Large Diameter Orifice Flowmeter Calculation for Liquid Flow

For pipe diameter > 5 cm.
Compute flowrate, orifice diameter, or differential pressure.
Equations: ISO 5167

Other Flowmeter Calculations using standard methodologies:
 Orifice for liquids (D<5cm) 
Orifice for gases (D<5 cm)   Orifice for gases (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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Types of Pressure Taps for Orifices:

Orifice Flowmeters

Topics:  Introduction    Equations    Discharge Coefficients    Error Messages    References

Introduction
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.   Equations for orifice meters have the advantage of no Reynolds Number upper limit for validity.

An orifice flowmeter 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 105, though Reynolds numbers as low as 4x103 are valid for certain d/D ratios as discussed below.  The calculation above is for liquids.   Orifice gas flow calculations (D<5 cm, D>5 cm) have an additional factor called expansibility.

Equations
The calculations on this page are for orifices carrying a liquid as described in ISO (1991) and ASME (1971).  The ISO reference has a more up-to-date discussion of orifices than the ASME reference, so the ISO equations are used in our calculations.

Orifice equations
Orifice definitions
k = Equivalent Roughness of the pipe material [L].

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).  Km is computed to allow you to design pipe systems with orifices and incorporate their head loss.  Head loss is computed as h=KmV2/2g where V is the pipe velocity.

Discharge Coefficients (ISO, 1998)
    Equation and applicability:

Orifice Discharge Coefficient

Corner Pressure Taps:  L1 = L'2 = 0
D and D/2 Pressure Taps:  L1 = 1  and  L'2 = 0.47
Flange Pressure Taps:  L1 = L'2 = 0.0254/D  where D is in meters

    Applicability:
All types of pressure taps:  d >= 1.25 cm,  5 cm <= D <= 1 m,  0.1 <= d/D <= 0.75

Corner Pressure Taps or D and D/2 Pressure Taps:
     ReD >= 4000  for  0.1 <= d/D <= 0.5   and  ReD >= 16,000(d/D )2  for  d/D>0.5

Flange Pressure Taps:  ReD >= 4000  and  ReD >= 170,000 D (d/D )2  where D is in meters

In addition, ISO recommends that in general  k/D <= 3.8x10-4   for Corner Taps and  k/D <= 10-3 for Flange or D and D/2 pressure taps.  k is the pipe roughness.

Error Messages given by calculation
"All inputs must be positve".  This is an initial check of user input.
"d, D, d/D, or ReD out of range".  The equation for discharge coefficient, C, is only valid for certain ranges of d, D, d/D, and ReD as shown in the Discharge Coefficients section above.  This message could be generated during the program's initial check for valid input.  If the input is valid, the message will be generated during computations if the program determines that a calculated value will be out of range of the validity of the equations.  d is orifice diameter, D is pipe diamter, and ReD is the Reynolds number based on D.
· Try the simpler orifice calculation on our Bernoulli page if your parameters are out of range.  It is not as accurate, but won't give "parameter out of range" error messages.

References
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).


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