Emerson Daniel 3414 - Pressure-Effect Expansion Correction

30 Pressure-effect expansion correction
Section 4: Flow measurement 3410 Series Gas Ultrasonic Meters Operations Manual
January 2018 3-9000-777 Rev E
4.5.3 Pressure-effect expansion correction
The meter is capable of correcting the raw volumetric flow rate for the effect of pipe expansion
due to pressure changes. Note that for the pressure-effect expansion correction factor to be
calculated, the correction must be enabled (via the
EnableExpCorrPress data point) and the flow-
condition pressure must be available (i.e., the
EnablePressureInput data point must be set to
‘Live’(1) or ‘Fixed’(2), see Section 5.10.3). The pressure-effect calculation is shown in Equation
4-10. If the pressure-effect expansion correction factor is not calculated, it is set to 1.0.
Equation 4-10 Pressure-effect expansion correction
where
Equation 4-11 Pressure-effect strain per unit stress
where
= expansion correction factor due to pressure (dimensionless)
(ExpCorrPressure)
= pipe strain per unit stress (MPaa-1) (StrainPerUnitStress) calculated
as shown in Equation 4-8
= flow-condition absolute pressure (MPaa) (AbsFlowPressure)
calculated as shown in Equation 4-15
= reference absolute pressure (MPaa) (0.101325 MPaa)
= pipe strain per unit stress (MPaa-1) (StrainPerUnitStress)
= outside diameter of the meter or pipe (m) (PipeOutsideDiameter)
= inside diameter of the meter or pipe (m) (PipeDiam)
= Poisson’s Ratio (dimensionless) (PoissonsRatio)
= Young’s Modulus of elasticity (MPaa) (YoungsModulus)
ExpCorr
P
13β¥P
abs f,
P
ref
–()¥[]+=
ExpCorr
P
β
P
abs f,
P
ref
β
D
out
2
1 υ+()D
in
2
12υ–()+
ED
out
2
D
in
2
–


Þ
-----------------------------------------------------------------------------------=
β
D
out
D
in
υ
E