 0,8668 0,9662 o,g654 I),* 4 o,g632 o,~l 6 o,~ 6 o,= 6 0,8523 13,9451 0,93136 o,&3784,6 0,9667 0,9663 0,8657 0,9650 0,8642 (),gQ 3 Cl,g621 r),g60 5 o,g564 0,8555 (),851 2 i),g43 9 0,9295 0,88674,8 0,8656 0,9651 0,8646 0,9639 r),g&j 1 (),g62 1 Cl,g609 (3,9594 0,9573 1),~ 4 (),g50 r) o,9428 0,9234 0,3857

5,0 O,w 5 0,9640 0,8634 0,%2 8 0,8620 0,8610 (),g5g 3 Cl,g563 (),g562 (),g533 (),* r) o,~l 8 0,8274 0,8647

NQTE – The number of significant figures given in the columns for coefficient of discharge should not be taken to imply a corresponding accuracybut only to assist in interpolation and analysis.

Table 2 – Velocity coefficients for rectangular throated flumes

W2(*)2C;q-ey’+l=o

bh

— CDIi

h+p

1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2

0,10 1,0022 1,0018 1,0014 1,0011 1,CO08 1,00Q60,15

1,0004l,bo51

1,00021,0Q41

1,00011,0032 1,0025 1,0018 1,0013

0,201,0008

1,00811,0005 1,0002

1,0Q7 3 1,0058 1,0044 1,0032 1,00220,25

1,0014 1,0008 1,00041,0143 1,0115 1,0091 1,0069 1,0051 1,0035

0,301,0022 1,0013 1,0006

1,0209 1,0168 1,0132 1,0100 1,00730,35

1,0051 1,0032 1,0018 1,00081,0290 1,0232 1,0181 1,0137 1,0100 1,0069 1,0044 1,0025

0,40 1,0386 1,03081,0011

1;024 O 1,0181 1,0132 1,0091 1,0058 1,00320,45 1,0500 1,0397 1,0308

1,00141,0232 1;0168 1,0115 1,0073

0,50 1,06351,0041 1,@318

1,0500 1,0386 1,0280 1,0209 1,01430,55

1,0091 1,0051 1,00221,0793 1,0620 1,0476 1,0357 1,0255 1,0175 1,0110

0,60 1,08801,0061

1,0760 1,05791,0027

1,0429 1,0308 1,0209 1,0132 1,00730,65

1,00321,1203 1,0921 1,0S95 1,0513 1,0367 1,0248 1,0156

0,701,0066 1,CKK38

1,1465 1,1108 1,0829 1,0W6 1,0429 1,0290 1,01810,75 1,1327 1,0980

1,0100 1,00441,0711 1,0500 1,033$ 1,0209 1,0115

0,301,0051

1,1153 1,0829 1,0579 1,0366 1,02400,85

1,0132 1,00581,1353 1,0960 1,0664 1,0441 1,0272 1,0149

0,901,0065

1,1108 1$760 1,0500 1,0308 1,0168 1,00730,85 1,1275 1,W64 1,0564 1,0346 1,01881,00

1,00621,1465 1,0860 1,0635 1,0366 1,0209 1,00%1

A---- -. .NWI E — Tfle number of aignificentfigures given in the columns for coefficient of veloqity should not be taken to imply a correspondingaccuracy butonly to assist in interpolation and analvsia.

33

IS 14869:2000

IS() 4359:1983

Table3 – Circular functions for use inderiving calibration-of U-throated flumes

9

rad

0,50,60,70,80,91,01,11,21,31,41,5rr/2

f, (e)

0,C61 210,08733

0,11760,15160,18820,22980,27320,3188

0,36620,41500,46460,5000

f* (8)

0,47940,56460,64420,71740,78330,64150,89120,93200,96360,98540,9975I.000o

f~ (e)

0,019620,033490,051820,075050,10330,13630,17390,21560,26060,30810,35740,3927

f,(o) = 1/2(1 -coSe)

fz (d) = sine

f~(a = 1/4(0- sinecose)

Table4– Recommended roughness values,“, ”== ,,, ,,, SC! O,, ,=L, V

Valuea of k~Surface claasificetion

Good example Normal value

Plastics (and similar)

Perspex, PVC or other smooth-faced plastics — 0,003

Asbestos cement — 0,015

Resin-bonded, glass fibre moulded against smooth forms of sheet metal or well-sanded and painted timber 0,03 0,06

Metal

Smooth, machined and polished metal 0,003 0,006

Uncoated sheet metal, rust free 0,015 0,03

Painted sheet metal 0,03 0,06

Galvanized metal 0,06 0,15

Painted or coated casting 0,06 0,15

Uncoated casting 0,15 0,3

Concrete

In-situ or precast construction using steel formwork, with all irregularitiesrubbed down or filled in 0,06 0,15

In-situ or precast construction using plywood or wrought timber formwork 0,3 0,6

Smooth trowelled cement rendering 0,3 0,6

Conciete with thin film or sewage slime 0,6 1,5

Wood

Planed timber or plywood 0,3 0,6

Well aended and painted 0;03 0,06

Table 5 – Viscosity of water

Temperature Kinematic viscosity, v“c m2/5

o 1,79 X 10-65 1,52 X 10-6

10 1,31 X 10-615 1,14 X 1o-I320 1,01 X 1o-I325

\ 0,80 X 10-630 0.81 X 1o-I3

34

IS 14869:2000ISO 4359:1983

----- Approach channel. . :;,:,)!,,., 1,:,’J > 01

‘Y., “c,‘% \ ‘“%

‘ . .

+

\ \ ... ..

‘, ,!’. ‘\.\ ’’’’..,

11‘, . .h ...

,,,% ..... Exjt transition

&“’ II X..k = ., ,/

? “ Example shown,rof truncation

t— &

~: -sill!,PgV,ell

/

\

Entrance transitior~–—

\

-\ ‘\\

\\

\\

a) Isometric view of level invert flume (p = 0)

When recovery of heao is not

R >2(B-b)important, the exit transition may be

m. -

7

truncated after half its length (see

=ab~ above)rrJ3~?%%

II

I t,

—— I Q, Q

I1

1A

l––

in a flume wthout a hump (p = 0),the iniert aver this length shall be

truly lsxfel——-..—.

----—~

wFront view

(level invert)

b) Plan view

- Connection to stilling well

III1

-Id

/////’/////////’/ / w/I

L

This radius shall be chosen so thatthe bottom contraction starts at thesame section as the side contractions.For a flume with a bottom contraction

only, the radius = 4 p.

Front view(raised invert)

c) Longitudinal section of flume with raised invert (hump)

Figure 1 – Rectangular throated flume

IS14869:2000

1S0

4359:1983

xLn

mi-ll

-J1I1

--qj--

,/

——

.

L4u

Baffle platform

AL1 L L2 ‘Lb L3

—a

Hump ~ Baffle wall

01

al Plan view

Height of hump = p— 1

~I II

I

.—— ——— ——— —.

L2=o,69H+2Ap Lb L33

b) Section

Figure3 – Designof a flumedstandingwavefall

IS 14869:2000

ISO 4359:1983

\

COnnect[rlg pipe._–_Stllllng well

<,<\ \FR

“b ‘- ...

$\

a) Isometric view of level invert flume (p = O)

/-- Exit transition

r—Entrance trt;r,~ll,(j,

-—Throat

‘\Approach channel —~

\\\ ‘“__Standing .ave

Head gauging section 1 in 6 expansion for high modular

limit and head recovery

I

I i -cl

Cl

I

stOL/7max. 71 NOtmore than I in 3.

+1 k]horizontal sectionThis radius chosen so that entrance

\ (or equivalent curve),transition lies entirely within a plane-

defining a 1 in 3 contraction,

b) Pien view(Example’ shown, no hump, ma = m, skew cylinder entrance transition)

r

Not more than I in 3stilling well

(or equivalent curve)

C) Longitudinal section of flume with raised invert (hump)

= -— _Conical ima # m, no hump)

plane (ma # m, no hump)

Generators are

-Eines ~—___

Warped (/na * m, no humD)

d) Examples of plans of entrance transitions

——

Figure 4 – Trapezoidal throated flume

IS 14869:2000ISO 4359:1983

\ /-ApprOachchanr’e’Entrance transition

,!’ ‘,

,.

Exit transition

/

\’L

.,

Connecting slot \

L Stilling well

\ .

Standing wave

\.

a) Isometric view

The straight sided contraction may

be replaced by curved surfaces,provided they lie within the full lines

I

2

Invert linem

7

mc~ ,2

\

+1A -y 1 in 6*xpansion for high

[–modular limit and head recovery

I I

Q

2hmax.’3to khmax ,* L * *>l,5(Da -D) w /r= “‘:‘=In a flume without hump

(p = 0), the invert over thislength shall be truly level 4 /

Front view

b) Plan view(level invert)

I

Connectionto-J Llnalevelflume,p=~ Front view

stilling well(raised invert)

—

For a flume with a hump, aconvenient value of p is 0,5 (Da - D)

c) Longitudinal section of flume with reiaed invert (hump)

Figure 5 – U-ahapad flume

IS 14869:2000ISo 4359:1983

--—

0.5 ‘0.6 0.7 0.8 0.9 1.01,2-5

1,20

1,15

1,10

1,05

1,00

, , r s- .,

0 0,1 0,2 0,3 0,4 0,5

Cubehe Cu(b-2d. )(h-d. )=

A A

NOTE – Foratrapezoidal throat flume Cuiareplaced by C&lna U-ahapedflumeh =-D.

Figure 6 – Coefficient of approach velocity, Cv

40

IS 14869:2000ISO 4359:1983

1,0

0,5

0,2

0,1

0,0:

—.

—

——

——

1

j-----rl—+.. ...+ ----

4“-=--..—.

0,2

—

I

w\

- -4--‘“--’7- :

I

0,5

J-.-L———J——l——L—II I I I

1 2

Side slope m (m horizontal to 1 vertical)

5 10

Figure 7 – Values of v for use in determining CD : trapezoidal flumes

41

IS 14869:2000ISO 4359:1983

b“

5,0

4,5

4,0

3,5

3,0

2,5

2,023 5 10 20

mHce/be

2,6

2,4

2,2

2,0

1,8

1,6

1,4

1,2

1,0

0,2 0,3 0,5 1,0 2,0mHce/be .

1,2

~m 1,1

1,00,02 0,03 0,05 0,1 0,2

mHce /be

—

NOTE - If ,)l//rf, /Je > 5 obtain C’~fromfigure9,

Figure 8 – Shape coefficient for trapezoidal flumes

.

IS14869:2000

ISO

4359:1983

tI

IIll[I

II

1

r

:\

——

:L–-----------–-

:11;~––__

———

--1

%-––”_

--I

-1111IIIllI

III

I

II

IIll

III

III

I

,___–—

——

__

II

l-—_

—___

1“II

[Ill

III

III

I

~.

‘1‘-1I

00

00-

—

43

IS 14869:2000ISO 4359:1983

Hce/De

1,0 1,5 2,0 3,01,0

0,95

~’ 0,90

0,85

0,80

0,85

0,80

0,75

“0,70

0,65

0,60

0,55

0,50

0,45

0,40

0,1 0,2 0,3 0,4

H,,ID,

Figure 10 – Shape coefficient for U-shaped

0,6 0,8 1,0

flumes

.

44

Is 14869:2000ISO 4359:1983

—

1,0 2,5

0,8 2,3

0,6 2,1Aucm3

0,4 1,9

0,2 1,7

0 1,5.0,01 Ops 0,1 0,5 1 5 10 50 100

Trapezoidal, mHClh; U-shaped, HCID

NOTE – w = O for U-shaped.

Figure 11 – Accuracy coefficients, y, V, @

45

IS 14869:2000ISO 4359:1983

(%+x’’’=”%a)

b)

/ \

d)

J08

1,0

=1,3

L“J

1,2

Average0,8

,

(%HX1’’=1’3%c)

/

f)

—

.,

Figure 12 – Examples of velocity profile in approach channel

0,010

0,009

0,008

0,002

0,001

I —

I

l==k,=3xlo5 \

.,, , ,,,~ Lower limit for smooth

laboratory installations

,05 106 107 108

Reynolds number I/e = VLI v

Figure 13 – Relative boundary layer displacement thickness

IS14869:2000

ISO

4359:1983

000moNou-l

(wvu-lo-

.CNo-

-0-

S0s.0F0.

0

—.

&c.-‘t

qJ/q

IS 14869:20001S0 4359:1983

2?- 0,7s

0,6

0,50,1 0,2 0,3 0,4 0,5 0,6 0,7

HclD,Hce/De

NOTE – WCID = 1,00when H.JD >0,70.

Figure 15 – Velues of wC/b for use in determining Re : U-shaped flumes

49

IS ~4869 :2000ISO 4359:1983

0,25da

0,20da

0,15daE2%Em.-2

0,10da

0,05da

0,00da

Figure 16 –

.

—— .

—._, — —— .

(),2 0,4 0,6 0,8

.

.

1,0Fraction J of design discharge

Showing height of hump required to give proportionality for a small variation in discharga

—

IS 14869:20001s04359:1983

0,25da1

0,2”Oda

0,15da?22%

O,lOda

0,05da

O,OOd:1,6 1,7 1,8 1,9 2,0

.—.—

z in Q= Cld~

Figure17 – Showing height ofhumpto ettainbulk proportioneli~

51

Bureauof Indian Standards

B“IS is a statutory institution established under the Bureau of lndian Standards Act, 1986 to promoteharmonious development of the activities of standardization, marking and quality certification of goodsand attending to connected matters in the country.

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Review of Indian Standards

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This Indian Standard has been developed from Doc : No. WRD I (229).

Amendments Issued Since Publication

Amend No. Date of Issue Text Affected

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IS 14869 (2000): Liquid Flow Measurement in Open Channels ... · The flow conditions considered are...

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Transcript of IS 14869 (2000): Liquid Flow Measurement in Open Channels ... · The flow conditions considered are...