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45
APPENDIX F. IMPROVING THE ACCURACY OF CALCULATED
PRESSURES
Most vibrating wire pressure transducers are sufficiently linear (± 0.2 % FS) that use of the linear
calibration factor satisfies normal requirements. However, it should be noted that the accuracy of
the calibration data, which is dictated by the accuracy of the calibration apparatus, is always ±
0.1 % FS.
This level of accuracy can be recaptured, even where the transducer is non-linear, by the use of a
second order polynomial expression, which gives a better fit to the data then does a straight line.
The polynomial expression has the form:
+ BR + C
2
Pressure = AR
Equation 14 - Second Order Polynomial Expression
Where;
R is the reading (digits)
A, B, and C, are coefficients
Figure 36 shows a calibration report of a transducer that has a comparatively high non-linearity.
G ( R
) -P
The figure under the "Linearity (%FS)" column is:
Calculated Pressure-True Pressure
-R
1
0
x 100%=
x 100%
Full Scale Pressure
F.S.
Equation 15 - Linearity Calculation
For example when P= 40 psi, G (R
- R
) gives a calculated pressure of 39.642 psi. The error is
0
1
0.357 psi or as much as 9.9 inches of water!
+ B (7773) + C =
2
Whereas the polynomial expression gives a calculated pressure of A (7773)
39.996 psi and the actual error is only 0.004 psi or 0.1 inch of water.
Note: If the polynomial equation is used, it is important that the value of C, in the polynomial
equation, be taken in the field. The field value of C is calculated by inserting the initial zero
reading into the polynomial equation with the pressure, P, set to zero. As of 8/2011, Geokon no
longer includes the C coefficient on its calibration reports, ensuring that, to properly use the
polynomial equation, users must calculate a C coefficient.
It should be noted that where changes of water levels are being monitored it makes little
difference whether the linear coefficient or the polynomial expression is used.
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