BS 1042-2.2-1983 ISO 7145-1982.pdf

BRITISH STANDARD BS 1042-2.2: 1983 ISO 7145:1982 Measurement of fluid flow in closed conduits Part 2: Velocity area methods Section 2.2 Method of measurement of velocity at one point of a conduit of circular cross section ISO title: Determination of flowrate of fluids in closed conduits of circular cross-section Method of velocity measurement at one point of the cross-section UDC 532.542:532.574:621.643.2-462.311 BS 1042-2.2:1983 This British Standard, having been prepared under the direction of the Industrial-process Measurement and Control Standards Committee, was published under the authority of the Board of BSI and comes into effect on 31 August 1983 © BSI 07-1999 The following BSI references relate to the work on this standard: Committee reference PCL/2 Draft for comment 81/25553 DC ISBN 0 580 13383 4 Committees responsible for this British Standard The preparation of this British Standard was entrusted by the Industrial-process Measurement and Control Standards Committee (PCL/-) to Technical Committee PCL/2 upon which the following bodies were represented: British Compressed Air Society British Gas Corporation British Industrial Measuring and Control Apparatus Manufacturers Association (BEAMA) Department of Energy (Gas Standards) Department of Industry (National Engineering Laboratory) Department of Trade (Consumer Safety Unit, CS Division) Department of Trade (National Weights and Measures Laboratory) Electricity Supply Industry in England and Wales Energy Industries Council Institute of Measurement and Control Institute of Petroleum Institute of Trading Standards Administration Institution of Gas Engineers National Water Council Society of Chemical Industry United Kingdom Atomic Energy Authority Coopted member The following bodies were also represented in the drafting of the standard, through subcommittees and panels: Fan Manufacturers Association Hevac Association National Coal Board Scientific Instrument Manufacturers Association (BEAMA) Amendments issued since publication Amd. No.Date of issueComments BS 1042-2.2:1983 © BSI 07-1999i Contents Page Committees responsible Inside front cover National foreword ii 1Scope and field of application1 2Symbols and definitions1 3Principle3 4Procedure4 5Uncertainties of measurement6 Annex A Determination of the transverse velocity gradient at the point of mean axial velocity11 Annex B Example of calculation of the uncertainty of a flow measurement when the primary device is placed at the point of mean axial velocity11 Annex C Example of calculation of the uncertainty of a flow measurement when the primary device is placed on the axis of the conduit12 Publications referred to Inside back cover BS 1042-2.2:1983 ii © BSI 07-1999 National foreword This British Standard has been prepared under the direction of the Industrial-process Measurement and Control Standards Committee and is identical with ISO 7145:1982 “Determination of flowrate of fluids in closed conduits of circular cross-section Method of velocity measurement at one point of the cross-section”, published by the International Organization for Standardization (ISO). Terminology and conventions. The text of the international standard has been approved as suitable for publication as a British Standard without deviation. Some terminology and certain conventions are not identical with those used in British Standards; attention is drawn especially to the following. The comma has been used as a decimal marker. In British Standards it is current practice to use a full point on the baseline as the decimal marker. Wherever the words “International Standard” appear, referring to this standard, they should be read as “British Standard”. The Technical Committee has reviewed the provisions of ISO 3354 and ISO 3966, to which reference is made in the text and for which there are no corresponding British Standards, and has decided that they are acceptable for use in conjunction with this standard. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Cross-references International standardCorresponding British Standard ISO 4006:1977BS 5875:1980 Glossary of terms and symbols for measurement of fluid flow in closed conduits (Identical) ISO 5168:1978BS 5844:1980 Methods of measurement of fluid flow: estimation of uncertainty of a flowrate measurement (Identical) Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, pages 1 to 14, an inside back cover and a back cover. This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on the inside front cover. BS 1042-2.2:1983 © BSI 07-19991 1 Scope and field of application 1.1 Scope This International Standard specifies a method for the determination of the volume rate of flow of a single phase fluid of a substantially constant density (Mach number u 0,25) under steady fully developed flow conditions in a closed conduit of circular cross-section running full by measurement of the flow velocity in a single point. The method provides for the possibility of placing the primary velocity measuring device either at the point where it is assumed the mean axial velocity prevails, i.e. at a distance of 0,242 R from the wall of the conduit (R being the radius of the conduit), or on the axis of the conduit. If there are doubts about the symmetry of the flow it is advisable to use at least two measuring points located symmetrically on one circumference at the distance from the wall specified above. 1.2 Field of application The method specified in this International Standard does not apply unless the following conditions have been fulfilled: a) The conduit shall have a straight length sufficiently long so that, in the measuring section, a distribution of velocities corresponding to fully developed turbulent flow can be observed (see 2.3.5). Hydraulic resistance coefficient 2 of the conduit should not exceed 0,06. b) The flow must be turbulent and the Reynolds number, ReD9 should exceed or be equal to the following values: When the velocity is measured on the conduit axis, the flow should be in fully rough turbulent regime (see 2.3.6). The Reynolds number, ReD, should then exceed or be equal to: c) The experimental data on which this International Standard is based principally relate to conduits of diameter equal to or greater than 300 mm, but there is every reason to believe that the method can be applied to conduits of smaller diameter. d) In any point of the measuring cross-section, the angle between the direction of local velocity and the axis should not exceed 5°. This condition can be verified either with the probe used for the measurements, if the design permits this, or with a different type of probe. It can be assumed that if the condition required is verified for a given flow q, then this condition is also met within the range q/3 to 3q. 1.3 Accuracy of the method As a guide, it can be considered that determination of flow from velocity measurement at a single point, carried out in accordance with the requirements of this International Standard, will lead to an uncertainty (at a confidence level of 95 %) not exceeding ± 3 %. However, the uncertainty on the flow shall be calculated for each individual application of this International Standard depending on the type of primary device, on the method of use and if necessary, on the method of calibration as well as on the measuring conditions. 2 Symbols and definitions 2.1 References The vocabulary and symbols used in this International Standard are defined in the following International Standards: ISO 3354, Measurement of clean water flow in closed conduits Velocity-area method using current-meters. ISO 3966, Measurement of fluid flow in closed conduits Velocity-area method using pitot-static tubes. ISO 4006, Measurement of flow of fluids in closed conduits Vocabulary and symbols. 2W 0,030,0250,020,01 ReD 1043 × 104105106 20,060,050,040,030,0250,02 0,01 ReD 3 × 1045 × 1041053 × 1055 × 1051065 × 107 BS 1042-2.2:1983 2 © BSI 07-1999 ISO 5168, Measurement of fluid flow Estimation of uncertainty of a flow-rate measurement. The definitions appearing in 2.3 are given only for terms used in a special sense for which it would seem useful to repeat the definition of meaning. 2.2 Symbols SymbolQuantityDimensionsaSI units AArea of the cross-section of the conduit L2m2 aHeight of any high spot or protrusion on the external wall of the conduit Lm DDiameter of the conduitLm dDiameter of the active part of the primary deviceLm eUncertainty, as an absolute value bb EUncertainty, as a relative value kUniform equivalent roughnessLm PExternal perimeter of the conduitLm qVVolume flow rate L3T1m3/s RRadius of the conduitLm ReDReynolds number, sStandard deviation bb UMean axial velocity LT1 m/s u*Friction velocity, LT1 m/s vLocal fluid velocity LT1 m/s v0Local velocity at centre of conduit LT1 m/s v*Local non dimensional velocity, yDistance from one measurement point to the wallLm y*Non dimensional distance from one measurement point to the wall, ÆUniversal coefficient of head loss as defined by the formula where %p is the pressure drop on the tube length L and A is the fluid density vKinematic viscosity of the fluid L2T1m2/s a L = length, T = time b The dimensions and units are those of the quantity to which the symbol refers, and which will be indicated by an index. ReD UD v - -= u*U Æ 8 - -= v* v U -= y* y R - -= pÆ L D - - 1 2 - -×AU2= BS 1042-2.2:1983 © BSI 07-19993 2.3 Definitions 2.3.1 primary velocity measuring device any device that changes a local flow velocity into a physical quantity suitable for measurement (for example, differential pressure, frequency of an electric signal, etc.) NOTEThroughout the rest of this document, the expression “primary device” is used instead of “primary velocity measurement device”. 2.3.2 measuring point any point where the local velocity of the flow is measured 2.3.3 mean axial velocity ratio of the volumetric flowrate and the area of the measuring section 2.3.4 point of mean axial velocity in a cross-section of the conduit this is a point where the local velocity of the flow is equal to the mean axial velocity 2.3.5 fully developed flow the flow in which the distribution of velocities does not change from one cross-section to another. It is generally obtained at the outlet of a straight length of conduit of sufficient length (see 4.1) 2.3.6 fully rough turbulent flow in a conduit of given relative roughness, this occurs when the hydraulic resistance coefficient is independant of the Reynolds number and may be assumed to be present when or 3 Principle 3.1 General The principle of the determination of flow by measurement of the local velocity at a single point is based on the existence of laws applicable to all conduits, provided that all parameters remain within the limits indicated in 1.2, which relate the value of the local velocity at a given point in the cross-section to the value of the mean axial velocity in this section. Two variants on this method, which differ in the position of the measuring point, are described in 3.2 and 3.3. It should however be emphasized that these two methods are not equivalent as the second one requires previous calibrations. 3.2 Measurement at the point of mean axial velocity From a large number of experimental results it has been possible to establish that under turbulent conditions and within the limits indicated in 1.2 the position of the circle centred on the pipe axis at which the local velocity is equal to the mean axial velocity remains fixed as the flowrate changes, and is the same for any pipe. This circle is at a distance from the wall y1 = (0,242 ± 0,013) R, R being the radius of the cross-section. U qV A - -= ReD 50010 1 2 2 - - × ReD1 850 D K - - BS 1042-2.2:1983 4 © BSI 07-1999 The principle of the method therefore consists of: a) Selecting a measurement cross-section (see 4.1). b) Measuring the dimensions of this cross-section in order to obtain its area A (see 4.2). c) Selecting, at the above-mentioned distance y1 from the wall, the point of measurement of velocity (see 4.4.1). d) Measuring the local velocity v1 of the flow, according to the special conditions required by the primary device used (see 4.3). e) Calculating the volume rate of flow equal to the product of the cross-sectional area and the measured velocity (v1) taken as being the mean axial velocity (U): qV = A × U = A × v1 f) Determining the uncertainty associated with this flow measurement (see clause 5). 3.3 Measurement on the axis of the conduit If the above method cannot be applied, the local velocity of the flow can be measured at the centre of the measurement cross-section on the axis of the conduit. However, it is then necessary to carry out calibrations by previous determination of the ratio U/v0 of the mean axial velocity at the velocity at the centre. This ratio remains approximately constant for a given pipe in fully rough turbulent conditions. The principle of the method therefore consists of: a) Selecting a measurement cross-section (see 4.1). b) Measuring the dimensions of this cross-section in order to obtain its area A (see 4.2). c) Measuring the local velocity of flow at the centre of the cross-section v0, in accordance with the special conditions required by the primary device used (see 4.3). d) Calculating the mean axial velocity U by multiplying the velocity measured at centre v0 by the previously determined calibration coefficient (see 4.4.2). e) Calculating the volume rate of flow equal to the product of the cross-sectional area and the mean axial velocity: f) Determining the uncertainty associated with this flow measurement (see section 5). 4 Procedure 4.1 Selection of the measurement cross-section The measurement cross-section shall be situated on a straight length of the conduit. In order to have the best chance of a fully developed flow, the length of the straight section upstream from the measurement cross-section shall be as large as possible and in all cases at least equal to the values specified in the table below: Type of disturbance upstream from the measuring cross-section Minimum upstream straight lengtha For a measurement at the point of mean axial velocity For a measurement on the axis of the conduit 90° elbow or a t-bend5025 Several 90° coplanar bends5025 Several 90° non-coplanar bends8050 Total angle con-vergent 18 to 36°3010 Total angle divergent 14 to 28°5525 Fully opened butterfly valve4525 Fully opened plug valve3015 a Expressed in multiples of the diameter of the conduit. qVAU×Av0 U v0 - -××= BS 1042-2.2:1983 © BSI 07-19995 Downstream from the measurement cross-sectio