Small Bore Orifice Flowmeter Calculation for Gas Flow

For pipe diameter < 5 cm.
Compute flowrate, bore diameter, or differential pressure.
Equations: ASME MFC-14M-2001

Other Flowmeter Calculations using standard methodologies:
Orifice for Gases (D>5cm)
Orifice for liquids (D<5cm)  Orifice for liquids (D>5cm) 
  Nozzle for liquids   Venturi for liquids
  Simpler orifice calculation (not as accurate but won't give "parameter out of range" messages): Bernoulli page
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Units: C=degrees Celsius, cm=centimeter, cP=centipoise, cSt=centistoke, F=degrees Fahrenheit, cfm=cubic feet per minute, cfs=cubic feet per second, ft=foot, g=gram, hr=hour, in=inch, K=degrees Kelvin, kg=kilogram, lb=pound, m=meters, mbar=millibar, min=minute, mm=millimeter, N=Newton, Pa=Pascal, psi=pound per square inch, R=degrees Rankine, s=second, scfm=standard cfm, std=standard.

Types of Pressure Taps for Small Bore Orifices:

Pressure Tappings

Topics:  Equations    Discharge Coefficient   Validity   Variables     Error Messages    References

Orifice flowmeters are used to determine a liquid or gas flowrate by measuring the differential pressure P1-P2 across the orifice plate.  They are generally less expensive to install and manufacture than the other commonly used differential pressure flowmeters; however, nozzle and venturi flow meters have the advantage of lower pressure drops.

The calculation on this page is for flow of gases.  Please see the links at the top of this page for liquid flow through orifice meters.  Gas flow calculations include an expansibility factor e, which is not present in the liquid calculation.  The expansibility factor accounts for the effect of pressure change on gas density as gas flows through the orifice.  Our calculation is valid for subsonic gas flow.

An orifice flowmeter is typically installed between flanges connecting two pipe sections (flanges are not shown in the above drawings).  The two standard pressure tapping arrangements are shown in the drawings; the location of the pressure taps affects the discharge coefficient somewhat.  Flange pressure taps penetrate the flange and are at a standard distance of 1 inch (2.54 cm) from either side of the orifice.  For corner taps, the pressure tap locations are as shown.  For exact geometry and specifications for orifices, see ASME (2001).

Equations                                Top of Page
The calculations on this page are for orifices carrying a gas as described in ASME (2001).

Orifice Gas Flow Equations

Discharge Coefficients (ASME, 2001)               To top of page
    Corner Taps:

Corner taps

    Flange Taps:

Flange taps

where D is in inches; and d/D and ReD are dimensionless.  C is dimensionless.

Validity (ASME, 2001)                               Top of Page
Pipe Diameter D
LMNO Engineering calculation requires 0.635 cm <= D <= 5.08 cm for both corner and flange taps.
ASME (2001) suggests 1.2 cm <= D <= 4 cm for corner taps and 2.5 <= D <= 4 cm for flange taps.

Diameter ratio d/D
LMNO Engineering and ASME (2001) require 0.1 <= d/D <= 0.8 for corner taps and 0.15 <= d/D <= 0.7 for flange taps.

Reynolds number based on pipe diameter ReD
LMNO Engineering and ASME (2001) require ReD >= 1000.

Expansibility e
The equation shown above for expansibility e is valid for P2/P1 >= 0.8.  Our calculation gives a warning message if  P2/P1 < 0.8, but still computes answers.

Built-in Properties for Certain Gases
To provide ease of use, our calculation has properties of some gases built-in to the calculation.  The user can select Air, Carbon dioxide, Hydrogen, Methane (natural gas), Nitrogen, or Oxygen.  The density is automatically computed using the ideal gas law based on the upstream pressure and temperature entered.  The dynamic viscosity is a function of temperature and uses the methodology shown on our Gas Viscosity page.  The isentropic exponent, K, is based on the specific heat ratio.  For methane, the dynamic viscosity value shown in the calculation is valid for 0 oF < T < 1000 oF.  If T<0 oF, then the viscosity value shown and used in the computation is the viscosity at 0 oF.  If T>1000 oF, then the viscosity value shown and used in the computation is the viscosity at 1000 oF (0 oF is -17.8 oC and 1000 oF is 537.8 oC).  For all other gases shown in the drop-down menu, there is no temperature limitation on the validity of the viscosity.   Dynamic viscosity is essentially independent of pressure.

If you know that your density, viscosity, or isentropic exponent is significantly different than the value shown in the calculation, then you can select "User enters P1, density, viscosity, K" and enter these values manually.  Also, if the gas is not listed in our drop-down menu, then you can select "User enters P1, density, viscosity, K" and enter these values manually.  K must be > 1.  Additionally, values for K can be found in Weast (1985, p. F-11), Perry and Green (1984, p. 3-144), and other sources.

Note that our calculation prior to February 2003 included helium as a gas in the drop-down gas menu, and the viscosities for the gases were set at 20 oC.  Now, the viscosity variation with temperature is included, but helium was removed because it doesn't have a simple viscosity relationship with temperature.

Pressure Loss
w is the static pressure loss occurring from a distance of approximately D upstream of the orifice to a distance of approximately 6D downstream of the orifice.  It is not the same as differential pressure.  Differential pressure is measured at the exact locations specified in ASME (2001) (shown in the above figures).

Minor Loss Coefficient
Km is computed to allow you to design pipe systems with orifices and incorporate their head loss.  Head loss is computed as h=KmV2pipe/2g.

Standard Volumetric Flowrate
Standard volumetric flowrate, Qs, is the volumetric flowrate computed at standard pressure and temperature, Pstd and Tstd (shown above in variables).  Actual flowrate, Qa, is computed at the gas's actual pressure and temperature.  Qs is useful to users who need to compute (or input) standard flowrate; often pump curves and flow measurement devices provide standard, rather than actual, flowrate.  The advantage of using standard flow instead of actual flow is that the same device (or pump curve) can be used for a gas at various temperatures and pressures without re-calibrating for an infinite range of actual pressures and temperatures.  The user can easily convert standard to actual flowrate if the actual temperature and pressure of the gas are known; our calculation does this automatically.

Variables:                             Top of Page
Dimensions: F=Force, L=Length, M=Mass, T=Time, t=temperature
Bore diameter and throat diameter both refer to d.
Orifice Gas Flow Definitions
Error Messages given by calculation                                Top of Page
"P2/P1<0.8. Out of range".  The equation for expansibility e is only valid for P2/P1>=0.8.  This is a just a warning message; all variables are computed.

For the following error messages, only some variables are computed.  For example if throat diameter d is to be computed, then pressure ratio, expansibility, pipe area, pipe velocity, ReD, and some other variables will be computed and shown.   However, if ReD is out of range for C to be valid, then C and d (and anything depending on d - such as throat area and throat velocity) will not be computed.  If an error message is shown and you think your input is correct, be sure to check that you have selected the correct units for your entries.

"Infeasible input".  While none of the inputs alone are out of range, they collectively result in a physically infeasible situation or a computed parameter will be out of range (e.g. ReD will be <1000 or d/D will be out of range) or the throat velocity will exceed the speed of sound (the calculation is only valid for subsonic velocities).
"P1 and T (abs) must be >0", "Need P1 and T(abs)>0".  Absolute pressure or absolute temperature was entered as zero or negative.  If temperature was entered in C or F, it was internally converted to absolute temperature.

"Need 0.64<D<5 cm".  Pipe diameter must be between 0.635 and 5.08 cm.
"Need 1e-20<Density<1e9 kg/m3".  Gas density must be entered between 10-20 and 109 kg/m3.
"Need 1e-19<Viscosity<1e9 m2/s".  Kinematic viscosity must be in this range.  Note that kinematic viscosity is dynamic viscosity divided by density.
"Need 0.1<d/D<0.8".  For corner taps, diameter ratio must be in this range.
"Need 0.15<d/D<0.7".  For flange taps, diameter ratio must be in this range.
"K must be >1".  Isentropic exponent was entered as <= 1.
"M or Q, and d must be >0".  Mass flowrate, volumetric flowrates, and/or orifice diameter were entered as zero or negative.
"Need Diff P > 0".  Differential pressure must be positive.
"Diff P must be < P1".  Differential pressure cannot exceed P1; this would cause P2(absolute) to be <0 which is impossible.
"M or Q, and Diff P must be >0".  Mass flowrate, volumetric flowrates, and/or differential pressure were entered as zero or negative
"Need ReD>1000".  ReD must be at least 1000.

· Try the simpler orifice calculation on our Bernoulli page if your parameters (for instance d/D, D, or ReD) are out of range.  It is not as accurate, but won't give "parameter out of range" error messages.

References                                  Top of Page
American Society of Mechanical Engineers (ASME).  2001.  Measurement of fluid flow using small bore precision orifice meters.  ASME MFC-14M-2001.

Perry, R. H. and D. W. Green (editors).  1984.  Perry's Chemical Engineers' Handbook.  McGraw-Hill Book Co.  6th ed.

Weast, R. C. (editor).  1985. CRC Handbook of Chemistry and Physics.   Chemical Rubber Company.  65th ed.

© 2002-2003 LMNO Engineering, Research, and Software, Ltd. (All Rights Reserved)

LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd.   Athens, Ohio  45701   USA   (740) 592-1890