Excel Calculations: orifice

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Small-Bore Liquid Orifice Flow Meter Calculator for Excel

This Excel spreadsheet calculates the liquid flowrate from a small-bore orifice meter using the equations defined in ASME MFC-14M-2001. The calculation is iterative, but the spreadsheet is conveniently set up to use Excel's Goal Seek functionality by simply clicking a button.

The equations implemented in the spreadsheet are sourced from ASME MFC-14M-2001 and are given below.

The notation is given below.

C is the discharge coefficient. D₁ must be supplied in m. The equation differs for flange taps and corner taps, but a menu in the spreadsheet allows you to pick between the two.
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)
ρ is the density of the liquid (kg m^-3)
V₁ is the liquid velocity in the pipe(m s^-1)
Re₁ is the Reynolds Number in the pipe
β is the diameter ratio
μ is the liquid viscosity (Pa s)
Q is the volumetric flowrate (m³s^-1)

The correlations for the Flange Taps and Corner Taps discharge coefficient are only valid for the following configurations.

The equations are only valid under the following conditions

Corner Taps: 0.1 < β < 0.8
Flange Taps: 0.15 < β < 0.7
25 mm < D₁< 50 mm
6 mm < D₂
Re > 1000

A β of between 0.3 and 0.7 is practical; below this, the pressure drop is too large for economical operation, and above this, the pressure drop is not large enough for an accurate reading.

The Excel spreadsheet will also calculate the static pressure loss and the head loss from a distance D₁ upstream and 6 D₁ downstream of the orifice.

The spreadsheet is free, and none of the cells are hidden, locked or password protected. Please visit this website regularly for more exclusive, professionally prepared Excel spreadsheets for engineering.

Download Excel Spreadsheet to Calculate Liquid Flow from a Small Bore 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)

Size a Liquid Orifice Meter with ISO 5167 and Excel

This Excel spreadsheet sizes a liquid orifice meter using the equations in ISO 5167. Orifice meters determine liquid flowrate by measuring the pressure difference across a constriction in a pipe.

The spreadsheet is free - all I ask is that you credit this website with its authorship (and perhaps provide a link!)

The equations given in ISO 5167 are given below.

C is the discharge coefficient (the equation is only valid for the three standard tap positions defined below)
Re is the Reynolds number
L₁ and L₂ are the upstream and downstream tap positions (ft)
P₁ and P₂ are the upstream and downstream pressures (psig)
D₁ and D₂ are the pipe and orifice diameters (inches)
V is the liquid velocity in the pipe (ft s^-1)
ρ is the liquid density slugs ft^-3
μ is the liquid viscosity lb-sec ft^-2

ISO 5167 defines three different tap positions for the pressure probes (Corner, D-D/2 and Flange taps). These positions the values of L₁ and L₂, and are given below

Corner Taps: L₁ = L₂ = 0
Flange Taps: L₁ = L₂ = 1 inch
D-D/2 Taps: L₁ = D₁, L₂ = D₁/2

The solution to the equations is iterative; you need Re to calculate C, but you need Q to calculate Re, but you need C to calculate Q. This requires the use of Excel's Goal Seek. We simply find the

Guess a value of Re,
Calculate C and Q
Use C and Q to calculate Re
Use Goal Seek to change the value of Re we guessed in Step 1 until it's equal to the value calculated in Step 3

This process is automated in the Excel spreadsheet with a button linked to a VBA macro. The VBA macro simply initiates Goal Seek with the requireed settings.

Download Excel spreadsheet to size an orifice meter with ISO 5167