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Flow Measurements using Orifices

It is commonly known that the flow of a gas relates to the measured pressure difference (DeltaP) over an orifice using the Square Root (SQRT).

In most cases the flow calculated formed by the Orifice Factor times SQRT(dP) for simplicity is sufficient.

Flow = Factor * SQRT( dP )

However for more critical requirements this is not.
Comparison of Totalized Flows to Displacement Metering for financial or fiscal purposes do not match.
Summing of individual flows compared to the total flow does not match either.

To get the flow calculation right several things has to be observed;
- Temperature and Pressure compensation
- Placement of Orifice

Temperature and Pressure is mostly measured at a central (convenient) location. Assumed is P&T at the orifice to be equal to this centralized reading.
State of the art dP Cells can have these readings internally.

However the Orifice has been designed at a given temperature and pressure whilst it is operating at a different temperature and pressure.
The formula used to calculate the flow needs to be corrected by the SQRT of P and T of the operating conditions (Po,To) compared to the design conditions (Pd,Td).

Flow(d) = Factor* SQRT( (Po*Td)/(Pd*To) ) * SQRT( dP )

P&T used are absolute values.

This will compensate for the changed molecular behavior at different conditions since the DeltaP relates to the SQRT of the density.

Flows for comparison need to be calculated to a reference Temperature and Pressure. Often the Normal Temperature and Pressure ( 273.15K and 101325 Pa) are used.

If the orifice is designed at the required reference P and T ( Pr,Tr) then the outcome is correctly compensated.
If this is not the case then further compensation is required using the IdealGasLaw ( PV/T = c).

Flow(r) = Flow(d) * (Pd/Pr ) * (Tr/Td)

If the above is not adhered to then errors of 10 to 20 % are quite normal.
When operating conditions are far from the design conditions then the error may go up to 100%!

Lack of space and costs will influence the straight pipe length before and after the orifice to be shorter than 20 times the pipe diameter.
Even piping diameter changes at the orifice location.
Faults in obtained results can easily be of magnitude of 10% which is commonly accepted but it also may lead to an attitude of carelessness.
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