E1C09 09/14/2010
15:4:52 Page 378
SOLUTION The absolute pressure is found directly from Equation 9.2. Using the pressure at
the free surface as the reference pressure and the datum line for h 0 , the absolute pressure must be
p abs ðhÞ ¼ 1:0132 Â 10
5 N=m
2
þ
997:4 kg=m
3
ð
Þ9:8 m=s
2
ð
Þ10 m
ð
Þ
1 kg-m=N-s 2
¼ 1:9906 Â 10
5 N=m
2 abs
This is equivalent to 199.06 kPa abs or 1.96 atm abs or 28.80 lb/in.
2 abs or 1.99 bar abs.
The pressure can be described as a gauge pressure by referencing it to atmospheric pressure.
From Equation 9.1,
pðhÞ ¼ p abs À p 0 ¼ gh
¼ 9:7745 Â 10
4 N=m
2
which is also equivalent to 97.7 kPa or 0.96 atm or 14.1 lb/in.
2 or 0.98 bar.
We can express this pressure as an equivalent column of liquid,
h ¼
p abs À p 0
rg
¼
1:9906 Â 10
5
À
Á À 1:0132 Â 10
5
À
Á
N=m
2
998:2 kg=m 3
ð
Þ9:8 m=s 2
ð
Þ1 N-s 2 =kg-m
ð
Þ
¼ 10 m H 2 O
9.3 PRESSURE REFERENCE INSTRUMENTS
The units of pressure can be defined through the standards of the fundamental dimensions of mass,
length, and time. In practice, pressure transducers are calibrated by comparison against certain
reference instruments, which also serve as pressure measuring instruments. This section discusses
several basic pressure reference instruments that can serve either as working standards or as
laboratory instruments.
McLeod Gauge
The McLeod gauge, originally devised by Herbert McLeod in 1874 (3), is a pressure-measuring
instrument and laboratory reference standard used to establish gas pressures in the subatmospheric
range of 1 mm Hg abs down to 0.1 mm Hg abs. A pressure that is below atmospheric pressure is also
called a vacuum pressure. One variation of this instrument is sketched in Figure 9.3a, in which the
gauge is connected directly to the low-pressure source. The glass tubing is arranged so that a sample
of the gas at an unknown low pressure can be trapped by inverting the gauge from the sensing
position, depicted as Figure 9.3a, to that of the measuring position, depicted as Figure 9.3b. In this
way, the gas trapped within the capillary is isothermally compressed by a rising column of mercury.
Boyle’s law is then used to relate the two pressures on either side of the mercury to the distance of
travel of the mercury within the capillary. Mercury is the preferred working fluid because of its high
density and very low vapor pressure.
At the equilibrium and measuring position, the capillary pressure, p 2 , is related to the unknown
gas pressure to be determined, p 1 , by p 2 ¼ p 1 ð8 1 =8 2 Þ where 8 1 is the gas volume of the gauge in
Figure 9.3a (a constant for a gauge at any pressure), and 8 2 is the capillary volume in Figure 9.3b.
But 8 2 ¼ Ay, where A is the known cross-sectional area of the capillary and y is the vertical length of
378 Chapter 9 Pressure and Velocity Measurements
15:4:52 Page 378
SOLUTION The absolute pressure is found directly from Equation 9.2. Using the pressure at
the free surface as the reference pressure and the datum line for h 0 , the absolute pressure must be
p abs ðhÞ ¼ 1:0132 Â 10
5 N=m
2
þ
997:4 kg=m
3
ð
Þ9:8 m=s
2
ð
Þ10 m
ð
Þ
1 kg-m=N-s 2
¼ 1:9906 Â 10
5 N=m
2 abs
This is equivalent to 199.06 kPa abs or 1.96 atm abs or 28.80 lb/in.
2 abs or 1.99 bar abs.
The pressure can be described as a gauge pressure by referencing it to atmospheric pressure.
From Equation 9.1,
pðhÞ ¼ p abs À p 0 ¼ gh
¼ 9:7745 Â 10
4 N=m
2
which is also equivalent to 97.7 kPa or 0.96 atm or 14.1 lb/in.
2 or 0.98 bar.
We can express this pressure as an equivalent column of liquid,
h ¼
p abs À p 0
rg
¼
1:9906 Â 10
5
À
Á À 1:0132 Â 10
5
À
Á
N=m
2
998:2 kg=m 3
ð
Þ9:8 m=s 2
ð
Þ1 N-s 2 =kg-m
ð
Þ
¼ 10 m H 2 O
9.3 PRESSURE REFERENCE INSTRUMENTS
The units of pressure can be defined through the standards of the fundamental dimensions of mass,
length, and time. In practice, pressure transducers are calibrated by comparison against certain
reference instruments, which also serve as pressure measuring instruments. This section discusses
several basic pressure reference instruments that can serve either as working standards or as
laboratory instruments.
McLeod Gauge
The McLeod gauge, originally devised by Herbert McLeod in 1874 (3), is a pressure-measuring
instrument and laboratory reference standard used to establish gas pressures in the subatmospheric
range of 1 mm Hg abs down to 0.1 mm Hg abs. A pressure that is below atmospheric pressure is also
called a vacuum pressure. One variation of this instrument is sketched in Figure 9.3a, in which the
gauge is connected directly to the low-pressure source. The glass tubing is arranged so that a sample
of the gas at an unknown low pressure can be trapped by inverting the gauge from the sensing
position, depicted as Figure 9.3a, to that of the measuring position, depicted as Figure 9.3b. In this
way, the gas trapped within the capillary is isothermally compressed by a rising column of mercury.
Boyle’s law is then used to relate the two pressures on either side of the mercury to the distance of
travel of the mercury within the capillary. Mercury is the preferred working fluid because of its high
density and very low vapor pressure.
At the equilibrium and measuring position, the capillary pressure, p 2 , is related to the unknown
gas pressure to be determined, p 1 , by p 2 ¼ p 1 ð8 1 =8 2 Þ where 8 1 is the gas volume of the gauge in
Figure 9.3a (a constant for a gauge at any pressure), and 8 2 is the capillary volume in Figure 9.3b.
But 8 2 ¼ Ay, where A is the known cross-sectional area of the capillary and y is the vertical length of
378 Chapter 9 Pressure and Velocity Measurements