n order to measure the flow rate in a 2 m _ 2 m air
conditioning duct, an engineer uses a pitot-static
probe to measure dynamic head. The duct is
divided into nine equal rectangular areas with the
pressure measured at the center of each. Based on
the resu
American Society of Mechanical Engineers (ASME), PTC 19.21987: Pressure
Measurement,
ASME International, New York, 1987.
2. Brombacher, W. G., D. P. Johnson, and J. L. Cross, Mercury Barometers and
Manometers,
National Bureau Standards Monograph 8, 1960.
frequency response. The frequency response can be found directly by
applying a constant amplitude
periodic input signal and varying its frequency. A flush-mounted transducer
places the sensor in
direct contact with the fluid at the measurement site. Becau
Then,
Mf 5 1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 _ f =f n
2
h i2
2z f =f n
2
r 1:03
With a dynamic error of only about 3%,
However, because point 2 is the stagnation point, U2 0, and
p2
pt
p1
rU2
1=2 9:17
Hence, it follows that p2 > p1 by an amount equal to pv rU21
=2, called the dynamic pressure, an
amount equivalent to the kinetic energy per unit mass of the flow as it
m
Convert the following gauge pressures into absolute pressure relative to one
standard atmosphere:
a. _12.0 psi
b. 200 mm Hg
c. 10.0 kPa
d. 7.62 cm H2O
9.3 A water-filled manometer is used to measure the pressure in an air-filled
tank. One leg of the
manom
Are commonly used for industrial flow monitoring, where a fast dynamic
response is desirable. There
is a natural upper frequency limit on a cylindrical sensor of diameter d that is
brought about by the
natural oscillation in the flow immediately downstrea
A 10cm diameter, square-edged orifice plate is used to meter the
steady flow of 16_C water through
an 20-cm pipe. Flange taps are used and the pressure drop
measured is 50 cm Hg. Determine the pipe
flow rate. The specific gravity of mercury is 13.5.
KNOWN
FIND U
SOLUTION Using Equation 9.51,
Ul
2 sin u=2
fD
632:8 _ 10
_9 m
2 sin 11
_=2
_
1:41 _ 106 Hz
_
4:655 m=s
Particle Image Velocimetry
Particle image velocimetry (PIV) measures the full-field instantaneous
velocities in a planar cross
section of a fl
digital (A/D) converter (accuracy: 2 LSB). In testing at 180 km/hr, the
maximum average pressure
difference between the rear deck and underbody is about 8 cm H2O _ 0.10
cm H2O (95%). The
engineer is asked two questions: (1) Will increasing the resolution
Bellows and Capsule Elements
A bellows sensing element is a thin-walled, flexible metal tube
formed into deep convolutions and
sealed at one end (Fig. 9.9). One end is held fixed and pressure is
applied internally. A difference
between the internal and ex
common laboratory standard for the calibration of pressuremeasuring devices over the
pressure range from 70 to 7 _ 107 N/m2 (0.01 to 10,000 psi). A
deadweight tester, such as
that shown in Figure 9.8, consists of an internal chamber filled
with an oil and
By using semiconductor technology in pressure transducer
construction, we now have a variety
of very fast, very small, highly sensitive strain gauge diaphragm
transducers. Silicone piezoresistive
strain gauges can be diffused into a single crystal of sili
Example 9.2
A high-quality U-tube manometer is a remarkably simple instrument to make.
It requires only a
transparent U-shaped tube, manometer fluid, and a scale to measure
deflection. While a U-shaped
glass tube of 6mm or greater internal bore is preferr
compliance, the tubing is removed at the wall tap, filled with water, and
purged of any residual air.
The transducer output is noted. Using a syringe, 1 mL of water is then added
to the system and the
corresponding measured pressure increases by 100 mm Hg
R
RL
Lf
Pm
Cvp
Pa
Ea C Em
(a)
(b)
Figure 9.22 An equivalent lumped parameter
network of the pressure transmission line model of
Figure 9.21 using an electrical analogy.
Substituting Equations 9.18 to 9.20 into Equation 9.22 gives the working
system respon
d 6 cm p1
93:7 kPa abs
b 0:4 T1 20
_
C 293 K
H 250 cm H2O
Properties (found in Appendix B)
Air : v 1:0 _ 10
_5 m2/s
Water: rH2O
999 kg/m3
ASSUMPTIONS Treat air behavior as an ideal gas p rRT
FIND Volume flow rate, Q
SOLUTION The orifice flow rate is fou
change the vapor pressure, for temperature and altitude effects
on the weight of mercury, and for
deviations from standard gravity (9.80665 m/s2 or 32.17405
ft/s2). Correction curves are provided
by instrument manufacturers.
Barometers are used as local s
Interpretation in strongly dynamic flows can be complicated
(17,25). Hot-film sensors are less
fragile and less susceptible to contamination than hot-wire
sensors. Probe blockage is not significant
in large ducts and away from walls. Thermal anemometers a
A deadweight tester indicates 100.00 lb/in.2 (i.e., 100.00 psi), at 70_F in
Clemson, SC (f 34_,
z 841 ft). Manufacturer specifications for the effective piston area were
stated at 72_F so that
thermal expansion effects remain negligible. Take gair 0.076 l
If we neglected the correlated effect of the pump oscillation, we would
instead be tempted to
calculate
sDp
qDp
qp1
s_p1
_ _2
qDp
qp2
s_p2
_ _2
" #1=2
0:899 kPa
which overstates the random standard uncertainty significantly and is wrong.
COMMENT Equati
Indicated by the probe? Local atmospheric pressure at 7000 mis
approximately 45 kPa, which results
in an air density of 0.66 kg/m3. Discuss additional factors that might affect
the accuracy of the static
temperature reading.
8.29 Consider the typical cons
KNOWN Fluid (of specific gravity S and specific weight g)
Manometer fluid (of specific gravity Sm and specific weight gm)
ASSUMPTION Densities of the fluids remain constant.
FIND Q f H
SOLUTION Equation 10.12 provides a relationship between flow rate and
A T type thermopile is used to measure temperature difference across
insulation in the ceiling of a
residence in an energy monitoring program. The temperature difference
across the insulation is used
to calculate energy loss through the ceiling from the r
Allowing measurements ranging from the order of 0.001mm of manometer
fluid to several
meters.
The U-tube manometer in Figure 9.5 consists of a transparent tube filled with
an indicating
liquid of specific weight gm. This forms two free surfaces of the man
Capsule displacement. The LVDT design has a high sensitivity and is
commonly found in pressure
transducers rated for low pressures and for small pressure ranges, such as
zero to several
hundred mm Hg absolute, gauge, or differential.
Diaphragms
An effecti
considering recovery and radiation errors, estimate the possible value for
total error in the
indicated temperature. Discuss whether this estimate of the measurement
error is conservative,
and why or why not. The heat-transfer coefficient may be taken as
Ceramic tube that houses the lead wires. A hot-film sensor usually
consists of a thin (2 mm) platinum
or gold film deposited onto a glass substrate and covered with a
high thermal conductivity coating.
The coating acts to electrically insulate the film an
It introduces a large permanent pressure loss, Dp
loss
rghL, into the flow system. The pressure
drop is illustrated in Figure 10.4 with the pressure loss estimated from Figure
10.7.
Rudimentary versions of the orifice plate meter have existed for several
measurement position. There are several options in selecting measuring
positions for differentshaped
ducts, and such details are specified in available engineering test standards
(1, 2, 4, 15). The
simplest method is to divide the flow area into smaller e