Whirling Catheter Method to Calibrate Low Pressure Sensors

Randall D. Peters

Department of Physics
1400 Coleman Ave.
Mercer University
Macon, Georgia 31207

It can be difficult to calibrate a highly sensitive pressure sensor using the techniques that are commonly employed with higher pressure instruments. Additionally in the case of a manometer, the fluid required for its operation is cause for inconvenience. In the whirling catheter method described in this article, the only items needed to simply perform an accurate calibration are: (i) a length of small-diameter rubber tubing about 2 m in length, (ii) a meter-stick, and (iii) a stopwatch-along with the electronics (including meter) to indicate the output voltage of the pressure sensor.

One end of the catheter is connected to the pressure sensor. The other end, which is open to the air, is swung in a horizontal overhead circle, as illustrated in Fig. 1. As true of all highly sensitive instruments known to the author, this requires that the sensor be operated in a differential pressure mode, with the reference port to the diaphragm being open to room air.

To begin calibration, one chooses an operating radius R (such as 0.75 m); which determines the point from the open end of the tubing where it is to be grasped between thumb and forefinger. With this point defining the ``center'' of the circle, the tubing is whirled overhead as if twirling a tethered ball.

The output voltage from the instrument is visually monitored- most readily by observing the needle of an analog rather than the numerals of a digital meter. While observing the needle, the speed of the tip v is maintained at a near constant value by manually adjusting the angular rate of motion. For example, if the voltage begins to fall slightly, then the dipping of the voltmeter needle shows that the tubing needs to be swung a little faster. With a little practice, one with average hand-eye coordination can by this feedback arrangement maintain the voltage constant to better than 10% full-scale reading of the meter, for R in the range from 0.5 - 1.0 m. A single observer can both control the speed of the catheter and also operate a stopwatch to measure the period of the motion. To reduce reaction time errors, it is convenient to measure through ten rotations of the catheter, as opposed to the challenge of a single rotation.

1  Relationship between v and the pressure differential P

Consider a differential length of air in the tubing dr at distance r from the center of the circle. For inner tubing cross-sectional area A, the differential mass of air contained in dr is given by rAdr; where r is the density of air. For angular rate, w  =  v/R, the centripetal force required to hold the differential mass in place is given by dF  =  rA(v2/R2)dr. Dividing this force by A yields the pressure difference between the ends of the differential mass. Integrating this expression for the pressure difference from r  =  0 to r  =  R yields the amount of pressure reduction from the open end of the tube to the center of the tube, where the value of the pressure is the same as that being measured by the sensor. The result turns out to be the same as the kinetic term in Bernoulli's equation; i.e.,

P  =   1

2  Results

Sample results of the use of this calibration technique are shown in Figures 2 and 3, where in both cases R  =  1.0 m and the density of air was set at r  =  1.29 kg/m3.
Figure 2. Calibration data, Pasco Low Pressure Sensor.

The Pasco sensor is specified to have a sensitivity of 1.0 mV/Pa rather than the measured 1.4 mV/Pa. Although this 40% difference is large, it may be partly due to nonlinearity and the fact that the pressures used for calibration are more than an order of magnitude smaller than the usual operating range of the instrument (as used in one of the Mercer University laboratories [] that demonstrates properties of a heat engine). It was noted, however, that several different Pasco units were observed to differ significantly from one another in the amount of zero-offset, which in all cases should have been zero for the conditions in which each was evaluated.

Figure 3. Calibration data, SDC Pressure Sensor.

The data of Fig. 3 were obtained using a pressure sensor of the type invented and patented by the author []. Using a thin aluminized mylar diaphragm and a doubly differential capacitive detector arrangement, the SDC pressure sensor is roughly 130 times more sensitive than the Pasco sensor, since the data shown in Fig. 3 were obtained with the electronics attenuated by a factor of 6-to be compatible with the voltmeter.


The laboratory writeup for this experiment can be found on the web at http://physics.mercer.edu/labs.
Randall D. Peters, Symmetric differential capacitive pressure sensor, Rev. Sci. Instrum. 64(8), 2256-2261 (1993).

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On 11 Jul 2000, 16:05.