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Small Bore Orifice Flow Meter Calculationfor Gas Flow

For pipe diameter < 5 cm. Compute flow rate, borediameter, or differential pressure. Equations: ASME

MFC­14M­2001

Small bore orifice for gas flow calculation is mobile­device­friendly as of October 23, 2014

Register to enable "Calculate" button.

Not registered user Mass Flow, M (kg/s): Will be computed

Click to Calculate Actual Vol Flow, Qa (m3/s): Will be computed

Solve for: Std Vol Flow, Qs (std m3/s): Will be computed

Flow Rate Upstream Abs Pressure, P1 (Pa): 800000.0 Differential Pressure, Δp (Pa): 10000.0

Select Meter Type and Gas: Pressure Ratio, P2/P1: Will be computedAir (enter P1, T) Throat Diameter, d (m): 0.01Corner Pressure Taps Pipe Diameter, D (m): 0.02

Ratio, d/D: Will be computedSelect Units for each Variable: Gas Temperature, T (K): 280.0Mass Flow in kg/s Density (kg/m3): 9.95867151322013733Qa and Qs in m3/s Dynamic Viscosity (N­s/m2): 1.77107588682272854E­5P1 in N/m2 or Pa Isentropic Exponent, K: 1.4Diff P and P Loss in N/m2 or Pa Gas Expansibility, e: Will be computedDiameters in meters Discharge Coefficient, C: Will be computedTemperature in Kelvin, K Reynolds No. based on d, Red: Will be computedDensity in kg/m3 Reynolds No. based on D, ReD: Will be computedViscosity in N­s/m2, kg/m­s Pressure Loss, w (Pa): Will be computedVelocity in m/s; Area in m2 Minor Loss Coefficient, Km: Will be computed

© 2014 LMNO Engineering, Throat Velocity, Vthroat (m/s): Will be computed

Research, and Software, Ltd. Pipe Velocity, Vpipe (m/s): Will be computed

http://www.LMNOeng.com Throat Area, Athroat (m2): Will be computed

Pipe Area, Apipe (m2): Will be computed

Units in small bore orifice for gas flow calculation: C=degrees Celsius, cm=centimeter, cP=centipoise, cSt=centistoke, F=degreesFahrenheit, 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

Topics: Equations Discharge Coefficient Validity Variables Error Messages References

Introduction to Small Bore Orifice for Gas Flow CalculationOrifice flow meters are used to determine a liquid or gas flow rate by measuring the differential pressure P1­P2 across the orifice plate.Orifice flow meters are generally less expensive to install and manufacture than the other commonly used differential pressure flow meters;however, nozzle and venturi flow meters have the advantage of lower pressure drops.

The orifice 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 forthe effect of pressure change on gas density as gas flows through the orifice. Our calculation is valid for subsonic gas flow.

An orifice flow meter 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 dischargecoefficient somewhat. Flange pressure taps penetrate the flange and are at a standard distance of 1 inch (2.54 cm) from either side of theorifice. For corner taps, the pressure tap locations are as shown. For exact geometry and specifications for orifices, see ASME (2001).

Equations for Small Bore Orifice for Gas Flow Top of PageThe calculations on this page are for orifices carrying a gas as described in ASME (2001).

To: LMNOEngineeringhome page(morecalculations)

Other flowmetercalculationsusing standardmethodologies:

Orifice forGases(D>5cm)

Orifice forliquids(D<5cm)

Orifice forliquids(D>5cm)

Nozzle forliquids

Venturi forliquids

Simpler orificecalculation(not asaccurate butwon't give"parameter outof range"messages):

Bernoulli page

UnitConversions

Troubleprinting?

Register

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Discharge Coefficients for Small Bore Orifice for Gas Flow (ASME, 2001) To top of page Corner Taps:

Flange Taps:

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

Validity of Small Bore Orifice Calculation for Gas Flow (ASME, 2001) Top of PagePipe Diameter DLMNO Engineering orifice 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/DLMNO 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 ReDLMNO Engineering and ASME (2001) require ReD ≥ 1000.

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

Built­in Properties for Certain GasesTo provide ease of use, our orifice calculation has properties of some gases built­in to the calculation. The user can select Air, Carbondioxide, Hydrogen, Methane (natural gas), Nitrogen, or Oxygen. The density is automatically computed using the ideal gas law based on theupstream pressure and temperature entered. The dynamic viscosity is a function of temperature and uses the methodology shown on our GasViscosity page. The isentropic exponent, K, is based on the specific heat ratio. For methane, the dynamic viscosity value shown in theorifice calculation is valid for 0 oF ≤ T ≤ 1000 oF. If T<0 oF, then the viscosity value shown and used in the orifice computation is theviscosity at 0 oF. If T>1000 oF, then the viscosity value shown and used in the orifice computation is the viscosity at 1000 oF (0 oF is ­17.8oC and 1000 oF is 537.8 oC). For all other gases shown in the drop­down menu, there is no temperature limitation on the validity of theviscosity. 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 orifice calculation, thenyou can select "User enters P1, density, viscosity, K" and enter these values manually. Also, if the gas is not listed in our drop­down 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 befound in Weast (1985, p. F­11), Perry and Green (1984, p. 3­144), and other sources.

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

Minor Loss CoefficientKm 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 Flow RateStandard volumetric flow rate, Qs, is the volumetric flow rate computed at standard pressure and temperature, Pstd and Tstd (shown above in

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variables). Actual flow rate, Qa, is computed at the gas's actual pressure and temperature. Qs is useful to users who need to compute (orinput) standard flow rate; often pump curves and flow measurement devices provide standard, rather than actual, flow rate. The advantageof using standard flow instead of actual flow is that the same device (or pump curve) can be used for a gas at various temperatures andpressures without re­calibrating for an infinite range of actual pressures and temperatures. The user can easily convert standard to actualflow rate if the actual temperature and pressure of the gas are known; our orifice calculation does this automatically.

Variables in Small Bore Orifice for Gas Equations: Top of PageDimensions: F=Force, L=Length, M=Mass, T=Time, t=temperatureBore diameter and throat diameter both refer to d.

Error Messages given by Orifice 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 arecomputed.

For the following error messages, only some variables are computed. For example if orifice throat diameter d is to be computed, thenpressure ratio, expansibility, pipe area, pipe velocity, ReD, and some other variables will be computed and shown. However, if ReD is out ofrange 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 anerror 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 computedparameter 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 (theorifice 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. Iftemperature 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 1e­20<Density<1e9 kg/m3". Gas density must be entered between 10­20 and 109 kg/m3."Need 1e­19<Viscosity<1e9 m2/s". Kinematic viscosity must be in this range. Note that kinematic viscosity is dynamic viscosity divided bydensity."Need 0.1<d/D<0.8". For orifice corner taps, diameter ratio must be in this range."Need 0.15<d/D<0.7". For orifice flange taps, diameter ratio must be in this range."Need K >1". Isentropic exponent was entered as ≤ 1."M or Q, and d must be >0". Mass flow rate, volumetric flow rates, and/or orifice diameter were entered as zero or negative."Need Δp > 0". Orifice differential pressure must be positive."Need Δp < P1". Orifice differential pressure cannot exceed P1; this would cause P2 (absolute) to be <0 which is impossible."M or Q, and Δp must be >0". Mass flow rate, volumetric flow rates, 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 asaccurate, but won't give "parameter out of range" error messages.

References for Small Bore Orifice for Gas Flow Calculation Top of PageAmerican Society of Mechanical Engineers (ASME). 2001. Measurement of fluid flow using small bore precision orifice meters. ASMEMFC­14M­2001.

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

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

© 2002­2014 LMNO Engineering, Research, and Software, Ltd. All rights reserved.

Please contact us for consulting or other questions.

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

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