# ISO 5167 Venturi Meter Calculations with Spreadsheets

## Where to Find ISO 5167 Venturi Meter Spreadsheets

For Excel spreadsheets to make ISO 5167 venturi meter calculations, click here to visit our spreadsheet store.  Obtain convenient, easy to use spreadsheets for ISO 5167 venturi meter calculations at reasonable prices. Read on for information about the use of Excel spreadsheets for venturi meter calculations.

## How a Venturi Meter Works

Venturi meters function by sending pipe flow through a constricted area (the venturi throat), as shown in the diagram at the right.  Due to the increased fluid velocity passing through the constriction, there will be a decreased pressure at that location.   The pipe flow rate can then be calculated from the measured pressure difference between the undisturbed pipe flow and the flow through the constriction.

A general equation for calculating flow rate through a venturi meter is shown at the left.  The parameters in the equation and their units are as shown below:

• Q is the flow rate through the pipe and through the meter  (cfs – U.S. or m3/s – S.I.)
• C is the discharge coefficient, which is dimensionless
• A2 is the constricted area perpendicular to flow (calculated from the venturi throat diameter)  (ft2 – U.S. or m2 – S.I.)
• P1 is the undisturbed upstream pressure in the pipe  (lb/ft2 – U.S. or N/m2 – S.I.)
• P2 is the pressure in the pipe at the constricted area, Ao (lb/ft2 – U.S. or N/m2 – S.I.)
• β = d/D = (diam. at A2/pipe diam.), which is dimensionless
• ρ is the fluid density (slugs/ft3 – U.S. or kg/m3 – S.I.)

## ISO 5167 Venturi Meter Guidelines

ISO 5167-4: 2003 provides discharge coefficient values for three venturi meter variations, subject to the venturi meeting a set of specifications and guidelines given in the publication.  The three venturi meter variations are i) “as cast” convergent section, ii) “machined” convergent section, and iii) “rough welded sheet iron” convergent section.  For each of these three variations, ISO 5167-4:2003 specifies a range for pipe diameter, diameter ratio (d/D), and Reynolds number in the pipe.

## A Spreadsheet Screenshot for ISO 5167 Venturi Meter Calculations

The image below shows part of an Excel spreadsheet that can be used for ISO 5167 venturi meter calculations, such as flow rate calculation, discharge coefficient, pressure difference, or venturi throat diameter.  For this spreadsheet and other low cost, easy to use spreadsheets for gas flow or liquid flow ISO 5167 venturi meter calculations in S.I. or U.S. units, click here to visit our spreadsheet store.

References

1. Munson, B. R., Young, D. F., & Okiishi, T. H., Fundamentals of Fluid Mechanics, 4th Ed., New York: John Wiley and Sons, Inc, 2002.

2. U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition, Water Measurement Manual, available for on-line use or download at: http://www.usbr.gov/pmts/hydraulics_lab/pubs/wmm/index.htm

3. International Organization of Standards -Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full. Part 4, Reference number: ISO 5167-4:2003

4. Bengtson, Harlan H., “Orifice or Venturi Pipe Flow Meters: for Liquid Flow or Gas Flow,” an Amazon Kindle ebook.

5. Bengtson, Harlan H., “Flow Measurement in Pipes and Ducts,” an online, self-study, continuing education course for Professional Engineers at www.CEDengineering.com.

6. Bengtson, Harlan H., “Orifice and Venturi Meters Pipe Flow Meters – for Liquid and Gas Flow,” an online, self-study, continuing education course for Professional Engineers at www.suncam.com.

# Spreadsheets for ISO 5167 Orifice Plate Flow Meter Calculations

## Orifice Meter Background for ISO 5167 Orifice Plate Flow Meter Calculations

For background on orifice meters and the orifice meter coefficient, see the articles, “Excel Spreadsheets for Orifice and Venturi Flow Meter Calculations” and “Calculate an Orifice Coefficient with ISO 5167.”  The diagram at the left shows the general orifice meter configuration and some of the parameters used in calculations.  Equations from ISO 5167-2:2003 are presented in the next section.

## Equations for ISO 5167 Orifice Plate Flow Meter Large Bore Calculations

The equations for pipes with diameter between 2 in. and 40 in (50 mm to 1000 mm) are given in Reference #1 at the end of this article, ISO 5167-2:2003.  The equations are summarized here.  The commonly used equation for compressible fluid (gas) flow rate is shown at the right, where the parameters are defined as follows:

• Q = flow rate through pipe and meter, cfs (m3/s for S.I. units)
• Co = orifice discharge coefficient, dimensionless
• Ao = orifice  area, ft2 (m2 for S.I. units)
• P1 = upstream absolute pressure in the pipe, lb/ft2 (kN/m2 for S.I. units)
• P2 = pressure at the downstream pressure tap, lb/ft2 (kN/m2 for S.I. units)
• β = Do/D1 = orifice diam./pipe diam., dimensionless
• Z = compressibility factor of the gas at P1, T1
• R = Ideal Gas Law Constant = 345.23 psia-ft3/slugmole-oR                                         ( or 8.3145 kN-m/kgmole-oK for S.I. units)
• MW = molecular weight of the gas
• T1 = upstream absolute temperature in the pipe, oR (oK for S.I. units)
• Y = Expansion Factor – see equation for Y below

Y  =  1  –  (0.351  +  0.265 β4 +  0.93 β8)[ 1 – (P2/P1)1/k ]

where:  k is the Specific Heat Ratio (Cp/Cv) of the flowing gas

The orifice coefficient, Co, can be calculated from the following equations:

Where Re is the Reynolds number in the pipe  ( Re  =  DVρ/μ )

## An Excel Spreadsheet as an Orifice Meter/Gas Flow Calculator

The Excel spreadsheet template shown below can be used to calculate gas flow rate, required orifice diameter, or pressure difference across the orifice, if the other two are known.  This spreadsheet is for large bore pipes (2 in. to 40 in diameter) and uses S.I. units.   The image shows just the first page of the worksheet to calculate gas flow rate.  Why bother to make these calculations by hand?  This Excel spreadsheet and others with similar calculations for ISO 5167 orifice plate flow meter calculations are available in either U.S. or S.I. units at a very low cost (only \$14.95 each) in our spreadsheet store.  There are also spreadsheets for large bore orifice meter calculations for liquid flow and for small bore orifice meter calculations (gas flow or liquid flow).  The small bore spreadsheets are for pipes with diameter between 1/2 inch and 1 1/2 inches (12 mm to 40 mm), and use slightly different equations from ASME MFC-14M:2001.

References:

1. U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition, Water Measurement Manual.

2. International Organization of Standards – Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full. Reference number: ISO 5167-2:2003.

4. Bengtson, Harlan H., “Orifice or Venturi Pipe Flow Meters: for Liquid Flow or Gas Flow,” an Amazon Kindle ebook.

5. Bengtson, Harlan H., “Flow Measurement in Pipes and Ducts,” an online, self-study, continuing education course for Professional Engineers at www.CEDengineering.com.

6. Bengtson, Harlan H., “Orifice and Venturi Meters Pipe Flow Meters – for Liquid and Gas Flow,” an online, self-study, continuing education course for Professional Engineers at www.suncam.com.

7. Bengtson, Harlan H. “Orifice Gas Flow Calculation Excel Spreadsheets,” an online blog article.

# ISO 5167 Orifice Coefficient Calculation Spreadsheet

Introduction to an ISO 5167 Orifice Coefficient Calculation Spreadsheet

For an ISO 5167 orifice coefficient calculation spreadsheetclick here to visit our spreadsheet store.   Read on for information about Excel spreadsheets that can be used to make these ISO 5167 orifice meter calculations.

When ISO 5167 came out in 1991, it included three standard configurations for the pressure taps in an orifice flow meter and equations to calculate the orifice discharge coefficient for a specified ratio of orifice diameter to pipe diameter for any of those three standard pressure tap configurations.  This provided greater flexibility for orifice meters, because orifice plates with different orifice diameters could be used in a given orifice meter, while still allowing accurate determination of the orifice discharge coefficient.

Background on ISO 5167 Orifice Coefficient Calculation Spreadsheet

An orifice meter is a simple device for measuring pipe flow rate through the use of a circular plate with a hole in the center (the orifice plate), held in place between pipe flanges, as shown in the diagram at the left.  The fluid pressure decreases downstream of the orifice plate due to the accelerated flow.  The pressure difference shown in the diagram as P1 – P2 can be measured and used to calculate the flow rate passing through the meter (and thus the pipe flow rate) using the equation shown at the right.  This equation allows calculation of pipe flow rate, Q, for measured pressure difference, P1 – P2, and known density of the fluid, ρ, the ratio of orifice diameter to pipe diameter, β, the cross-sectional area of the orifice, Ao, and the orifice discharge coefficient, Cd.

For more details about the orifice, flow nozzle, and venturi meter, see the article, “Excel Spreadsheets for Orifice and Venturi Flow Meter Calculations.”

ISO 5167 Standard Pressure Tap Locations

Prior to ISO 5167 coming out in 1991, the downstream pressure tap of an orifice meter was typically located at the vena contracta (the minimum jet area downstream of the orifice plate) as shown in the diagram above.  The correlations in place for determining the orifice discharge coefficient were for the downstream pressure tap at the vena contracta.  Unfortunately, the distance of the vena contracta fro the orifice plate changes with orifice diameter, so changing to an orifice plate with a different hole diameter required moving the downstream pressure tap in order to be able to accurately estimate the orifice discharge coefficient.

The three standard pressure tap configurations identified for orifice flow meters, known as corner taps, flange taps, and D – D/2 taps, are shown in the diagram at the left.  As shown in the diagram, the distance of the pressure taps from the orifice plate is given as a fixed distance, or as a function of the pipe diameter, independent of the orifice diameter, so the orifice discharge coefficient can be calculated for several orifice diameters in a given orifice meter.

Equations for ISO 5167 Orifice Coefficient Calculation Spreadsheet

Included in ISO 5167 is an equation allowing calculation of the orifice discharge coefficient, Cd, for known values of β (d/D), Reynolds number, Re, and L1 & L2, where L1 is the distance of the upstream pressure tap from the orifice plate and L2 is the distance of the downstream pressure tap from the orifice plate.  For corner taps:  L1 = L2 = 0;  for flange taps:  L1 = L2 = 1″ ;  and for D-D/2 taps:  L1 = D & L2 = D/2.   The ISO 5167 equation for the orifice discharge coefficient is:

Cd – 0.5959 + 0.0312 β2.1 – 0.1840 β8 + 0.0029 β2.5(106/Re)0.75 + 0.0900(L1/D)[β4/(1 – β4)] – 0.0337(L2/D)β3

This equation is usable  to find the orifice discharge coefficient for an orifice flow meter with any of the three standard pressure tap configurations, but not for any other arbitrary values of L1 and L2. The introduction of these standard pressure tap configurations and the equation for Cd, allows a given orifice flow meter to conveniently use different size orifice openings and cover a wide flow measurement range.

An iterative (trial and error) calculation is needed to get a value for Cd, because the upstream velocity needed for Re isn’t known until Cd is known.  The ISO 5167 orifice coefficient calculation spreadsheet template shown in the screenshot at the right will calculate the orifice discharge coefficient based on the indicated input information.  The spreadsheet uses an iterative calculation procedure.  It is necessary to assume a value for Re to start the process and replace that value with the calculated Re as any times as necessary until the two Re values are the same.  This ISO 5167 orifice calculation spreadsheet is available in either U.S. or S.I. units at a very low cost in our spreadsheet store.

References:

1. U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition, Water Measurement Manual.

2. International Organization of Standards – ISO 5167-1:2003 Measurement of fluid flow by means of pressure differential devices, Part 1: Orifice plates, nozzles, and Venturi tubes inserted in circular cross-section conduits running full. Reference number: ISO 5167-1:2003.

3. Bengtson, Harlan H., Flow Measurement in Pipes and Ducts, An online continuing education course.

4. Bengtson, Harlan H., “Orifice and Venturi Pipe Flow Meters: for Liquid Flow or Gas Flow,”  an Amazon Kindle e-book.

# Excel Spreadsheets for Orifice and Venturi Flow Meter Calculations

Introduction

For Excel spreadsheets to use for orifice and venturi meter calculations, click here to visit our spreadsheet store.  Read on for information about Excel spreadsheets that can be used as orifice and venturi flow meter, pipe flow rate calculators.

Excel spreadsheets are convenient for differential pressure flow meter calculations,  for meters such as the commonly used orifice flow meter and venturi meter.  The general equation for differential pressure flow meters can be built into the spreadsheets with Excel formulas.  Also, for gas flow, the ideal gas law can be used to calculate the gas density based on its temperature, pressure, and molecular weight.  An Excel spreadsheet can also be used to calculate the orifice coefficient for anorifice meter with one of the ISO standard pressure tap configurations.

Venturi and Orifice Flow Meter Background

Orifice and venturi meters both function by sending pipe flow through a constricted area (the orifice plate or the venturi throat), as shown in the diagrams at the right.  Due to the increased fluid velocity passing through the constriction, there will be a decreased pressure at that location.   The pipe flow rate can then be calculated from the measured pressure difference between the undisturbed pipe flow and the flow through the constriction.

The general equation for calculating flow rate through either an orifice or venturi meter is shown at the left, where the parameters in the equation and their units are as follows:

• Q is the flow rate through the pipe and through the meter  (cfs – U.S. or m3/s – S.I.)
• Cd is the discharge coefficient, which is dimensionless
• Ao is the constricted area perpendicular to flow  (ft2 – U.S. or m2 – S.I.)
• P1 is the undisturbed upstream pressure in the pipe  (lb/ft2 – U.S. or N/m2 – S.I.)
• P2 is the pressure in the pipe at the constricted area, Ao (lb/ft2 – U.S. or N/m2 – S.I.)
• β = D2/D1 = (diam. at A2/pipe diam.), which is dimensionless
• ρ is the fluid density (slugs/ft3 – U.S. or kg/m3 – S.I.)

Excel Spreadsheets for Flow Rate Calculation

The image below shows an Excel spreadsheet that can be used as a pipe flow rate calculator, based on the measured pressure difference across a flow nozzle, venturi, or Orifice flow meter.  This spreadsheet is suitable when the fluid density is known (as for a liquid) and the meter coefficient, C, is known.  For this spreadsheet and another to calculate the density of a gas using the ideal gas law model, click here to visit our spreadsheet store.

References

1. Munson, B. R., Young, D. F., & Okiishi, T. H., Fundamentals of Fluid Mechanics, 4th Ed., New York: John Wiley and Sons, Inc, 2002.

2. U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition, Water Measurement Manual, available for on-line use or download at: http://www.usbr.gov/pmts/hydraulics_lab/pubs/wmm/index.htm

3. International Organization of Standards – ISO 5167-1:2003 Measurement of fluid flow by means of pressure differential devices, Part 1: Orifice plates, nozzles, and Venturi tubes inserted in circular cross-section conduits running full. Reference number: ISO 5167-1:2003.

4. Bengtson, Harlan H., “Orifice and Venturi Flow Meters: for Liquid Flow and Gas Flow.” an Amazon Kindle e-book.