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.
Figure
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.
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.,
|
(1) |
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
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
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.
