Analysis of hydraulic piston gauge calibration data by the development of linear and quadratic equations

In earlier papers it has been shown that an apparent pressure dependence of effective area of gas piston gauges and ball gauges was due to non-constancy of effective area as conventionally defined; the ratio of F, the force due to the load of weights on the piston, to P, the pressure at the gauge, was not in general constant for these devices. The relationship between P and F was generally much better represented by an equation of the form P = a + bF derived from linear least squares analysis of calibration data. To investigate whether the addition of a quadratic term, cF2, would improve the agreement of calculated values of P with calibration values of P, calibration data were collected for 6 oil-operated gauges (8 points in each data set). For each data set, the data were analyzed using a least squares regression technique. For 5 of the 6 gauges, the agreement of calculated with calibration values of P was significantly improved by the development of a linear or a quadratic equation relating P to F.