Small Bore Orifice Flowmeter Calculation for Gas Flow |
For pipe diameter < 5 cm. |

Other Flowmeter
Calculations using standard methodologies: |

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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:**

Topics: Equations Discharge Coefficient Validity Variables Error Messages References

**Introduction**

Orifice flowmeters are used to determine a liquid or gas flowrate by measuring the
differential pressure *P _{1}-P_{2}* 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 **
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The calculations on this page are for orifices carrying a gas as described in ASME (2001).

**Discharge Coefficients** (ASME,
2001) To top of page

*Corner Taps:*

*Flange Taps:*

where *D* is in inches; and *d/D* and *Re _{D}* are
dimensionless.

**Validity **(ASME, 2001)**
**
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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 *Re _{D}*

LMNO Engineering and ASME (2001) require

Expansibility *e*

The equation shown above for expansibility *e* is valid for *P _{2}/P_{1}
>= 0.8*. Our calculation gives a warning message if

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^{ o}F__ <__ T__ <__ 1000^{ o}F. If T<0^{
o}F, then the viscosity value shown and used in the computation is the viscosity at 0
^{o}F. If T>1000^{ o}F, then the viscosity value shown and used
in the computation is the viscosity at 1000 ^{o}F (0^{ o}F is -17.8 ^{o}C
and 1000 ^{o}F is 537.8 ^{o}C). 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 P_{1},
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 P_{1},
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 ^{o}C.
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

*K _{m}* is computed to allow you to design pipe systems with orifices and
incorporate their head loss. Head loss is computed as

Standard Volumetric Flowrate

Standard volumetric flowrate, *Q _{s}*, is the volumetric flowrate computed
at standard pressure and temperature,

**Variables:**
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Dimensions: F=Force, L=Length, M=Mass, T=Time, t=temperature

Bore diameter and throat diameter both refer to *d*.

**Error Messages given by calculation **
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*"P _{2}/P_{1}<0.8. Out of range".* The equation for expansibility

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, *Re _{D}*, and some other variables will be computed
and shown. However, if

*"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. *Re _{D}* will be <1000 or

*"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 10^{9} kg/m^{3}.

*"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 < P _{1}".* Differential pressure cannot
exceed

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

**References **
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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.

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LMNO Engineering, Research, and Software, Ltd.

7860 Angel Ridge Rd. Athens, Ohio 45701 USA
(740) 592-1890

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