Large Diameter Orifice Flow Meter Calculation for Gas Flow |
For pipe diameter > 5 cm. |

Other Flow
Meter Calculations using standard methodologies: |

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Types of Pressure Taps for Orifices:

Topics: Introduction Equations Discharge Coefficient Variables Validity and Discussion Error Messages References

**Introduction**

Orifice flow meters are used to determine a liquid or gas flow rate by measuring the
differential pressure (P_{1} - P_{2}) across the orifice plate.
Orifice meters are typically 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. Equations for orifice meters have the advantage of no Reynolds Number upper
limit for validity.

An orifice flow meter is typically installed between flanges connecting two pipe sections (flanges are not shown in the above drawings). The three 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 or D and D/2 taps, the pressure tap locations are as shown.

Orifices are typically less than 0.05D thick. For exact geometry and
specifications for orifices, see ISO (1991) or ASME (1971).
The ASME and ISO have been working on guidelines for orifices since the early 1900s.
The organizations have the most confidence in orifice accuracy when the Reynolds number
exceeds 10^{5}, though Reynolds numbers as low as 4x10^{3} are valid for
certain d/D ratios as discussed below. The calculation above is for flow of gases.
For liquid flow through orifices, please visit our orifice calculations for
liquids: Pipe diameter < 5 cm or pipe diameter > 5 cm. 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. LMNO Engineering also has an orifice calculation for gas flow in pipes less than 5 cm
diameter.

**Equations **
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The calculations on this page are for orifices carrying a gas as described in ISO (1991 and 1998).

**Discharge Coefficient** (ISO, 1998)

Corner Pressure Taps: L_{1} = L'_{2} = 0

D and D/2 Pressure Taps: L_{1} = 1 and L'_{2} = 0.47

Flange Pressure Taps: L_{1} = L'_{2} = 0.0254/D where D is in
meters

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

For all types of pressure taps:

For Corner Pressure Taps or D and D/2 Pressure Taps:

*Re _{D} >= 4000 for 0.1 <= d/D <=
0.5 and Re_{D} >= 16,000(d/D )^{2} for
d/D>0.5*

For Flange Pressure Taps: *Re _{D} >= 4000* and

The calculation does not provide results if these values are out of range.

*Expansibility:
*The equation shown above for expansibility,

*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.

*ISO Pipe Roughness Recommendation:*

ISO recommends that in general *k/D <= 3.8x10 ^{-4}* for
Corner Taps and

*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 ISO (1991) (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 Flow Rate:*

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

**Error Messages given by calculation **
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*"P _{2}/P_{1}<0.75. Out of range".* The
equation for expansibility, e, is only valid for P

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

**References **
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American Society of Mechanical Engineers (ASME). 1971. Fluid meters: Their
theory and application. Edited by H. S. Bean. 6ed. Report of ASME
Research Committee on Fluid Meters.

International Organization of Standards (ISO 5167-1). 1991. Measurement of fluid flow by means of pressure differential devices, Part 1: Orifice plates, nozzles, and Venturi tubes inserted in circular cross-section conduits running full. Reference number: ISO 5167-1:1991(E).

International Organization of Standards (ISO 5167-1) Amendment 1. 1998. Measurement of fluid flow by means of pressure differential devices, Part 1: Orifice plates, nozzles, and Venturi tubes inserted in circular cross-section conduits running full. Reference number: ISO 5167-1:1991/Amd.1:1998(E).

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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