Small Diameter Orifice Flow Meter Calculation for Liquid Flow

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

Other Flow Meter Calculations using standard methodologies:
 Orifice for liquids, D>5 cm 
Orifice for gases, D<5 cm   Orifice for gases, D>5 cm 
  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: bbls=barrels, C=degrees Celsius, cm=centimeter, cP=centipoise, cSt=centistoke, F=degrees Fahrenheit, cfs=cubic feet per second, ft=feet, g=gram, gpm=US gallons per minute, gph=US gallons per hour, gpd=US gallons per day, hr=hour, kg=kilogram, lb=pound, m=meters, min=minute, mm=millimeter, N=Newton, Pa=Pascal, psi=pound per square inch, s=second

Types of Pressure Taps for Small Bore Orifices:

Pressure Tappings

Topics:  Introduction    Equations    Discharge Coefficients    Error Messages    References

Orifice flow meters are used to determine a liquid or gas flow rate by measuring the differential pressure (P1 - P2) across the orifice plate.  The two standard pressure tapping arrangements for small bore orifices 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, tappings are right up against the orifice.

The LMNO Engineering small diameter orifice calculation is valid for orifices installed in pipes having pipe diameters between 1 cm and 5 cm (2 inch), and pipe Reynolds numbers greater than 1000.  For larger diameter pipes, please see our Large Diameter Orifice Calculation for Liquids.  We also have orifice calculations for gas flow (D<5 cm and D> 5 cm); and calculations for flow through nozzle and venturi flow meters.

Equations        To top of page
The calculations on this page are for orifices carrying a liquid as described in ASME (2001).

Orifice equations
Orifice definitions
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).  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 (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.

Pipe Diameter, D
LMNO Engineering calculation requires 1 cm < D < 5.1 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.

Error Messages given by calculation       To top of page
Messages indicating input values are out of the acceptable ranges:
"Need 1<Density<1e9 kg/m3", "Need 1e-19<Viscosity<1e9 m2/s", "Need 0.01<D<0.051 m", "Need 1e-30<Qv<1e30 m3/s", "Need 1e-30<Qm<1e30 kg/s", "Need 1e-99<Pdiff<1e99 Pa", "Need ReD > 1000".
"Need 0.1<d/D<0.8" for corner taps.  "Need 0.15<d/D<0.7" for flange taps.

Run-time messages.  Computations not completed:
"ReD will be <1000".  If solving for flow rate.  Unable to compute Q's.  Value for Q will cause ReD to be < 1000 (out of range of validity).
"Diff P too large".  If solving for flow rate.  Unable to compute Q's because the differential pressure that you entered will cause the throat velocity to exceed 1000 m/s, a velocity for which the calculation is not valid.  The calculation is not valid for supersonic flows.
"d/D will be too small" or "d/D will be too large".   If solving for d.  Unable to compute d; value for d will cause d/D to be out of range of validity.

If your pipe diameter, D, is 2 inch (5.1 cm) or greater, use our Large Diameter Orifice Calculation for Liquids based on ISO 5167.  Or, try the simpler orifice calculation on our Bernoulli page if your parameters are out of range.  The Bernoulli calculation is not as accurate, but won't give "parameter out of range" error messages.

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

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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