26
| IMPROVING THE ACCURACY OF THE CALCULATED PRESSURE | GEOKON
APPENDIX C.
IMPROVING THE ACCURACY OF THE
CALCULATED PRESSURE
Most vibrating wire pressure transducers are sufficiently linear (±0.2% F.S.) that
the 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% F.S.
This level of accuracy can be recaptured, even where the transducer is
nonlinear, using a second order polynomial expression, which gives a better fit
to the data then does a straight line.
The polynomial expression has the form:
Pressure = AR
2
+ BR + C
EQUATION 8:
Second Order Polynomial Expression
Where:
R is the reading (digits channel B)
A, B, and C are coefficients
Appendix D shows a typical calibration report of a transducer that has fairly
normal nonlinearity. The figure under the "Linearity (%F.S.)" column is
EQUATION 9:
Linearity Calculation
Note:
The linearity is calculated using the regression zero for R
0
shown on the
calibration report.
For example, when P= 420 kPa, G (R
1
– R
0
) =
–
0.1795(6749-9082), gives a
calculated pressure of 418.8 kPa. The error is 1.2 kPa equal to 122 mm of water.
Whereas the polynomial expression gives a calculated pressure of A (6749)
2
+ B
(6749) + 1595.7 = 420.02 kPa and the actual error is only 0.02 kPa or two
millimeters of water.
Note: If the polynomial equation is used it is important that the value of C be
taken in the field following the procedures described in Section 3.2. The field
value of C is calculated by inserting the initial field zero reading into the
polynomial equation with the pressure, P, set to zero.
If the field zero reading is not available, the value of C can be calculated by using
the zero-pressure reading on the calibration report. In the above example the
value of C would be derived from the equation: 0 = A(9074)
2
+ B(9074) from
which C = 1595.7
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.
Calculated Pressure
–
True Pressure
x 100% =
G(R
1
–
R
0
)
–
P
x 100%
Full Scale Pressure
F.S.
