A method of correcting absolute-air-pressure measurements for small differences in the elevations of pressure taps and pressure transducers has been devised. The variation in air pressure with elevation is well documented; nevertheless, in such disciplines as process control and laboratory experimentation, it has been common practice to account for pressure differences associated only with large differences in elevation along tubes that connect pressure taps to transducers. The emergence of highly accurate multiport pressure-measurement systems, coupled with the need for increasingly accurate pressure measurements, has made it necessary to correct for pressure differences associated with elevation differences as small as a meter or so. The present method can be readily incorporated into future pressure-measurement procedures to provide the necessary corrections; it can also be used to reprocess previous measurements to increase their accuracy.
The method is based on the fact that pressure at the bottom of a measurement tube will be higher than the pressure at the top due to weight of the column of air in the tube. It is assumed that the fluid (air) is at a static equilibrium and that the temperature and the gravitational acceleration do not vary significantly over the measured height. The resulting equation for correcting a pressure reading is
P = P0e–(gρ0/P0)y
where P is the pressure at the pressure tap (the corrected or actual pressure, which one seeks), P0 is the reading of the pressure transducer, g is the gravitational acceleration, ρ 0is the known density of air at the known temperature and pressure P0, and y is the difference in elevation from the transducer to the pressure tap. At 20°C, g = 9.8 m/s², ρ 0= 1.205 kg/m³, and P0 = 1.01325 × 105Pa; therefore,
P = P0e(–1.16546x10-4)y
The method was tested in a series of measurements in air at a temperature of 70 ± 5°F (≈21± 3°C) on two commercial pressure gauges at various pressures and elevations. After corrections for biases between the two gauges, the results (see figure) indicate that the predicted and measured variations of pressure with height agree with each other to within 0.001 psi (≈7 Pa).
This work was done by Joseph W. Panek and Mark R. Sorrells of Lewis Research Center. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com under the Physical Sciences category, or circle no. 127 on the TSP Order card in this issue to receive a copy by mail ($5 charge).
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