ISO 4360:2020

INTERNATIONAL ISO
STANDARD 4360
Fourth edition
2020-06
Hydrometry — Open channel flow
measurement using triangular
profile weirs
Hydrométrie — Mesure de débit des liquides dans les canaux
découverts au moyen de déversoirs à profil triangulaire
Reference number
©
ISO 2020
© ISO 2020
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ii © ISO 2020 – All rights reserved

Contents Page
Foreword .v
1 Scope . 1
2 Normative references . 1
3  Terms and definitions . 1
4 Symbols . 1
5 Principle . 2
6 Installation . 2
6.1 General . 2
6.2 Selection of site . 2
6.3 Installation conditions. 3
6.3.1 General. 3
6.3.2 Measuring structure . 4
6.3.3 Approach channel . 5
6.3.4 Downstream channel . 5
7 Maintenance . 6
8 Measurement of head(s) . 6
8.1 General . 6
8.2 Location of head measurement(s) . 6
8.2.1 Modular (free) flow . 6
8.2.2 Non-modular (drowned) flow . 6
8.3 Gauge wells . 7
8.4 Zero setting . 9
8.5 Dimensions .10
9 Discharge characteristics .10
9.1 Formulae of discharge .10
9.1.1 Modular (free) flow .10
9.1.2 Non-modular flow .11
9.2 Coefficients .11
9.2.1 Coefficient of discharge, C .11
d
9.2.2 Coefficient of velocity for modular flow, C .11
v
9.2.3 Non-modular flow reduction factor, f, with crest tappings .11
9.2.4 Non-modular flow reduction factor, f, with tailwater recorder .11
9.3 Limitations .12
10  Uncertainties of flow measurement .12
10.1 General .12
10.2 Combining measurement uncertainties .13
10.3 Uncertainty of discharge coefficient u(C ) for the triangular profile weir .14
d
10.4 Uncertainty budget.14
11 Example .15
11.1 General .15
11.2 Characteristics — Gauging structure .15
11.3 Characteristics — Gauged head instrumentation .15
11.4 Discharge coefficient .15
11.5 Discharge calculation .16
11.6 Uncertainty statement .16
Annex A (informative) Introduction to measurement uncertainty .18
Annex B (informative) Sample measurement performance for use in
hydrometric worked examples .26
Annex C (informative) Spreadsheet for use with this document .29
Bibliography .30
iv © ISO 2020 – All rights reserved

Foreword
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different types of ISO documents should be noted. This document was drafted in accordance with the
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URL: www .iso .org/ iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 113, Hydrometry, Subcommittee SC 2,
Flow measurement structures.
This fourth edition cancels and replaces the third edition (ISO 4360:2008), which has been technically
revised.
The main changes compared to the previous edition are as follows.
— The calculations and examples have been updated to correct an error in the previous edition.
— A URN has been added containing a spreadsheet that has been developed to support the standard
and facilitate calculation of discharge and uncertainty (see Annex C).
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
INTERNATIONAL STANDARD ISO 4360:2020(E)
Hydrometry — Open channel flow measurement using
triangular profile weirs
1 Scope
This document specifies methods for the measurement of the flow of water in open channels under
steady flow conditions using triangular profile weirs. The flow conditions considered are steady flows
which are uniquely dependent on the upstream head and non-modular (drowned) flows which depend
on downstream as well as upstream levels.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 772, Hydrometry — Vocabulary and symbols
3  Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 772 apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
4 Symbols
Unit of
Symbol Quantity
measurement
α dimensionless Coriolis coefficient
A m area of approach channel
B m width of approach channel
b m breadth of weir crest perpendicular to flow direction
C dimensionless coefficient of discharge
d
C dimensionless coefficient of velocity
v
C f dimensionless combined coefficient of velocity for non-modular flow
v
f dimensionless non-modular (drowned) flow reduction factor
g m/s acceleration due to gravity
H m total head relative to crest level
gauged head relative to crest level (upstream head is inferred if no subscript
h m
is used)
N dimensionless number of measurements in a set
p m height of weir (difference between upstream mean bed level and crest level)
Q m /s volumetric rate of flow
as parameter standard uncertainty in parameter specified in parentheses
u ()
Unit of
Symbol Quantity
measurement
*
% percentage uncertainty in parameter specified in parentheses
u ()
v m/s mean velocity
U % expanded percentage uncertainty
Subscripts:
0 datum
1 upstream
2 downstream
c combined
p measured crest tapping head above crest level
max maximum
min minimum
5 Principle
The discharge over a triangular profile weir is a function of the upstream head on the weir (for modular
flow), upstream and downstream head (for non-modular flow), the geometrical properties of the weir
and approach channel and the dynamic properties of the water.
6 Installation
6.1 General
The required conditions regarding selection of site, installation conditions, the measuring structure,
the approach channel, the downstream channel, maintenance, measurement of head, and gauge wells
which are generally necessary for flow measurement are given in the following subclauses.
6.2 Selection of site
A preliminary survey shall be made of the physical and hydraulic features of the proposed site, to check
that it conforms (or can be made to conform) to the requirements necessary for accurate measurement
by a weir.
Particular attention should be paid to the following features in selecting the site:
a) availability of an adequate length of channel of regular cross-section;
b) the existing velocity distribution;
c) the avoidance of a steep channel, if possible;
d) the effects of any raised upstream water level due to the measuring structure;
e) conditions downstream including such influences as tides, confluences with other streams, sluice
gates, mill dams and other controlling features which might cause non-modular flow;
f) the impermeability of the ground on which the structure is to be founded, and the necessity for
piling, grouting or other means of controlling seepage;
2 © ISO 2020 – All rights reserved

g) the necessity for flood banks to confine the maximum discharge to the channel;
h) the stability of the banks, and the necessity for trimming and/or revetment in natural channels;
i) the clearance of rocks or boulders from the bed of the approach channel;
j) the effect of wind; wind can have a considerable effect on the flow in a river or over a weir, especially
when these are wide and the head is small and when the prevailing wind is in a transverse direction.
If the site does not possess the characteristics necessary for satisfactory measurement, the site shall be
rejected unless suitable improvements are practicable.
If an inspection of the stream shows that the existing velocity distribution is regular, then it may be
assumed that the velocity distribution will remain satisfactory after the construction of a weir.
If the existing velocity distribution is irregular and no other site for a gauge is feasible, due consideration
shall be given to checking the distribution after the installation of the weir and to improving it if
necessary.
A complete and quantitative assessment of velocity distribution may be made by means of a current-
meter, other point velocity measurement technique or an acoustic Doppler profiler. Information about
[1] [2]
the use of current-meters is given in ISO 748 and information on Doppler profilers in ISO 24578 .
Figure 1 gives examples of satisfactory velocity distributions.
NOTE The contours refer to values of local flow velocity relative to the mean cross-sectional velocity.
Figure 1 — Examples of satisfactory velocity distributions
6.3 Installation conditions
6.3.1 General
The complete measuring installation consists of an approach channel, a measuring structure and a
downstream channel. The conditions of each of these three components affect the overall accuracy of
the measurements.
Installation requirements include features such as the surface finish of the weir, the cross-sectional
shape of the channel, the channel roughness and the influence of control devices upstream or
downstream of the gauging structure.
The distribution and direction of velocity have an important influence on the performance of the weir,
these factors being determined by the features mentioned above.
Once an installation has been installed, the user shall prevent any change which could affect the
discharge characteristics.
6.3.2 Measuring structure
The structure shall be rigid and watertight and capable of withstanding flood flow conditions without
distortion or fracture. It shall be at right angles to the direction of flow and shall conform to the
dimensions given in the relevant clauses.
The weir comprises an upstream slope of 1 (vertical) to 2 (horizontal) and a downstream slope of 1
(vertical) to 5 (horizontal). The intersection of these two surfaces forms a straight line crest, horizontal
and at right angles to the direction of flow in the approach channel. Particular attention shall be given
to the crest itself, which shall possess a well-defined corner of durable construction. The crest may be
made of pre-formed sections, carefully aligned and jointed, or may have a non-corrodible metal insert,
as an alternative to in situ construction throughout.
The dimensions of the weir and its abutments shall conform to the requirements indicated in Figure 2.
Weir blocks may be truncated but not so as to reduce their dimensions in plan to less than h for the
max
1:2 slope and 2 h for the 1:5 slope.
max
Figure 2 shows the general arrangement of the triangular profile weir.
Key
1 upstream head measurement
2 crest tapping head measurement
3 gauge wells
4 crest tappings
5 limit of truncated sections
6 downstream head measurement
7 direction of flow
Figure 2 — General arrangements of the triangular profile weir
4 © ISO 2020 – All rights reserved

6.3.3 Approach channel
On all installations, the flow in the approach channel shall be smooth, free from disturbance and shall
have a velocity distribution as satisfactory as possible over the cross-sectional area. This can usually
be verified by inspection or measurement. In the case of natural streams or rivers, this can only be
attained by having a long straight approach channel free from projections into the flow. Figure 1 gives
examples of satisfactory velocity distributions.
The following general requirements shall be complied with.
a) As the altered flow conditions due to the construction of the weir might cause a build-up of shoals
of debris upstream of the structure, which in time might affect the flow conditions, the likely
consequential changes in the water level shall be taken into account in the design of gauging
stations.
b) In an artificial channel, the cross-section shall be uniform and the approach channel shall be
straight for a length equal to at least 5 times its water-surface width.
c) In a natural stream or river, the cross-section shall be reasonably uniform and the approach
channel shall be straight for a sufficient length to ensure a satisfactory velocity distribution.
d) If the entry to the approach channel is through a bend, or if the flow is discharged into the channel
through a conduit or a channel of smaller cross-section, or at an angle, then a longer length of
straight approach channel is likely to be required to achieve a regular velocity distribution.
e) Flow conditioning devices such as baffles and flow straighteners shall not be installed closer to the
points of measurement than a distance 10 times the maximum head to be measured.
f) Under certain conditions, a standing wave can occur upstream of the gauging device, for example
if the approach channel is steep. Provided that this wave is at a distance of not less than 30 times
the maximum head upstream, flow measurement is feasible, subject to confirmation that a regular
velocity distribution exists at the gauging station and that the Froude number in this section is no
more than 0,6.
If a standing wave occurs within this distance, the approach conditions and/or the gauging device shall
be modified.
6.3.4  Downstream channel
The channel downstream from the structure is usually of no importance if the weir has been designed
so that the flow is modular (i.e. unaffected by tailwater level) under all operating conditions. A
downstream gauge may be provided to measure tailwater levels to determine if and when non-modular
flow occurs. The downstream gauge shall be installed sufficiently far downstream to avoid excessively
disturbed flow and be truly representative of downstream channel conditions. This shall be determined
on a site by site basis.
In the event of the possibility of scouring downstream, which phenomenon can also lead to the
instability of the structure, particular measures to prevent this happening should be adopted. The
design of such measures is outside the scope of this document.
A crest tapping and separate gauge well shall be fitted if the weir is designed to operate in a non-
modular condition or if there is a possibility that the weir could drown in the future.
The latter circumstance could arise if the altered flow conditions due to the construction of the weir
have the effect of building up shoals of debris immediately downstream of the structure or if river
works are carried out downstream at a later date.
Fish passage baffles can be installed on the downstream face of the weir to improve fish passage as set
[3]
out in ISO/TR 19234 .
7 Maintenance
Maintenance of the measuring structure and the approach channel is important to secure accurate
continuous measurements.
The approach channel shall be kept free of silt, vegetation and obstructions which might have
deleterious effects on flow conditions specified for the standard installation.
Where used, gauge wells and their entry from the channel shall also be kept clean and free from deposits.
The downstream channel shall be kept free of obstructions which could result in non-modular flow.
The weir structure shall be kept clean and free from clinging debris and care shall be taken in the
process of cleaning to avoid damage to the weir crest.
Head-measurement piezometers, connecting conduits and gauge wells shall be cleaned and checked for
leakage. The device used to measure head shall be checked periodically to ensure accuracy.
If a flow straightener or similar is used in the approach channel, it shall be kept clean.
8 Measurement of head(s)
8.1 General
Where spot measurements are required, the heads can be measured by staff gauges, hooks, points,
wires or tape gauges.
Where continuous records are required, recording gauges shall be used.
[4]
Devices for the measurement of head are described in ISO 4373 .
Periodic checks on the measurement of the head in the approach channel shall be made.
The accuracy of the head measuring device shall be considered when considering the uncertainty of the
flow measurement (see Clause 10).
NOTE As the size of the weir and head reduces, small discrepancies in construction and in the zero setting
and reading of the head measuring device become of greater relative importance.
8.2 Location of head measurement(s)
8.2.1  Modular (free) flow
Flow is modular when it is independent of variations in tailwater level. This requirement is met when
the tailwater total head is equal to or less than 75 % of the upstream total head.
The location for the measurement of head on the weir should be at a sufficient distance upstream from
the weir to avoid the region of surface drawdown. On the other hand, it should be close enough to the
weir to ensure that the energy loss between the section of measurement and the control section on the
weir shall be negligible. Taking these considerations into account, the head-measurement section shall be
located at a distance between 2 and 4 times the maximum head (2 h to 4 h ) upstream of the crest.
max max
8.2.2  Non-modular (drowned) flow
A significant error in the calculated discharge will develop if the tailwater total head above crest
level exceeds 75 % of the upstream total head, unless a crest tapping or downstream (tailwater)
measurement is provided and two independent head measurements are made.
When a crest tapping is used, non-modular flow occurs when the head recorded by the crest tapping
exceeds 25 % of the upstream total head. Where the weir is designed to operate under non-modular
flow, a second measurement of head is required. For more accurate flow measurement, the head shall be
6 © ISO 2020 – All rights reserved

measured within the separation pocket immediately downstream of the crest. Alternatively, the head
can be measured in the channel downstream (tailwater) of the structure. However, the uncertainties in
the flow measurements made using tailwater data will generally be greater than those obtained from
a well-maintained crest tapping. The optimum position for the crest tapping is at the centre of the weir
crest. The tapping may be off-centre on weirs wider than 2,0 m provided that the distance from the
centreline of the crest tapping to the nearer side wall or pier is greater than 1,0 m.
8.3  Gauge wells
Where there are water surface irregularities, a gauge well (sometimes referred to as a stilling well)
may be used to improve the stability of the measurement and thus reduce the effect of short period
variations due to surface movements caused by wind or waves.
Gauge wells shall be vertical and of sufficient height and depth to cover the full range of water levels. In
field installations, they shall have a minimum height of 0,6 m above the highest water levels expected.
Gauge wells shall be connected to the appropriate head measurement positions by means of pipes, slots
or holes.
Both the well and the connecting pipe shall be watertight. Where the well is provided for the
accommodation of the float of a level recorder, it shall be of adequate size and depth. Care shall be taken
to ensure that there is sufficient clearance around the float such that it cannot foul on the sides of the well.
The connecting pipe shall have its invert not less than 0,10 m below the lowest level to be gauged.
Pipe connections to the upstream and downstream head measurement positions shall terminate flush
with, and at right angles to, the boundary of the approach and downstream channels. The channel
boundary shall be plain and smooth (equivalent to carefully finished concrete) within a distance
10 times the diameter of the pipes from the centre line of the connection. The pipes may be oblique to
the wall only if they are fitted with a removable cap or plate, set flush with the wall, through which a
number of holes are drilled. The edges of these holes shall not be rounded or burred. Perforated cover
plates are not recommended where weed or silt are likely to be present.
Adequate additional depth shall be provided in wells to avoid the danger of floats (if used) grounding
either on the bottom or on any accumulation of silt or debris.
The gauge well arrangement may include an intermediate chamber of similar size and proportions to
the gauge well, to enable silt and other debris to settle out where it may be readily seen and removed.
The diameter of the connecting pipe or width of slot to the upstream well shall be sufficient to permit
the water level in the well to follow the rise and fall of head without appreciable delay. Care should be
taken however not to oversize the pipe, in order to ensure ease of maintenance and to damp out any
oscillations due to short period waves.
No firm rule can be laid down for determining the size of the connecting pipe to the upstream well,
because this is dependent on a particular installation, e.g. whether the site is exposed and thus subject
to waves, and whether a larger diameter well is required to house the floats of recorders.
The static head at the separation pocket immediately downstream of the crest of the weir shall be
transmitted to its gauge well as follows.
a) An array of tapping holes shall be set into a plate covering a cavity in the crest of the weir block.
b) The underside of the plate shall be supported on a manifold into which the static head is
communicated via an array of feed tubes.
c) A horizontal conduit shall lead from the cavity through the weir block beneath the crest and
terminating at the gauge well.
d) A flexible transmission tube shall communicate static head within the manifold to the gauge well.
e) A watertight seal around the transmission tube shall prevent static head within the cavity (which
can be different because of leakage around the perimeter of the cover plate) from influencing the
static head transmitted from within the manifold.
These arrangements minimize the occurrence of silting within the communication path between the
separation pocket and the gauge well and allow effective purging of the pipework by the occasional
backflushing of the system. For this purpose, a volume of water shall periodically be introduced to the
gauge well.
Figure 3 shows the general arrangement for the crest tapping installation.
The crest tapping shall consist of five to 10 holes of 10 mm diameter drilled in the weir block with
centres 75 mm apart, 20 mm down from the weir crest on the 1:5 slope. The edges of the holes shall not
be rounded or burred. The number of holes shall be sufficient to ensure that the water level in the gauge
well follows variations in crest separation pocket pressure without significant delay.
8 © ISO 2020 – All rights reserved

a)   Side view (in direction of flow) b)   Side view (normal to flow)
c)   View of tappings from underneath the weir
Key
1 crest tappings
2 feed tubes communicating crest head to the manifold (some shown as single lines only)
3 manifold [Figure 3 b)]
4 cavity in the crest of the weir block
5 conduit leading to a gauge well
6 transmission tube (other end sealed within the conduit but communicating head in the manifold to the
gauge well)
7 holes for screw-mounting the crest plate onto the weir block
Figure 3 — General arrangement for the crest tapping installation
8.4 Zero setting
Accurate initial setting of the zeros of the head measuring devices with reference to the level of the
crest, and subsequent regular checking of these settings, is essential.
An accurate means of checking the zero at frequent intervals shall be provided. Benchmarks, in the
form of horizontal metal plates, shall be set up on the top of the vertical side walls and in the gauge
wells. These shall be accurately levelled to ensure their elevation relative to crest level is known.
NOTE Instrument zeros can be checked relative to these benchmarks without the necessity of resurveying
the crest each time. Any settlement of the structure can, however, affect the relationships between crest and
benchmark levels and it is advisable to make occasional checks on these relationships.
A zero check based on the water level (either when the flow ceases or just begins) is susceptible to
serious errors due to surface tension effects and shall not be used.
The crest elevation shall be measured with respect to benchmarks at regular intervals across the
breadth of the weir with not less than 10 measurements in total. The mean of these crest elevation
measurements shall be used to define the gauge zero.
8.5 Dimensions
To minimize uncertainty in the flow calculation, it is essential that the “as built” and post construction
surveyed dimensions of the structure are used to determine discharge.
9 Discharge characteristics
9.1 Formulae of discharge
A spreadsheet (available at: https:// standards .iso .org/ iso/ 4360/ ed -4/ en/ ) has been developed to
accompany this document to facilitate discharge calculations. See Annex C.
9.1.1  Modular (free) flow
In terms of total upstream head, the basic discharge formula for a triangular profile weir operating
under modular flow conditions is shown as Formula (1):
15,
QC= gbH (1)
d 1
The total upstream head, H , is given by Formula (2):
αv
Hh=+  (2)
2g
For straight open channels, the Coriolis coefficient lies in the range 1,03 to 1,10. For practical purposes,
a value of 1,05 may be assumed.
The total head formula is solved by iteration. An initial assumption is made that H = h and an initial
1 1
value of Q is computed. The mean velocity of approach, v , is then computed from values of Q and A, the
cross-sectional area of the approach channel. Formula (2) then provides a refined value of H . This
process is repeated until successive values of H are within the bounds of accuracy required.
Alternatively, the discharge modular flow formula may be expressed in terms of gauged head by
introducing a coefficient of velocity dependent upon the weir and flow geometries, as shown in
Formula (3):
15,
QC= Cgh (3)
dv 1
15,
where C is the coefficient allowing for the effect of approach velocity (/Hh ) (non-dimensional)
v 11
and is determined as described in 9.2.2.
10 © ISO 2020 – All rights reserved

9.1.2  Non-modular flow
In terms of total head, the basic discharge formula for a triangular profile weir operating under non-
modular flow conditions is shown as Formula (4):
15,
QC= fgbH (4)
d 1
where f is the non-modular flow reduction factor (non-dimensional).
Alternatively, the non-modular flow discharge formula may be expressed in terms of gauged head by
introducing a coefficient of velocity dependent formula the weir and flow geometries, as shown in
Formula (5):
15,
QC= Cf gbh (5)
dv 1
9.2  Coefficients
9.2.1  Coefficient of discharge, C
d
C is almost independent of h , except at very low heads (h < 0,1 m) when surface tension effects
d 1 1
become important. C is given Formula (6):
d
15,

0,000 3 
C =− 0,633 1 (6)
 
d
h
 
where h is expressed in metres. For practical purposes, C can be set equal to 0,633 for h ≥ 0,1 m for
d 1
manual calculations. The spreadsheet solution provided with this document uses Formula (6) for the
full range of h values.
9.2.2  Coefficient of velocity for modular flow, C
v
The coefficient of velocity, C , for the modular flow formula is obtained from Figure 4 where A is the
v
area of the approach channel.
9.2.3  Non-modular flow reduction factor, f, with crest tappings
The non-modular flow reduction factor f when using crest tappings is determined from Formula (7)
with a tolerance of ± 1 %.
NOTE Under modular flow conditions, the value of h /H is constant at 0,20 and the value of f is 1,00.
p 1
0,256
15,
 
h
 
p
 
f =−10,,40 945  (7)
 
 
 H 
 1 
 
9.2.4  Non-modular flow reduction factor, f, with tailwater recorder
The non-modular flow reduction factor f when using a tailwater recorder is determined from
Formula (8) or Formula (9) depending on the ratio H /H .
2 1
0,0647
 
 H 
 
f =− 1,,035 0 817       if 0,75 < H /H ≤ 0,93 (8)
 
2 1
H
 
 
 
H
f =− 8,,686 8 403                 if 0,93 < H /H ≤ 0,98 (9)
2 1
H
9.3 Limitations
The following general limitations are recommended:
— h ≥ 0,03 m (for a crest section of smooth metal or equivalent);
— h ≥ 0,06 m (for a crest section of fine concrete or equivalent);
— P ≥ 0,06 m;
— b ≥ 0,1 m;
— h /P ≤ 4,5;
— b/ h ≥ 2,0.
Key
Y C
v
X C bh
d 1
1 C bh /A ≥ 0,25
d 1
2 C bh /A ≤ 0,25
d 1
bh
Figure 4 — Coefficient of velocity, C, in terms of C
v d
A
10 Uncertainties of flow measurement
10.1 General
The spreadsheet (see Annex C) for use with this document incorporates uncertainty calculations.
10.1.1 This clause provides information to state the uncertainty of a measurement of discharge.
12 © ISO 2020 – All rights reserved

NOTE In accordance with former practice in hydrometry, the expression for uncertainty is continued to be
expressed at the 95 % confidence level for the discharge coefficient and the determined flow rate.
[5]
ISO/IEC Guide 98-3 (referred to hereafter as the GUM) and ISO/TS 25377 (referred to hereafter as
[6]
the HUG) operate using standard uncertainties (i.e. at the 68 % confidence level). However, the HUG
requires final resultant uncertainty of measurement to be expressed at the 95 % confidence level.
Some components of uncertainty are expressed at the 95 % level, i.e. u (C ) while others are standard
95 d
uncertainties, i.e. those derived from Type A and Type B methods (see A.5 and A.6). Before these can be
combined, those at the 95 % level shall be converted to the 68 % confidence level by dividing them by the
coverage factor, k. Having so combined these components to determine the standard uncertainty, this
result is now multiplied by the coverage factor (k = 2) to express uncertainty at the 95 % confidence level.
10.1.2 Annex A is an introduction to measurement uncertainty. It provides supporting information
based on the GUM and the HUG.
10.1.3 A measurement result comprises:
a) an estimate of the measured value, with
b) a statement of the uncertainty of the measurement.
10.1.4 A statement of the uncertainty of a flow measurement made using a flow measurement structure
has four separate components of uncertainty:
a) uncertainty of the measurement of head in the channel;
b) uncertainty of the dimensions of the structure;
c) uncertainty of the discharge coefficient stated in this document from laboratory calibration of the
flow structure being considered;
d) uncertainty of channel velocity distribution related to the velocity coefficient, C .
v
This subclause does not accommodate component d). It is assumed that the channel hydraulics
are substantially equivalent to those existing in the calibration facility at the time of derivation of
component c).
10.1.5 The estimation of measurement uncertainty associated with items a) and b) of 10.1.4 is provided
in Annex B.
Values taken from Annex B are used in the example in Clause 11. These values are for illustrative
purposes only, they should not be interpreted as norms of performance for the types of equipment
listed. In practice, uncertainty estimates should be taken from test certificates for the equipment,
[7]
preferably obtained from a laboratory conforming to ISO/IEC 17025 .
10.2 Combining measurement uncertainties
See A.7.
The proportion in which each flow formula parameter contributes to flow measurement uncertainty,
U(Q), is derived by analytical solution using partial differentials of the discharge formula.
The general formula of discharge for modular and for non-modular flow is Formula (4) where f = 1 for
modular flow conditions.
The effect on the value Q due to small dispersions of C , C (or C f ), b and h is ΔC , ΔC , (or ΔC f ), Δb
d v v 1 d v v
and Δh . These are calculated from Formula (10). Note that the quantities ΔC , or ΔC f are assumed to
1 v v
be determined without error from Figure 4. Also, because H is calculated from h and geometry, the
1 1
uncertainty in H is already accounted for.
∂Q ∂Q ∂Q
ΔΔQ = C + Δb+ Δh (10)
d
∂C ∂b ∂h
d
The partial derivatives are the sensitivity coefficients of A.7 that relate to the discharge formula. ΔQ is
the resultant dispersion of Q. Evaluating the partial differentials and using Formula (3), the relationship
can be written as shown in Formula (11):
ΔC
ΔQ Δb Δh
d
=+  +15, (11)
Q C b h
d
Thus, the relative sensitivity coefficients are given by Formulae (12) to (14):
∂Q
=1 (12)
∂C
d
∂Q
=1 (13)
∂b
∂Q
=15, (14)
∂h
ΔC
ΔΔQ b Δh
d
The values ,, and are referred to as dimensionless standard uncertainties and are
Q b C h
d
given the notation u*(Q), u*(C ), u*(b) and u*(h ). The uncertainties of b, C and h are independent of
d 1 d 1
each other and the covariance is zero, so, probability requires summation in quadrature rather than a
simple summation, as shown in Formula (15).
** **
 
uQ()≅ uC + ub() + 15, uh() (15)
()
d  1 
10.3 Uncertainty of discharge coefficient u(C ) for the triangular profile weir
d
The discharge coefficient C has been determined from a series of hydraulics tests using a high-
d
resolution calibration facility.
For well-constructed triangular profile weirs which are installed in a channel in which the approach
conditions comply with those given in 6.3.3, the relative standard uncertainty of the coefficient of
discharge C is given in Formula (16).
d
*
uC =−54C ,%5 (16)
() ()
dv
10.4 Uncertainty budget
In repor
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