Small-Bore Gas Orifice Meter Flow Calculator

This Excel spreadsheet calculates the flowrate from a small-bore gas orifice meter using the ASME MFC-14M-2001 standard. This calculator is valid for pipe diameters of less than 40 mm (other restrictions are given below).

The equations are as follows

• C is the discharge coefficient. D₁ has to be supplied in m
• D₁ and D₂ are the diameter of the pipe and orifice respectively (m)
• A₁ and A₂ are the cross sectional areas of the pipe and orifice (m²)
• ΔP is the pressure drop across the orifice (Pa)
• P₁ and P_std are the upstream pressure and standard pressure
• T and Tstd are the gas temperature and standard temperature is the 
• ρ is the gas (kg m^-3)
• μ is the gas viscosity (Pa s)
• V₁ is the liquid velocity in the pipe (m s^-1)
• Re₁ is the Reynolds Number in the pipe
• β is the diameter ratio
• MW is the molecular weight of the gas (kg mol^-1)
• R is the universal gas constant (8314 J kmol^-1 K^-1)
• γ is the specific heat ratio
• e is the gas expansivity
• Q is the volumetric flowrate (m³s^-1)
• Q_std is the volumetric flowrate at standard conditions (m³s^-1)

The spreadsheet uses the ideal gas law to calculate the gas density (you just have to supply the molecular weight, pressure and temperature of the gas).

Note these restrictions to the validity of the equations

• Corner Taps: 0.1 < β < 0.8 and 12 mm < D₁ < 40 mm
• Flange Taps: 0.15 < β < 0.7 and 25 mm < D₁ < 40 mm
• D₂ > 6 mm
• Re >1000

Additionally, the discharge coefficients are only valid for the tap configurations illustrated below (as specified by the ASME MFC-14M-2001 standard).

You can choose either Corner or Flange taps with a drop-down menu in the spreadsheet, and Excel automatically uses the correct correlation for the discharge coefficient.

These equations (like nearly all orifice flow meter calculations) require an iterative solution. This is easily done with Excel's Goal Seek.  All you have to do is click a button.

Goal Seek uses an initial guess value for the Reynolds Number to calculate the discharge coefficients, and uses this to calculate the flowrate. The calculated flowrate is then used to calculate the Reynolds Number.  Goal Seek then automatically adjusts the guess and calculated values of the Reynolds number until they are the same.

Download Excel Spreadsheet to Calculate Flowrate from a Small Bore Gas Orifice Meter

Model a Gas Orifice Meter with Excel

This Excel spreadsheet calculates the flowrate from the pressure drop across a gas orifice meter with the equations defined in ISO 5167.

Orifice meters use the pressure loss across a constriction (that is, the orifice plate) in a pipe to determine the flowrate.  While orifice meters are cost effective, they have several disadvantages. 

• The relationship between flowrate and pressure is non-linear,
• accurate values of the physical parameters are required,
• and high Reynolds numbers (>10⁴) are required for the greatest confidence in their accuracy, and the resulting pressure drop can be significant.

Accordingly, orifice meters are only used with the pressure drop is not critical, and accuracy is around 2% at best.

These are the equations implemented in the spreadsheet (as specified in ISO 5167)

Gas Orifice Meter Equations in ISO 5167

The notation is given below

• C is the discharge coefficient (only valid for the three standard tap positions given below)
• Re is the Reynolds number
• L₁ and L₂ are the upstream and downstream tap positions (m)
• P₁ and P₂ are the upstream and downstream pressures (Pa)
• D₁ and D₂ are the pipe and orifice diameters (m)
• V is the gas velocity in the pipe (m s^-1)
• ρ is the gas density (kg m^-3)
• μ is the gas viscosity (Pa s) 
• M is the molecular weight
• Y is the expansion coefficient
• Z is the gas compressibility factor
• K is the specific heat ratio
• R is the gas constant (8314 J kg^-1 k^-1)
• A_o is the cross-sectional area of the orifice (m²) 

There are three standard tap positions that determine the values of L₁ and L₂, as illustrated below. For corner taps, L₁ = L₂= 0, for D-D/2 taps L₁ = D₁ and L₂= D₁/2, and for flange taps L₁ = L₂= 1 inch. 

Tap positions in ISO 5167

The equations use the ideal gas law to calculate the gas density (you could override this with your own value), and are only valid for pipes with internal diameters from 50 mm to 1000 mm, and for pressure ratios greater than 0.75.

This is a screen grab of part of the spreadsheet.

The calculation is iterative: you need Re to calculate C, you need V to calculate Re, but you need C to calculate V.  Excel's Goal Seek functionality is used to iteratively solve the equations for the flowrate. This process is automated with a button - just fill in the parameters, click a button, and some VBA initiates Goal Seek with the correct settings

The spreadsheet provides an initial guess value for Re. This is used to calculate C and V. V is then used to calculate Re.  Excel's Goal Seek varies the guess value of Re until it matches the calculated value of Re.

By carefuly altering the equations (and the parameters used by Goal Seek), you could also solve for any other variable - for example, you could find the pressure drop for a specific flowrate (let me know if you need help in implementing this).

You'll find a spreadsheet  that models a liquid orifice meter here.

Visit http://excelcalculations.blogspot.com regularly for more free engineering spreadsheets.

Download Excel Spreadsheet to Calculate Flowrate in a Gas Orifice Meter (ISO 5167)