E1C09 09/14/2010
15:4:53 Page 386
Example 9.4
A deadweight tester indicates 100.00 lb/in.
2 (i.e., 100.00 psi), at 70
F in Clemson, SC (f ¼ 34
,
z ¼ 841 ft). Manufacturer specifications for the effective piston area were stated at 72
F so that
thermal expansion effects remain negligible. Take g air ¼ 0.076 lb/ft
3 and g mass ¼ 496 lb/ft
3 . Correct
the indicated reading for known errors.
KNOWN p i ¼ 100:00 psi; z ¼ 841 ft; f ¼ 34
ASSUMPTION Systematic error corrections for altitude and latitude apply
FIND p
SOLUTION The corrected pressure is found using Equation 9.8. From Equation 9.9, the
correction for buoyancy effects is
e 2 ¼ Àg air =g masses ¼ À0:076=496 ¼ À0:000154
The correction for gravity effects is from Equation 9.6a:
e 1 ¼ Àð2:637 Â 10
À3 cos2f þ 9:6 Â 10
À8
z þ 5 Â 10
À5
Þ
¼ Àð0:0010 þ 8 Â 10
À5
þ 5 Â 10
À5
Þ ¼ À0:001119
From Equation 9.8, the corrected pressure becomes
p ¼ 100:00 Â ð1 À 0:000154 À 0:001119Þ lb=in:
2
¼ 99:87 lb=in:
2
COMMENT This amounts to correcting an indicated signal for known systematic errors. Here
that correction is % 0.13%.
9.4 PRESSURE TRANSDUCERS
A pressure transducer is a device that converts a measured pressure into a mechanical or electrical
signal. The transducer is actually a hybrid sensor-transducer. The primary sensor is usually an elastic
element that deforms or deflects under the measured pressure relative to a reference pressure. Several
common elastic elements used, as shown in Figure 9.9, include the Bourdon tube, bellows, capsule, and
diaphragm. A secondary transducer element converts the elastic element deflection into a readily
measurable signal such as an electrical voltage or mechanical rotation of a pointer. There are many
methods available to perform this transducer function, and we examine a few common ones.
General categories for pressure transducers are absolute, gauge, vacuum, and differential.
These categories reflect the application and reference pressure used. Absolute transducers have a
sealed reference cavity held at a pressure of absolute zero, enabling absolute pressure measurements. Gauge transducers have the reference cavity open to atmospheric pressure and are intended
to measure above or below atmospheric pressure or both. Differential transducers measure the
difference between two applied pressures. Vacuum transducers are a special form of absolute
transducer for low-pressure measurements.
Pressure transducers are subject to some or all of the following elemental errors: resolution,
zero shift error, linearity error, sensitivity error, hysteresis, noise, and drift due to environmental
temperature changes. Electrical transducers are also subject to loading error between the transducer
output and its indicating device (see Chapter 6). Loading errors increase the transducer nonlinearity
386 Chapter 9 Pressure and Velocity Measurements
15:4:53 Page 386
Example 9.4
A deadweight tester indicates 100.00 lb/in.
2 (i.e., 100.00 psi), at 70
F in Clemson, SC (f ¼ 34
,
z ¼ 841 ft). Manufacturer specifications for the effective piston area were stated at 72
F so that
thermal expansion effects remain negligible. Take g air ¼ 0.076 lb/ft
3 and g mass ¼ 496 lb/ft
3 . Correct
the indicated reading for known errors.
KNOWN p i ¼ 100:00 psi; z ¼ 841 ft; f ¼ 34
ASSUMPTION Systematic error corrections for altitude and latitude apply
FIND p
SOLUTION The corrected pressure is found using Equation 9.8. From Equation 9.9, the
correction for buoyancy effects is
e 2 ¼ Àg air =g masses ¼ À0:076=496 ¼ À0:000154
The correction for gravity effects is from Equation 9.6a:
e 1 ¼ Àð2:637 Â 10
À3 cos2f þ 9:6 Â 10
À8
z þ 5 Â 10
À5
Þ
¼ Àð0:0010 þ 8 Â 10
À5
þ 5 Â 10
À5
Þ ¼ À0:001119
From Equation 9.8, the corrected pressure becomes
p ¼ 100:00 Â ð1 À 0:000154 À 0:001119Þ lb=in:
2
¼ 99:87 lb=in:
2
COMMENT This amounts to correcting an indicated signal for known systematic errors. Here
that correction is % 0.13%.
9.4 PRESSURE TRANSDUCERS
A pressure transducer is a device that converts a measured pressure into a mechanical or electrical
signal. The transducer is actually a hybrid sensor-transducer. The primary sensor is usually an elastic
element that deforms or deflects under the measured pressure relative to a reference pressure. Several
common elastic elements used, as shown in Figure 9.9, include the Bourdon tube, bellows, capsule, and
diaphragm. A secondary transducer element converts the elastic element deflection into a readily
measurable signal such as an electrical voltage or mechanical rotation of a pointer. There are many
methods available to perform this transducer function, and we examine a few common ones.
General categories for pressure transducers are absolute, gauge, vacuum, and differential.
These categories reflect the application and reference pressure used. Absolute transducers have a
sealed reference cavity held at a pressure of absolute zero, enabling absolute pressure measurements. Gauge transducers have the reference cavity open to atmospheric pressure and are intended
to measure above or below atmospheric pressure or both. Differential transducers measure the
difference between two applied pressures. Vacuum transducers are a special form of absolute
transducer for low-pressure measurements.
Pressure transducers are subject to some or all of the following elemental errors: resolution,
zero shift error, linearity error, sensitivity error, hysteresis, noise, and drift due to environmental
temperature changes. Electrical transducers are also subject to loading error between the transducer
output and its indicating device (see Chapter 6). Loading errors increase the transducer nonlinearity
386 Chapter 9 Pressure and Velocity Measurements