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UDC 532.57 Ref. No.: IS0 / R 541 - 1967 [E)
IS0
FOR STAND AR D I2 ATION
I NT ERN AT I ON AL ORGAN I ZAT I O N
IS0 RECOMMENDATION
R 541
MEASUREMENT OF FLUID FLOW
BY MEANS OF ORIFICE PLATES AND NOZZLES
1st EDITION
January 1967
COPYRIGHT RESERVED
The copyright of IS0 Recommendations and IS0 Standards
belongs to IS0 Member Bodies. Reproduction of these
documents, in any country, may be authorized therefore only
by the national standards organization of that country, being
a member of ISO.
For each individual country the only valid standard is the national standard of that country.
Printed in Switzerland
Also issued in French and Russian. Copies to be obtained through the national standards organizations.
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BRIEF HISTORY
The IS0 Recommendation R 541. ibfeasurement of Fluid Flow b,v Means of Orifice
Plotes ond Nozl~~s, was drawn up by Technical Committee lSO/TC 30, Measurement of
Fluid Fio~s in Closed Conduits. the Secretariat of which is held by the Association Française
de Normalisation (AFNOR).
Work on this question by the Technical Committee began in 1948, laking into account
the studies which had been made by the foriner Tnternational Federation of the National
Standardizing Associations (ISA), and led in 1962 to the adoption of a Draft IS0
Recommendation.
In February 1963, this Draft IS0 Recommendation (No. 532) was circulated to all
the IS0 Member Bodies for enquiry. It was approved, subject to a few modifications of
an editorial nature, by the following Member Bodies :
Australia Hungary Sweden
Austria India Switzerland
Belgium Iran United Kingdom
Chile Italy U.S.A.
Czechoslovakia Japan U.S.S.R.
France Netherlands
Germany Portugal
No Member Body opposed the approval of the Draft.
The Draft IS0 Recommendation was then submitted by correspondence to the IS0
Council, which decided, in January 1967, to accept it as an IS0 RECOMMENDATJON.
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IS0 / R 541 . 1967 (E)
CONTENTS
Page
1 . General . 5
1.1 Principle of the method of measurement . 5
1.2 Standard primary elements . 5
. .
2 General requirements for validity of the measurements 5
............................
2.1 Primary element 5
2.2 Type of fluid . 6
2.3 Installation . 6
2.4 Straight lengths . 7
. .
3 Symbols and definitions 9
.
3.1 Symbols . 9
3.2 Pressure measurement: Definitions . 10
...................... 10
3.3 Primary elements: Definitions
3.4 Flow . 10
4 . Computation . Formulae . 12
4.1 Basicformula . 12
4.2 Method of determination of a standard primary element . 12
4.3 Computation of rate of flow . 12
5 . Errors . 12
of the tolerance . 12
5.1 Definition
5.2 Definition of the standard deviation . 13
5.3 Practical computation of the standard deviation . 13
5.4 General method . 15
5.5 Errors due to installation conditions . 15
.
6 . Orifice plates . 15
6.1 Description . 15
6.2 Pressure taps . 19
6.3 Installation of orifice plate . 22
6.4 Coefficients and standard deviations of orifice plates with corner taps . 23
6.5 Coefficients and standard deviations of orifice plates with vena contracta taps . . 27
6.6 Coefficients and standard deviations of orifice plates with flange taps . 30
6.7 Pressure loss AW . 32
7 . Nozzles . 33
7.1 ISA 1932 nozzle . 33
7.2 Long-radius nozzles . 38
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IS0 / R 541 - 1967 (E)
I SO Recommendation R 541 January 1967
MEASUREMENT OF FLUID FLOW
BY MEANS OF ORIFICE PLATES AND NOZZLES
1. GENERAL
1.1 Principle of the method of measurement
A device such as an orifice plate or a nozzle is placed in a pipe-line through which a fluid is
flowing.
A static pressure difference then exists between the upstream side and the downstream side
of the device and whenever the device is geometrically similar to one on which direct calibra-
tion has been made, the conditions of use being the same, the rate of flow can be determined
from the measured value of this pressure difference and from a knowledge of the circum-
stances under which the device is being used.
This IS0 Recommendation describes the shape and method of use of ceriain of these devices,
on which direct calibration experiments have been made, sufficient in number and quality
to enable coherent systems of application to be based on their results.
The devices introduced in the pipe are called " primary elements ", which term includes the
pressure taps; all other instruments or devices required for measuring are known as " second-
ary devices ". This IS0 Recommendation covers the primary elements; secondary devices
will be mentioned only occasionally.
1.2 Standard primary elements
The standard primary elements are the following:
1.2.1 Ori$ce plate, a sharp square-edged orifice in a thin plate, with which are used various
arrangements of pressure tappings, known as
- Corner taps,
- Vena contracta taps,
- Flange taps.
1.2.2 Nozzles, which differ in shape and/or in position of the pressure taps and are known
as either
- ISA 1932 nozzle,
- Long-radius nozzle.
2. GENERAL REQUIREMENTS FOR VALIplITY OF THE MEASUREMENTS
It is necessary to ensure that all the following requirements, some of which are explained in detail
in the following sections, are completely fulfilled during the period of measurement.
2.1 Primary element
2.1.1 The primary element should be manufactured, installed and used in accordance with
this IS0 Recommendation.
2.1.2 The condition of the primary element should be checked after each measurement or
each series of measurements.
2.1.3 The primary element should be manufactured from material the coefficient of thermal
expansion of which is known.
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IS0 / R 541 - 1967 (E)
' , ' 2.2 Type of fluid
2,2.1 The fluid may be either compressible (gas) or considered as incompressible (liquid).
-. . -.
2.2.2 The fluid should be physically and thermally homogeneous and of single (gas or liquid)
phase.
Colloidal solutions with a high degree of dispersion (such as milk), and those only, are
considered to behave as a single phase fluid.
2.3 Installation
2.3.1 The measuring process applies only to fluids flowing through a pipe-line.
2.3.2 The primary element is fitted between two sections of straight cylindrical pipe of constant
cross-sectional area, in which there is no obstruction or branch connection (whether or
not there is flow into or out of such connections during measurement) other than those
specified in this IS0 Recommendation.
The pipe is considered straight when it appears so by mere visual inspection.
The required minimuin straight lengths of pipe, which conform to the description above,
vary according to the nature of the fittings and are indicated in Table 1, on page 7.
The pipe bore is truly circular over the entire minimum lengths of straight pipe required.
The cross-section is taken to be circular if it appears so by mere visual inspection.
The circularity of the outside of the pipe may be taken as a guide, except in the immediate
vicinity of the primary element.
Over an upstream length of at least 2 D measured from the upstream face of the primary
element, the pipe should be cylindrical. The value of the diameter D of the pipe should
be taken as the mean of the measurements of several diameters situated in meridian
planes at approximately even angles to each other and in several planes normal to the
pipe centre line within the specified length of 2 D. Four diameters at least should be
measured.
The pipe is said to be cylindrical when no diameter in any plane differs by more than
0.3 per cent from the value of D obtained as a mean of all measurements.
Attention is called to the fact that it is possible to check circularity of a pipe bore,
within the accuracy required, without measuring the mean diameter oî the pipe bore
itself.
The mean diameter of the downstream straight length, considered along a length of at
least 2 D from the upstream face of the primary element, should not differ from the
mean diameter of the upstream straight length by more than it 2 per cent, this being
judged by the check of a single diameter of the downstream straight length.
2.3.3 The inside diameter of the pipe should be equal to or more than 2 in (50 mm) and equal
to or less than the maximum diameters specified for each device.
2.3.4 The inside surface of the measuring pipe should be clean, free from pitting and deposit
and not encrusted. However, it may be either " smooth " or " rough ".
2.3.5 The pipe should run full at the measuring section.
2.3.6 The rate of flow should be constant or, in practice, vary only slightly and slowly with
time. This IS0 Recommendation does not provide for the measurement of pulsating flow.
2.3.7 The flow of fluid through the primary element should not cause any change of phase.
To determine whether there is a change of phase, the computation of flow should be
carried out on the assumption that the expansion is isentropic if the fluid is a gas, or
isothermal if the fluid is a liquid.
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IS0 / R 541 - 1067 (E)
2.3.8 If the fluid is a gas, the ratio of the downstream to the upstream absolute pressures
should be greater than 0.75.
2.4 Straight lengths
2.4.1 The minimum straight lengths to be installed upstteam and downstream of any primary
element, according to clause 2.3.2, are the same regardless of the actual type of the
primary element, as described in clauses 1.2.1 and 1.2.2.
The minimum upstream and downstream straight lengths required for installation
between various fittings and the primary element are given in Table 1 below.
-
On
downstream
On upstream (inlet) side of the primary element
(outlet)
side
Reducer
(2 D to D
B Two or more
Two or more )ver a length
Globe All fittings
90" bends Gate
90" bends of 3 D).
in valve valve included
in the same Expander
--
differeri t fully open fully open n this Table
plane (0.5 D to D
planes
>ver a length
of 1.5 D)
-
:0.20 34 (17) 16 (8)
14 (7) 18 (9) 4 (2)
0.25 34 (17) 16 (8)
14 (7) 18 (9) 4 (2)
5 (2.5)
0.30 34 (17) 16 (8) 18 (9)
16 (8)
0.35 5 (2.5)
36 (18) 16 (8) 18 (9)
16 (8)
0.40 (9) 36 (18) 16 (8) 20 (10)
18 6 (3)
0.45 18 (9) 38 (19) 18 (9) 20 (10)
6 (3) :
0.50 40 (20)
20 (10) 20 (10) 22 (11)
6 (3)
0.55 44 (22) 24 (12)
22 (il) 20 (10) 6 (3)
7 (3.5)
0.60 26 (13) 48 (24) 22 (il) 26 (13)
0.65 54 (27) 7 (3.5)
32 (16) 24 (12) 28 (14)
0.70 7 (3.5)
36 (18) 62 (31) 26 (13) 32 (16)
0.75 42 (21) 36 (18)
70 (35) 28 (14) 8 (4)
U
0.80 50 (25) 30 (15) 44 (22)
80 (40) 8 (4)
-
Minimum upstream (iniet)
Fittings
straight length required
Abrupt symmetrical reduction having a diameter
30 (15)
ratio 2 0.5
I--
Thermometer pocket of diameter < 0.03 D
5 (3)
Thermometer pocket of diameter between 0.03 D and
20 (10)
0.13 D
NoTE.-Table 1 is valid for all primary elements defined in this IS0 Recommendation.
The unbracketed values are '' zero additional tolerance. " values (see clause 2.4.3).
The bracketed values are "& 0.5 per cent additional tolerance " values (see clause 2.4.4).
AU straight lengths are expressed as multiples of the diameter D. They should be measured from the upstream
face. of the primary element.
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IS0 / R 541 - 1967 (E)
2.4.2
The straight lengths given in Table 1 are minimum values, and it is always recommended
to have straight lengths longer than those indicated. For research work especially, it
is recommended to double at least the upstream values given in Table 1 for “ zero
additional tolerance ”.*
2.4.3 When the straight lengths comply with the requirements of Table I and when they are
longer than or equal to the values given for “ zero additional tolerance ”,* there is no
need to add any additional deviation to the flow measurement error to take account
of the effect of such installation conditions.
2.4.4 When the upstream or downstream straight lengths are shorter than the “ zero additional
tolerance ” values * and equal to or greater than the “& 0.5 per cent additional
tolerance ” values,** as given in Table 1, an additional deviation of f 0.5 per cent
should be added to the error in flow measurement, in the following manner:
First computation Compute the tolerance for the flow measurement as if there
was no additional tolerance for installation conditions. This
computation should be made as shown in section 5 dealing
with errors. Assume the result to be rt 2n, per cent.
Second computation Then add to this value of the tolerance an additional devia-
tion of & 0.5 per cent. This should be made arithmetically,
in such a way that the final result will be f (2 nq + 0.5)
per cent.
If the straight lengths are shorter than the “ & 0.5 per cent additional tolerance” values **
given in Table 1, this IS0 Recommendation gives no information by which to predict
the value of any further tolerance to be taken into account; this is also the case when the
upstream and downstream straight lengths are simultaneously shorter than the “ zero
additional tolerance ” values.*
2.4.5 The valves mentioned in Table 1 should be fully open. It is recommended that control
be effected by valves located downstream of the primary element. Isolating valves
located upstream should be preferably of the “ gate ” type and should be fully open.
2.4.6 After a single change of direction (bend or tee), it is recommended that the tappings
(if single tappings) be in a plane at right angles to the plane containing the change of
direction (plane of the bend or tee).
2.4.1 The values given in Table 1 were obtained experimentally with a very long straight length
upstream of the particular fitting in question. Usually, such conditions are not available
and the following remarks may be used as a guide in usual installation practice.
(a) If the primary element is installed in a pipe leading to an upstream open space or
large vessel, either directly or through any fitting given in Table 1, the total length
of pipe between the open space and the primary element should never be less
than 30 D.
* Unbracketed values in Table 1.
** Bracketed values in Table 1.
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IS0 1 R 541 - 1987 (E)
(b) If several fittings other than 90" bends are placed in series upstream from the
primary element, the following rule should be applied: between the closest fitting
(1) to the primary element and the primary element itself, there should be a minimum
straight length such as is indicated for the fitting (1) in question and the actual
value /3 in Table 1. But, in addition, between this fitting (1) and the preceding one
(2), there should be a straight length equal to one half of the value given in the
Table 1 for fitting (2) applicable to a primary element of diameter ratio /3 = 0.7,
whatever the actual value of /3 may be. This requirement does not apply when the
fitting (2) is an abrupt symmetrical reduction, which case is covered by paragraph
(a) above.
2.4.8 The primary element should be calibrated under actual installation conditions in cases
which are not covered by the above statements.
3. SYMBOLS AND DEFINITIONS
The symbols used in this 1SO Recommendation are given in Table 2, under clause 3.1.
The definitions, in the following clauses, are given only for terms used in some special sense or
for terms the meaning of which it seems useful to emphasize.
3.1 Symbols
TABLE 2. - Symbols
~~
Represented quantity Dimensions *
Symbol
U Flow coefficient Pure number
d
Diameter ratio, /3 = - Pure number
P
D
U
C Coefficient of discharge, C = - Pure number
E I
E Pure number
Velocity of approach factor, E = (1 - fi4))-'
F
Expansibility (expansion) factor Pure number
K Isentropic exponent ** Pure number
m Area ratio, m = Bz Pure number
Reynolds number of upstream pipe referred to D Pure number
Re,
AP
X Differential pressure ratio, x = - Pure number
Pi
X
Pure number
X Acoustic ratio, X = -
K
Diameter of ordice or throat of primary element at
d
L
operating conditions
L
D Upstream pipe diameter at operating conditions
L
k Absolute roughness (see clause 6.4.1.2)
Differential pressure ML-IY2
AP
ML-lT-l
Dynamic viscosity of the fluid
'1
,U L2T-l
Kinematic viscosity of the fluid
ML-1T-2
Absolute static pressure of the fluid
P
Mass rate of flow MT-1
9m
9ü Volume rate of flow L3T-l
Mass density of the fluid ML-3
P
O
t Temperature of the fluid
-
Mean axial velocity of the fluid in the pipe LT-i
V
M = mass. L = length. T = time.
** For ideal gases, the ratio of the specific heat capacities and the isentropic exponent have the same values.
Subscript 1 applies to conditions (of the fluid, etc.) in the plane of the upstream pressure tap.
Subscript 2 applies to conditions (of the fluid, etc.) in the plane of the downstream pressure tap.
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IS0 / R 541 - 1967 (E)
3.2 Pressure measurement: definitions
3.2.1 Pipe-wallpressure tap. Hole drilled in the wall of a pipe, the inside edge of which is flush
with the inside surface of the pipe.
The hole is usually circular but in certain cases may be an annular slit.
3.2.2 Static pressure of a fluid flowing through a straight pipe-line. Pressure which can be
measured by connecting a pressure gauge to a pipe-wall pressure tap. Only the value of
the absolute static pressure is used in this IS0 Recommendation.
3.2.3 DifSerential pressure. Difference between the static pressure measured by pipe-wall taps,
one of which is on the upstream side and the other on the downstream side of a primary
element inserted in a straight pipe through which flow occurs, when there is no variation
in gravitational energy between the upstream and downstream taps.
The term “ differential pressure ” is used only if the pressure taps are in the positions
specified by the IS0 Recommendation for each standard primary element.
3.2.4 Diferential pressure ratio. The differential pressure divided by the absolute static
pressure existing at the level of the centre of the cross-section of the pipe in the plane
containing the centre-line of the upstream pressure tapping.
3.2.5 Pressure loss. Difference in static pressure between the pressure measured on the upstream
side of the primary element. at a point free from the influence of approach impact
pressure, and that measured on the downstream side of the element, at a point where
static pressure recovery by expansion of the jet is completed.
3.3 Primary elements: Definitions
3.3.1 Orifice or throat. Opening of minimum cross-sectional area in a primary element.
Standard primary element orifices are always circular and coaxial with the pipe-line.
3.3.2 Orijïceplate. Thin plate in which a circular aperture has been machined.
1
Standard orifice plates are described as “ thin plate ” and “ with sharp square edge ”,
because the thickness of the plate is small compared with the diameter of the measuring
section and because the upstream edge of the orifice is sharp and square.
3.3.3 Nozzle. Device which consists of a convergent inlet to a cylindrical portion generally
called the ‘‘ throat ”.
3.3.4 Diameter ratio of a primary element in a given pipe. The diameter of the orifice of the
primary element divided by the diameter of the measuring pipe upstream of the primary
element.
3.4 Flow
3.4.1 Rate offlow of fluid passing through a primary element. Quantity of fluid passing through
this orifice in unit time.
This quantity can be characterized by its mass or its volume and the rate of flow can be
expressed in units of mass or volume per unit time.
In all cases, it is necessary to state explicitly whether the type of flow rate referred to
is expressed by mass or by volume per unit time.
3.4.2 Pipe Reynolcki number. The pipe Reynolds number used in this IS0 Recommendation
is referred to the upstream condition of the fluid and to the upstream diameter of the
pipe, i.e.
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IS0 / R 541 - 1987 (E)
3.4.3 Isentropic exponent. The isentropic exponent K appears in the different formulae for
expansibility (expansion) factor t' either directly or in the ratio X. There are many
gases and vapours for which no values for K have been published so far. For gases,
however, the behaviour of which fairly equals that of ideal gases, the isentropic exponent
may be replaced by the ratio of the specific heat capacities. The isentropic exponent,
as well as the ratio of the specific heat capacities, vary in general whenever the gas
temperature and/or pressure vary.
3.4.4 Acoustic ratio. The differential pressure ratio divided by the isentropic exponent (com-
pressible fluid).
3.4.5 Velocity of approach factor. It is equal to:
I
1
-- -- -
E-(l -p4) 2, D2/VD4-d4 = (1 --mz) 2
3.4.6 Flow coeficient. Calibration of standard primary elements by means of incompressible
fluids (liquids) shows that the quantity U defined by the following relation is dependent
only on the Reynolds number for a given primary element in a given installation.
The quantity a, a pure number, is called the " flow coefficient ",
The numerical value of K is the same for different installations, whenever such installa-
tions are geometrically similar and the flows are characterized by the identical Reynolds
number.
U
The ratio C == - is called the " coefficient of discharge ".
E
The numerical values of U and of C given in this IS0 Recommendation were determined
experimentally.
3.4.7 Expansibility (expansion) factor. Calibration of a given primary element by means of
a compressible fluid (gas), shows that the ratio
4m
.-
2 d2 2/21ppi
4
is dependent both on the value of the Reynolds number and on those of the relative
differential pressure and the isentropic exponent of the gas.
The method adopted for representing these variations consists in multiplying the flow
coefficient x of the considered primary element, as determined by direct calibration
effected by means of liquids for the same value of Reynolds number, by the " expansi-
bility ", a so-called (expansion) factor defined by the relation
t differs from and is less than unity, when the fluid is compressible.
This method is possible because experiments show that practically t is independent of
Reynolds number, and, for a given diameter ratio of a given primary element, depends
on the differential pressure ratio and the isentropic exponent.
The numerical values of F given in this IS0 Recommendation have been determined
experimentally.
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IS0 / R 541 - 1967 (E)
4. COMPUTATION - FORMULAE
4.1 Basic formula
4.1.1 For calculating the mass rate of flow, qm, the Bow coefficient a and expansibility (expan-
sion) factor E, as specified in this IS0 Recommendation, should be used in the following
formula :
I- is equal to unity when the fluid is incompressible.
4.1.2 Similarly, the value of the volume rate of flow, at the upstream conditions of the fluid,
may be calculated by the following relation:
q,, = qm I pi
4.1.3 The formulae of clauses 4.1.1 and 4.1.2 apply for any consistent system of units.
4.2 Method of determination of a standard primary element
The principle of the method consists essentially in selecting a priori
- the type of standard primary element to be used,
- a rate of flow and the corresponding value of the differential pressure.
The related values of qm and Ap should be inserted in the basic formula rewritten in
the form below:
a p = 4qm
t ;c 0'
112 Ap pi
and the diameter ratio of the selected primary element is determined by successive
approximations.
4.3 Computation of rate of flow
Computation of the rate of flow is effected by replacing the different terms on the right-
hand side of the basic formula
d2 \I2 AP Pi
qm = at
4
by their numerical values, obtained in the course of the measurement, and by calculating
their product. The computation itself involves no difficulty other than of an arithmetical
nature and merely calls for the following comments :
(1) a may be dependent on Reo, which is itself dependent on qm. Therefore, the final
value of qm may be obtained by successive approximations, after first calculating
qm from a value of ReD (or of CL) chosen a priori. For instance, a = a. can be taken
as a first value.
(2) Ap represents the differential pressure, as defined under clause 3.2.3.
5. ERRORS
5.1 Definition of the tolerance
5.1.1 For the purpose of this IS0 Recommendation, tolerance is defined as a value equal
to twice the standard deviation; this deviation should be calculated and given under
this name whenever a measurement is claimed to be in conformity with this IS0 Recom-
mendation.
5.1.2 When the partial deviations, the combination of which gives the standard deviation, are
independent of one another, are small and numerous, and have a distribution con-
forming to the so-called Laplace-Gauss normal law, there is a 95 per cent probability
that the absolute value of the true error does not exceed twice the standard deviation.
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IS0 1 R 541 - 1967 (E)
5.1.3 When the standard deviation oq of the flow measurement q has been calculated,
the absolute tolerance ea is therefore defined as
e, = 2 uq
The relative tolerance e, is
The result of the flow measurement q should be then given in any one of the following
forms :
rate of flow = q $1 e,
or rate of flow = q (1 f e,)
or rate of flow = q, within (100 er) per cent
Definition of the standard deviation
5.2.1 If the different independent quantities which are used to compute the flow rate are called
XI, X,, . . . , Xi, then the flow rate can be expressed as a certain function of these quantities :
q = function (XI, X,, . . . . . ., Xi)
and if the standard deviations of the quantities X,, X,, . . ., Xi are designated ux ,
1
0 , . . . , fi , the standard deviation of the rate of flow q is defined as
XP xi
3q
where the partial derivatives - depend on the manner in which q is a function of
the quantities Xi. 34
5.2.2 If a certain quantity Xi has been measured several times, each measurement being
independent of the others.
the standard deviation of an individual measurement of X, is
where Xi is the most probable value of the quantity;
Xj are the values obtained of each individual measurement;
n is the total number of measurements.
5.2.3 If repeated measurements of a quantity Xi are not available or are so few that direct
computation of the standard deviation oxi is likely to be unreliable, it is assumed that
one is able to, at least, estimate the maximum deviation of the measurements, above
and below the adopted value of Xi.
It is then permissible to take the standard deviation as % of this estimated total devia-
tion (that is to say as one half of the mean maximum deviation above or below the
adopted value of Xi).
5.2.4 The ruling in clause 5.2.2 is valid only if the deviations such as are given by clause
5.2.2 or 5.2.3 are independent, or is only applicable to those deviations which can be
considered as such.
5.3 Practical computation of the standard deviation
5.3.1 The basic formula of computation of the mass rate of flow qm is
-
qm= u~Ld~v2 Appi
4
As a matter of fact. the various quantities which appear on the right-hand side of this
formula are not independent, so that it is not correct to compute the standard deviation
of qm directly from the standard deviations of these quantities.
For example U is a function of d, D, k, IIi, v1
I: is a function of d, D, Ap, pi, U
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IS0 / R 541 - 1967 (E)
5.3.1.1 However. it is sufficient, for most practical purposes, to assume that the standard
deviations of t, Ap and pi are independent of each other and are also independent of
the standard deviations of CI and d.
5.3.1.2 A practical working formula for ou, may then be derived, which takes account of
the interdependence of a on d and on D, that enters into the calculations as a con-
sequence of the dependence of ci on p. It should be noted that a may also be depen-
D
dent on the pipe diameter D or on --, as well as on the Reynolds number Re,.
k
However, the deviations of a due to these influences are negligible in most actual
cases and will be neglected.
Similarly, the deviations of : which are due to uncertainties in the value of p, the
pressure ratio and the isentropic exponent will also be neglected.
5.3. i .3
The standard deviations which should be included in a practical working formula
for oqm are therefore those of the quantities a, t, d, D, Ay and pi.
5.3.2 The pructicnl working.formulci for the standard deviation of the mass rate of flow U,,,,,
is as follows:
U% '5:
5.3.2.1
In the formula abobe, the values of ~ and of should be taken from clauses
W
...