# Theory overview of flow measurement using differential pressure devices based on ISO-5167 standard.

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1 Theory overview of flow measurement using differential pressure devices based on ISO-567 standard. rian FL40 flow computer description. Flow Cad software users manual. Technical note, Differential pressure mass flow meter, rev. b,

2 Introduction Basic theory...4. Origin of differential pressure flow measurements ISO-567 standard and its mass flow rate formula The FL40 flow computer rian ISO-567 Flow Cad software Software Installation Start up Fluid selection Primary device Flow conditions set up Calculating results Instrument parameters...5 References...7 Technical note, Differential pressure mass flow meter, rev. b,

3 Introduction Differential pressure flow measurement is old and reliable. With the aid of microprocessor technology now discharge coefficient calculations can be done in real time. Even more, properties of the fluid can be stored on the instrument and measuring temperature and absolute pressure allows to correct fluid parameters such as density and viscosity and then to obtain the mass flow rate. This are called multivariable mass flow meters. By other side years of research and experiments had been done obtaining better characterization of typical differential pressure devices nozzles, orifice plate, etc. The ISO567 standard condenses all this experimental information giving the formulas and procedures for manufacturing a differential pressure flow measurement device of the standard types with a predictable uncertainty. For sample calculations of ISO567 formulas referred on this document you may try our site Technical note, Differential pressure mass flow meter, rev. b, 3

4 .0 Basic theory. This overview intention is only to refresh the knowledge you already have from your technical studies. lso can be a introduction to the problem, but reader must have some knowledge on fluid dynamics.. Origin of differential pressure flow measurements. Bernoulli equation represents energy conservation for a fluid element: Const = g h + υ + P υ P Fluid Density Linear velocity of the fluid element Pressure The first term g h is the potential energy coming from height on the gravitational field. For our development we will suppose constant height of our fluid, so this term is discarded and the equation is: Const = υ + P The term υ is kinetic energy, here the density replaces mass. Pressure P can be understand as a potential energy. Work is stored in compressing the fluid the same way as a compressed string stores energy. We apply this equation to a circular cross section pipe that is reduced in diameter as it goes down stream in horizontal direction Technical note, Differential pressure mass flow meter, rev. b, 4

5 Technical note, Differential pressure mass flow meter, rev. b, 5 P + P = + υ υ 3, υ, P Up stream density, velocity and pressure, υ, P Down stream density, velocity and pressure By other side mass is conserved not created nor destroyed as it flows along the pipe, this is represented by the formulas Q M = = υ υ 4 M Q Mass flow rate along the pipe, units are e.g. Kg/sec, Up and down stream cross sectional area of the pipe Squaring both sides of 4, and solving for υ we have = υ υ 5 From 3, we have υ υ = P P Substituting υ from 5 into this equation P P = = υ υ From this equations, υ can be written as P P = υ This value of is substituted on 4

6 Q M = υ = P P 4a Those who are familiar with orifice plates, will recognize the pressure difference square root dependence of the mass flow. Now since the pipes are circular with diameters D d Up stream diameter Down stream diameter Circular cross areas are = d = D π π Substituting on 4a and ordering terms we obtain finally π Q M = d P P 4b 4 β 4 d with, β = D The equation 4b was obtained only from Bernoulli and mass conservation. Is very similar to the equation on page 6 of ISO 567-:99E document, from now on ref- document. In fact for a uncompressible fluid liquid, = similar. gets even more This equation 4b comes only from a theoric analysis, does not take consider turbulent flow or thermo-dynamical energy conservation for the fluid in order to be used in a practical flow rate measurement. It is useful only to get some insight on the ISO567 equations. Technical note, Differential pressure mass flow meter, rev. b, 6

7 . ISO-567 standard and its mass flow rate formula. The general equation for mass flow rate measurement used by ISO567 standard is: Q M C π 4 = ε 4 d p β You will find it on section 5. of ref-, this formula is obtained in part from additional complex theoric analysis but comes mostly from experimental research done along years and presented in several publications. What is interesting about ISO567 standard is that condenses all the experimental research and gives it in a simple and practical form well not so simple but useful. We will classify the parameters on the formula by 3 different groups, this will help us understanding the formula and also on using rian flow software. Fluid property, This are intrinsic fluid properties, e.g. density or viscosity at given temperature or pressure. Primary device parameter This are the primary device physical properties such as: pipe diameter, bore size, device material temperature expansion coefficient. Flow conditions This are the specific flow conditions, e.g., pressure, temperature, differential pressure. Q M Mass flow rate, in mass/time units p Differential pressure p = p p Difference between the static pressures measured at the wall pressure tappings, one of which is on the upstream side and the other of which is on the downstream side of a primary device or in the throat for a Venturi tube inserted in a straight pipe through which flow occurs, when any difference in height between the up-stream and downstream tappings has been taken into account. Technical note, Differential pressure mass flow meter, rev. b, 7

8 d D β Up stream fluid density. Bore diameter Pipe diameter Diameter ratio This is a geometric parameter of the device, that is calculated using β = d D ε Expansion factor. Up stream evaluated Coefficient used to take into account the compressibility of the fluid. The numerical values of ε for orifice plates given in ISO567 are based on data determined experimentally. For nozzles and Venturi tubes they are based on the thermodynamic general energy equation. For liquids uncompressible fluids, is always ε = For steam and gases compressible fluids ε <. Is calculated with different formulas depending on the device geometry. For example for a orifice plate, ISO567-:99E section gives on the following formula: ε 4 = β p k p Where k is the isentropic exponent, a Fluid property that depends on fluid pressure and temperature. Is related with adiabatic expansion of the fluid in the bore zone. C Discharge coefficient Is a coefficient, defined for an incompressible fluid flow, which relates the actual flow-rate to the theoretical flow-rate through a device. Is related with turbulent flow and the restriction the devices makes to the flow. gain the formula for evaluating it, comes from empirical data, for example for a orifice plate, the formula used by ISO567-:99 section on page. Technical note, Differential pressure mass flow meter, rev. b, 8

9 C = β L ' β β β.5 0 Re 6 D L 4 β β 4 Where, ' L, L are geometrical parameters of the orifice plate as described on same page of the document. Re D υ D µ = is the Reynolds number for up stream flow υ, µ re the Up stream velocity and viscosity of the fluid. The viscosity is fluid property that depend on pressure and mostly on temperature. This formula for discharge coefficient is named the Stolz equation and on 998 ISO567 amendment, ref-, was substituted for the larger Reader-Harris/Gallagher formula not included here because of space lack. s you may see, this formulas are large but, there is no problem since you will use our flow software for evaluating them with just one mouse click. You may notice that here seems to be a problem related to self reference of the formula : You need υ Re C D To calculate Re D C Q M Q M υ using density and area of the pipe This problem is solved by iteration searching for self consistent results and is done automatically by rian Flow Cad software. lso is to be considered that the formulas given by ISO567 have certain validity range, depending on β, Re D values. Take a look for example at ISO567- section gain the rian Flow Cad will help advising if flow conditions are out the norm. Sample calculations of this formulas can be found on our site Technical note, Differential pressure mass flow meter, rev. b, 9

10 .0 The FL40 flow computer. The FL40 is a powerful multivariable flow computer specifically designed for use on primary devices designed under the ISO567 standard. Calculates actual mass flow from the 3 following parameters measured continuously dp P T Differential pressure input e.g. 4-0ma, 0-0V,.. Up stream fluid pressure input e.g. 4-0ma, 0-0V,.. Up stream fluid temperature input Pt00, thermocouples The fluid physical properties are stored on the FL40 so it calculates actual mass flow rate or volumetric flow if you prefer. dditionally haves a 6 digit flow totalizer with alarms and communications functionalities that are described in detail in it s user manual. Here we will concentrate on describing the input configuration for the FL40 witch is done with the help of the rian Flow Cad software. Technical note, Differential pressure mass flow meter, rev. b, 0

11 3.0 rian ISO-567 Flow Cad software. The rian Flow Cad software is used for calculating discharge coefficient and expansion factor as ISO567 describes. The software generates a configuration file that is downloaded to the FL40 with the RPS PC configuration system. So you don t need to introduce manually a large set of configuration parameters. Is strongly recommend to have a copy of the ISO 567 document while you read this manual. 3. Software Installation. You need a PC computer with -windows 95 operating system or better. -svga 800x600 color monitor. Uncompress it in any empty folder of your PC. That is all what you need to do, you are ready for start up. Since the program does not make any change on windows registry, for removing it just delete all the files on the folder. Technical note, Differential pressure mass flow meter, rev. b,

12 3. Start up. Execute application rianiso567flowcad_v.exe. Within the program go to [File / Open] in the upper context menu. Open the example file air.flw as an example On this main form you fill the Flow conditions The other forms in the context menu are the following [Fluid] [Device] [Notes] [Instrument] Fluid properties. Primary device description and parameters. dd here comments about the project. Configuration of the FL40. Technical note, Differential pressure mass flow meter, rev. b,

13 The file menu haves the following options: [File / Open] [File / Save] [File / Save as] [File / Report] [File / Exit] Opens a new project file with extension.fld Saves the project file. Saves with different name. Generates a project report file to be printed later. In this example air.flw will generate air_report.txt and air_report_data.csv Quits Press now the lower left button Calculate and see how calculates the coefficients for the example. Technical note, Differential pressure mass flow meter, rev. b, 3

14 3.3 Fluid selection. The rian Flow Cad stores about 00 common fluid properties so you simply select from the list the one you will use and if it is liquid or gas. The internal stored parameter allows to compute the fluid density, viscosity, isentropic constant at operating temperature and pressure conditions. Go to the [Fluid] menu on top, the following form appears. Now you have several fluid type options: Super heated steam T, P measured. In this case you are using steam at a temperature higher than the boiling temperature at the working pressure conditions. Is needed to measure both pressure and temperature. Properties of steam are calculated with IPWS-IF97 Saturated steam, P only measured. Upstream pressure is the same of the chamber where steam is produced. water boiled. The steam temperature is inferred by the pressure of the chamber. Pressure is measured and the steam temperature calculated from tables. For example at tm water boils at 00C, at.tm boils at 05C, etc. Properties of steam are calculated also with IPWS-IF97 Saturated steam, T only measured. This is the same last case but is measured the temperature. Pressure is obtained from vapor pressure tables at working measured temperature. Technical note, Differential pressure mass flow meter, rev. b, 4

15 Fluid from table: This allows to select the fluid gas or liquid from a list. Properties of the pure compounds are stored on a data base. lso must be specified the state of the element. Technical note, Differential pressure mass flow meter, rev. b, 5

16 Natural Gas: The G No.8 DC9 formulas are used for computing the properties of natural gas. Molar concentration in % of each component must be specified. Technical note, Differential pressure mass flow meter, rev. b, 6

17 Normalize button is used for setting the sum of molar concentrations equal to 00%. That is done multiplying all concentrations to a fixed constant that modifies each individual concentration in order to be the sum 00%. Selected components can be set as fixed so they are not changed on normalization. Technical note, Differential pressure mass flow meter, rev. b, 7

18 3.4 Primary device. On the [Device] menu you will have the following form The options are: Iso Type Select the exact standard under you want to do the calculations. Iso 567-:99 Sec.8 Orifice plate Iso 567-:99 Sec.9 Nozzle Iso 567-:99 Sec.0 Venturi tube Iso 567-:99 Sec.0. Venturi tube Iso 567-:99 Sec.0. Venturi nozzle Iso 567-:99/md.:998 Orifice plate Iso 567-:003 Orifice plate Iso 567-3:003 Nozzle Iso 567-4:003 Venturi tube Case Once the standard is defined, there are usually different cases you must specify. For example for a orifice plate, you must specify this design options: Corner Taps D and D/ Taps Flange Taps Or for a nozzle, cases are: IS 93 Nozzle Long radius Nozzle Technical note, Differential pressure mass flow meter, rev. b, 8

19 Bore diameter d You must set the bore diameter and the units e.g. mm, inch,.. Optionally you may introduce the bore material and the temperature at witch you measured that diameter. This information is used for example in a situation where the primary device will operate with a gas at 00C. The bore diameter changes by thermal expansion. The used diameter must be the one at that temperature, but is not easy to put a caliper inside a pipe at 00C. So you may measure the diameter with a caliper at environmental temperature e.g. 5C and specify the bore material and temperature of your measurement. The software haves thermal expansion coefficients tables for typical bore and Pipe material and will correct continuously for the diameter at operating temperature. Upstream Pipe diameter D Here accounts same considerations as for bore diameter. Technical note, Differential pressure mass flow meter, rev. b, 9

20 3.5 Flow conditions set up. Once you have set all the information requested on [Fluid] and [Device] menus, you may set the flow limits in the main form. Here is an explanation of the parameter to be set: Flow conditions In this frame you must set the expected limits maximum and minimum for: P Upstream fluid pressure range. The fluid pressure you will have must be contained within this limits. If your pressure sensor/transmitter measures absolute pressure referred to absolute vacuum then select: [Units Type] = bsolute But if the sensor measures relative to atmospheric pressure, then you must specify [tmospheric pressure] and set: [Units Type] = Gauge T Upstream fluid temperature range. The fluid operating temperature must be within this range. dp Differential pressure range. This is the maximum and minimum differential pressure you expect to have. The minimum can not be cero, mainly because ISO567 needs a minimum Reynolds number of about 4000 typically. With cero differential pressure you have cero fluid linear velocity and cero Reynolds. Technical note, Differential pressure mass flow meter, rev. b, 0

21 Flow Units Here you set the rate units for calculated results. Results will be mass, volumetric and linear velocity flow rate in the specified units. Mass units can be of the Volumetric equivalent type e.g. [Standard Cubic feet] or [Standard Cubic Meter] If you set volumetric equivalent mass flow units for mass flow rate, the you must then specify the Standard conditions Pressure and Temperature. For example if you are working with air a you set [Q mass] = [StndCubic Ft] [Standard Conditions Pressure] = tm [Standard Conditions Temperature] = C Then the mass flow rate will be expressed in units of mass equivalent to the mass contained in cubic feet of air at tm and C. That is grams. Technical note, Differential pressure mass flow meter, rev. b,

22 3.6 Calculating results. Once you have set [Fluid], [Device] and [flow conditions], then press the calculate button on the lower left corner of the main form. The results will be given for the 8 combinations resulting from the limits min. and max. given for P, T, dp. You may think as 3 dimensional space composed of 3 axes P, T and dp in a cube with 8 corners. The flow conditions must always be kept inside this cube. The calculation results are contained on the 8 lines of the list as follows: Technical note, Differential pressure mass flow meter, rev. b,

23 Density of the fluid at specified T, P limits in MKS units. µ Viscosity of the fluid at specified T, P limits in Pascal*Sec units. Pa*Sec = 000 centi Poise k Isentropic exponent of the fluid at specified T, P limits dimensionless. Q M Mass flow rate in specified units at T, P, dp limits. Q V Volumetric flow rate in specified units at T, P, dp limits. υ Fluid linear velocity in specified units at T, P, dp limits. Re D Reynolds number upstream Technical note, Differential pressure mass flow meter, rev. b, 3

24 C ε The discharge coefficient The expansion factor upstream P loss The pressure loss is the difference in static pressure between the pressure measured at the wall on the upstream side of the primary device at a section where the influence of the approach impact pressure adjacent to the plate is still negligible approximately D upstream of the primary device and that measured on the downstream side of the primary device where the static pressure recovery by expansion of the jet may be considered as just completed approximately 6D downstream of the primary device. This is good approximation not exact for the effect of the primary device on flow before it is installed. Must not be confused with dp, the pressure difference on the primary element walls. In general is expected to have dp greater than P loss. Uncertainty % The quadratic sum for the estimated uncertainty of C and estimated uncertainty on ε as predicted by the ISO567 standard. This is the uncertainty on the flow rate Q M, if no additional errors are made on measurements. For details refer to ISO567-:99, Section.. ISO567 Condition not satisfied This last column expresses if the ISO567 standard is satisfied or not. If you read the document you will find that there are several restrictions on the bore and pipe diameter, the Reynolds number, etc. This restriction comes from the fact that the ISO standard was obtained from experimental results that are bounded under certain limits. Is important to take care in being within the ISO567 limits unless you want the uncertainty on C and ε to be undetermined. The ISO standard warranties that errors uncertainties are predicted. So you must change your flow limits or primary device if you find a message in this column. The message will tell you which is the limit or restriction that is not satisfied. Technical note, Differential pressure mass flow meter, rev. b, 4

25 3.7 Instrument parameters. Once you have made the calculations and no restrictions are reported you can prepare the configuration of your FL40 flow computer. On the [Instrument] menu you have this form: Pressure sensor frame is for specifying calibrated limits of the up stream pressure sensor been used. Low and high are the pressure value at low and high scale of the sensor e.g. 4ma-0ma or 0v-0v. Later on the instrument you will set the input type, but now you must specify only the limits. Set also the units type depending on transmitter type absolute or gauge units. The same must be done for the scale settings of the differential pressure transmitter. Technical note, Differential pressure mass flow meter, rev. b, 5

26 On the [Flow rate display] you will set the flow rate type, units and scale on the front display of the instrument. Set first for Mass or Volumetric flow rate and units to be used. [K mult] a constant to be multiplied to the flow rate. [Dec point] is the fixed position of the decimal point on the display When you press [Calculate], the contents of the bottom list will be calculated. re listed for the 8 limit flow conditions the 4 digit display reading for the rate flow. Finally pressing the [Config File] button generates a configuration file and detailed calculations file. The configuration file, extension.sfg e.g. air.sfg in this case is binary format data file containing all the information to be downloaded to the FL40 by the RPS software. Take the air.sfg configuration file that is generated in the same folder of the project file and place a copy of it in "files" subdirectory of the RPS software. Then run RPS software with the FL40 connected to the PC and go to Menu / Device / FileWrite. complete list of calculated coeffients are saved on file in the same folder of the actual file but with extension *.csv coma separated variables format that can be opened as a spread sheet. e.g. air.csv Technical note, Differential pressure mass flow meter, rev. b, 6

27 References ISO-567: ISO-567-:99E Measurement of fluid flow by means of pressure differential devices. Part: Orifice plates, Nozzles and Venturi tubes inserted in circular cross-section conduits running full. Ref. No.: ISO567-:99E ISO-567-:99/md.:998E mendment ISO-567: Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full- Part: General principles and requirements, Second edition, , Ref. No.: ISO 567-:003E. Part: Orifice plates, Second edition, , Ref. No.: ISO 567- :003E. Part3: Nozzles and Venturi Nozzles, Second edition, , Ref. No.: ISO 567-3:003E. Part4:Venturi tubes, Second edition, , Ref. No.: ISO 567-4:003E. G No.8 DC9: Starling, K.E., Savidge, J.L.: Compressibility Factors for Natural Gas and Other Hydrocarbon Gases", merican Gas ssociation G Transmission Measurement Committee Report No. 8, merican Petroleum Institute PI MpMS, chapter 4., second edition, November 99. ISO 3: Natural gas - Calculation of Compression factor Part: Introduction and guidelines Part: Calculation using molar-composition analysis IPWS-IF97: Release on the IPWS Industrial Formulation 997 for the Thermodynamic Properties of Water and Steam The International ssociation for the Properties of Water and Steam, Erlangen, Germany, September 997, General: Richard W. Miller, Flow Measurement Engineering Handbook. Third edition McGraw-Hill. ISBN Online ISO567 sample calculation service: Technical note, Differential pressure mass flow meter, rev. b, 7

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