E1C09 09/14/2010
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9.14 The pressure drop across a valve through which air flows is expected to be 10 kPa. If this
differential were applied to the two legs of a U-tube manometer filled with mercury, estimate the
manometer deflection. What is the deflection if a 30-degree inclined tube manometer were used?
S Hg ¼ 13.6.
9.15 Estimate the sensitivity (pF/mm) of a capacitance transducer, such as in Figure 9.13, using water as
the dielectric medium. The transducer plates have an overlap area of 8.1 Æ 0.01 mm
2 with an average
gap separation of 1 mm.
9.16 A diaphragm pressure transducer is calibrated against a pressure standard that has been certified by
the National Institute of Standards and Technology (NIST) (b ¼ 0.25 psi). Both the standard and
pressure transducer output a voltage signal, which is to be measured by a voltmeter (b ¼ 5 mV;
resolution: 1mV). A calibration curve fit yields: p ¼ 0.564 + 24.0E Æ 0.5 psi (68%) based on 35
points over the 0- to 100-psi range. When the transducer is installed for its intended purpose,
installation effects are estimated to affect its reading by 0.25 psi (68%). Estimate the uncertainty
associated with a pressure measurement using the installed transducer-voltmeter system.
9.17 A diaphragm pressure transducer is coupled with a water-cooled sensor for high-temperature
environments. Its manufacturer claims that it has a rise time of 10 ms, a ringing frequency of 200 Hz,
and damping ratio of 0.8. Describe a test plan to verify the manufacturer’s specifications. Would this
transducer have a suitable frequency response to measure the pressure variations in a typical fourcylinder engine? Show your reasoning.
9.18 Find the natural frequency of a 1-mm-thick, 6-mm-diameter steel diaphragm to be used for highfrequency pressure measurements near atmospheric pressure. What would be the maximum
operating pressure difference that could be applied? What is the effect of a larger diameter for
this application?
9.19 Estimate the differential pressure limit for a 0.5-mm-thick, 25-mm-diameter steel diaphragm
pressure transducer. v p ¼ 0.32, E m ¼ 200 GPa.
9.20 The pressure fluctuations in a pipe filled with air at 20
C at about 1 atm is to be measured using a
static wall tap, rigid connecting tubing, and a diaphragm pressure transducer. The transducer has a
natural frequency of 100,000 Hz. For a tap and tubing diameter of 3.5 mm, a tube length of 0.25 m,
and a transducer dead volume of 1600 mm
3
, estimate the resonance frequency of the system. What is
the maximum frequency that this system can measure with no more than a 10% dynamic error? Plot
the frequency response of the system.
9.21 What is the sensitivity of a pitot-static tube pressure relative to velocity?
9.22 A pitot-static pressure probe inserted within a large duct indicates a differential pressure of 20.3 cm
H 2 O. What is the velocity measured?
9.23 A tall pitot-static tube is mounted through and 1.5-m above the roof of a performance car such that it
senses the freestream flow. Estimate the static, stagnation, and dynamic pressure sensed at 325 kph, if
(a) the car is moving on a long, straight section of road; and (b) the car is stationary within an opencircuit wind tunnel where the flow is blown over the car.
9.24 The pressure transmission line response equation of Equation 9.23 can be derived by considering
the forces acting on a fluid element within the connecting tubing. Develop a model for the
system measured pressure response based on an applied pressure force, shear resistance force,
and restoring compliance related force through Newton’s momentum (second law) principles. Refer
to Figure 9.31.
Problems 419
15:5:1 Page 419
9.14 The pressure drop across a valve through which air flows is expected to be 10 kPa. If this
differential were applied to the two legs of a U-tube manometer filled with mercury, estimate the
manometer deflection. What is the deflection if a 30-degree inclined tube manometer were used?
S Hg ¼ 13.6.
9.15 Estimate the sensitivity (pF/mm) of a capacitance transducer, such as in Figure 9.13, using water as
the dielectric medium. The transducer plates have an overlap area of 8.1 Æ 0.01 mm
2 with an average
gap separation of 1 mm.
9.16 A diaphragm pressure transducer is calibrated against a pressure standard that has been certified by
the National Institute of Standards and Technology (NIST) (b ¼ 0.25 psi). Both the standard and
pressure transducer output a voltage signal, which is to be measured by a voltmeter (b ¼ 5 mV;
resolution: 1mV). A calibration curve fit yields: p ¼ 0.564 + 24.0E Æ 0.5 psi (68%) based on 35
points over the 0- to 100-psi range. When the transducer is installed for its intended purpose,
installation effects are estimated to affect its reading by 0.25 psi (68%). Estimate the uncertainty
associated with a pressure measurement using the installed transducer-voltmeter system.
9.17 A diaphragm pressure transducer is coupled with a water-cooled sensor for high-temperature
environments. Its manufacturer claims that it has a rise time of 10 ms, a ringing frequency of 200 Hz,
and damping ratio of 0.8. Describe a test plan to verify the manufacturer’s specifications. Would this
transducer have a suitable frequency response to measure the pressure variations in a typical fourcylinder engine? Show your reasoning.
9.18 Find the natural frequency of a 1-mm-thick, 6-mm-diameter steel diaphragm to be used for highfrequency pressure measurements near atmospheric pressure. What would be the maximum
operating pressure difference that could be applied? What is the effect of a larger diameter for
this application?
9.19 Estimate the differential pressure limit for a 0.5-mm-thick, 25-mm-diameter steel diaphragm
pressure transducer. v p ¼ 0.32, E m ¼ 200 GPa.
9.20 The pressure fluctuations in a pipe filled with air at 20
C at about 1 atm is to be measured using a
static wall tap, rigid connecting tubing, and a diaphragm pressure transducer. The transducer has a
natural frequency of 100,000 Hz. For a tap and tubing diameter of 3.5 mm, a tube length of 0.25 m,
and a transducer dead volume of 1600 mm
3
, estimate the resonance frequency of the system. What is
the maximum frequency that this system can measure with no more than a 10% dynamic error? Plot
the frequency response of the system.
9.21 What is the sensitivity of a pitot-static tube pressure relative to velocity?
9.22 A pitot-static pressure probe inserted within a large duct indicates a differential pressure of 20.3 cm
H 2 O. What is the velocity measured?
9.23 A tall pitot-static tube is mounted through and 1.5-m above the roof of a performance car such that it
senses the freestream flow. Estimate the static, stagnation, and dynamic pressure sensed at 325 kph, if
(a) the car is moving on a long, straight section of road; and (b) the car is stationary within an opencircuit wind tunnel where the flow is blown over the car.
9.24 The pressure transmission line response equation of Equation 9.23 can be derived by considering
the forces acting on a fluid element within the connecting tubing. Develop a model for the
system measured pressure response based on an applied pressure force, shear resistance force,
and restoring compliance related force through Newton’s momentum (second law) principles. Refer
to Figure 9.31.
Problems 419