The document discusses various methods for measuring pressure, including diaphragms, bourdon tubes, capsules, and different transduction methods like potentiometric, strain gauge, variable reluctance, LVDT, variable capacitance, and piezoelectric devices. It also covers topics like pressure multiplexers, calibration using dead weight testers, and force balance transducers using feedback principles. Piezoelectric transducers use materials that generate voltage under mechanical stress, with quartz and ceramics being common choices.

1. MEASUREMENT OF PRESSURE
Module -5 Measurement of Pressure:
• Introduction,
• Diaphragms, Other elastic elements,
• Transduction methods –
• Potentiometric device,
• Strain gauge transducer ,
• Variable reluctance,
• LVDT type,
• Variable capacitance device (principle & working, no derivation),
• Force balance transducer with analysis,
• Thin-film pressure transducers,
• Piezoelectric pressure transducer,
• Pressure multiplexer,
• Pressure calibration.

2. Module -5
Transducers/Instruments for Measurement of Pressure: Introduction, Diaphragms,
Other elastic elements, Transduction methods – potentiometric device, strain gauge
transducer, variable reluctance, LVDT type, variable capacitance device (principle &
working, no derivation), force balance transducer with analysis, Thin film pressure
transducers, Digital pressure transducer, Piezoelectric pressure transducer, Pressure
multiplexer, Pressure calibration.

3. Pressure : ( 1 atmospheric pressure =14.7 Psi )
• Force acting per unit area N/m2
• Measurement involved can be static or dynamic.
• Pressure is a compressive stress exerted uniformly in all directions
(considering fluid (can be liquid or Gas) pressure)
• Pressure transducers can be classified as
1. Gravitational type ( Manometer is the simplest device)
2. Elastic type ( Pressure exert force over area of elastic device
example : Diaphragm , Capsule, Bellows, Bourdon tube )
• With respect to applied pressure Elastic device output is
displacement or strain developed and it is measured by electrical
sensor

4. • The transduction principles (involves) displacement measurements
with resistive (strain gauge), inductive, and capacitive principles or
measurement of change in natural resonance frequency of a
stretched member.
• Accordingly they are classified as potentiometric, bonded and
unbonded strain gauge, piezoresistive, inductive, LVDT, capacitive,
piezoelectric types.
DIAPHRAGMS : (Materials used Elastomers and polyamide, polyester,
polyacrylamide, and rayon staple fiber fabrics)
• Common pressure sensing member
• Consists of a circular plate & fastened (connected) at its periphery.
• Structure can be flat or corrugated.
• Used when high Accuracy required and provide good dynamic
response.

6. • Main characteristics of diaphragms are
1. Ruggedness
2. Stability
3. Reliability
4. Low Hysteresis
5. Low creep
6. Good dynamic response
• Diaphragms are made from
1. Metal alloys
2. Bronze
3. Phosphor bronze
4. Stainless steel

7. Diagram shown below is not for exam

8. • Flat diaphragms can be designed to have high natural
frequencies and as such are ideally suited for dynamic
measurements.
• Due to imperfections in the material and in the
manufacturing process, the Pressure deflection curve can
have certain nonlinear characteristics and other errors, such
as hysteresis.
• To avoid this, the diaphragm is usually stretched radially and
then clamped.
• Deflections of the diaphragm of small magnitude. are mainly
due to bending deformations only.

9. • With increased load on the diaphragm, when the deflection
reaches the value roughly equal to its thickness, tensile stresses
also develop along with bending and the deflection characteristics
become non-linear.
• For larger deflection requirements, corrugated diaphragms are
ideally suited.
Corrugated Diaphragms:
• corrugated diaphragms are also encountered in pressure
measurements, especially where larger deflections are required
than those normally obtained with flat diaphragms.
• Diaphragm profiles take different forms, such as sawtooth.
trapezoidal, and sinusoidal shapes, as shown in Fig. 7.3

11. Capsule :
• A capsule consists of two identical annular corrugated metal diaphragms
sealed together at the periphery to obtain a shell like enclosure.
• One of the diaphragms is provided with a central reinforced port to admit the
pressure to be measured, and the other is linked to a mechanical member.
• The displacement of this ,member is proportional to the difference of the
inner and outer pressures.
• The seal is made by brazing, soldering, or electron-beam welding, and the
whole capsule is heat treated to relieve the stresses built up during welding
and subsequent cooling.
• The factors influencing the deflections of the capsule are the same as those
for the diaphragms.

12. Bourdon Tube:
• The bourdon tube is a curved or twisted metallic tube having an
elliptical cross-section, and scaled at one end.
• The tube tends to straighten out on the application of pressure, and
the angular deflection of the free end is taken as a measure of the
pressure.
• The deflection sensitivity is a function of the aspect ratio of the
tube cross-section.
• The main advantages are high sensitivity and good repeatability.

13. • The C-shaped tube has a total angle of curvature of 180 to 270°, and
the angular Deflection (output) is normally measured with a
mechanical pointer moving over a calibrated scale or with a
potentiometric or L VDT transducer.
• The deflection of a bourdon tube varies
• With the ratio of its major to minor cross-sectional axis,
• Tube length,
• Difference between the internal and external pressures,
• Radius of curvature, and
• Angle of twist.
• It also varies inversely with the tube wall thickness and the
modulus of elasticity of the material used.

14. • The angular deflection of the helical-type and C-type
bourdon tubes can be expressed by the equation.
Where Ø = angle of rotation of the tip of the tube.
Ø0 = angle of tube/total angle of helix
P = pressure in pascals
r = radius of the tube/helix in meters
t = wall thickness in meters
E = Young's modulus of material
b = minor axis of the tube, measured from the middle of one
wall to the middle of the other wall, in meters.

15. PRESSURE MULTIPLEXER :
Problem ?
• In certain experiments, such as wind-tunnel testing of models,
a simultaneous measurement of pressures at various locations is
required for detailed investigations.
• If a pressure transducer is individually used at each pressure
point, the entire equipment tends to be large, expensive, and
cumbersome, since each sensor needs a separate balance
control, zero control and signal conditioner.
ANS : Hence for simultaneous measurement of pressure at various
location pressure multiplexer is used

17. • However, by incorporating a pressure-transfer valve, the.
pressures at a large number of points can be measured
with a single transducer. A typical pressure multiplexer
system using a scanivalve arrangement is illustrated in Fig.
7.21.
• The scanivalve with 24 or 48 ports is driven either by a
motor or solenoid, and connects a small unbonded strain
gauge type pressure transducer to the pressure ports
sequentially, one at a time.

18. • The signal from the transducer is processed with a
suitable signal conditioner and converted equivalent
value that is analog / digital printed out or displayed in
required units.
• The transducer is housed within the body of the valve
itself to keep the transfer volume minimum, thereby
ensuring good response even at low pressure levels.
• The maximum speed of sampling can be as high as 48
ports per minute.

19. • In some experiments it may be necessary to freeze several
unknown pressure values simultaneously and then
measure the pressure magnitudes later for this, cut-off
valves with storage tubes are incorporated ahead. of the
pressure multiplexer.
• The system is extensively used for many aeronautical and
allied measurements.

20. PRESSURE CALIBRATION: ( pressure gauge calibration)
• A basic standard calibrating device widely used under laboratory
conditions is the hydraulic or pneumatically-operated dead weight
tester.
• Range is from 50 to 50x 106 Pascal's in steps of 0.1% with
an uncertainty of 0.01 to 0.5%.
• The dead-weight tester consists of two accurately
machined cylinders, honed to micron tolerances, inserted
into two closed and known cross-sectional areas coupled
together to a reservoir, as shown in Fig. 7 .22.

22. • One of the cylinders is fitted with a close-fitting precision
piston with a top platform where accurately known weights,
In the form of discs can be loaded.
• The transducer under test is connected to the other
cylinder.
• The fluid pressure is then gradually applied until the force is
large enough to just lift the precision piston-weight
combination.
• When the piston is floating freely, the piston gauge with
arranged weights is in equilibrium with the pressure
developed in the cylinder.

23. • The relationship can be expressed as
F =PA , where F is the equivalent force of the
piston weight combination ( Total mass X acceleration due
to gravity)
P is the pressure and A is the area of the piston
cylinder combination.
• By changing the weights appropriately, the sensor can be
calibrated to a high order of accuracy.
• For high-precision measurements, the air weight testers
are preferred which offer an accuracy as high as 0.01 %.

24. FORCE-BALANCE TRANSDUCER :
• The performance of the transducers based on the measurement of
deflection of elastic elements, such as, diaphragms, membranes,
capsules or bellows is dependent on the long term stability
• characteristics of elastic elements, such as HYSTERESIS, CREEP degrade
the accuracy.
• For higher sensitivity, these elements must have low stiffness and/or
large area but the size of transducer becomes big and affected by
vibrations.
• Therefore the remedy is to go for Force balance transducer principle
which uses feed back principle

26. • In principle, force balance transducers employ
electrodynamic devices to balance the forces
produced by the elastic element which is subjected
to the pressure.
• force-balance system using electrodynamic force
balancing principle is shown in Fig. 7.12.
• Any pressure difference between inside and outside
of the bellows gives rise to a force F at the point A.
• The resultant displacement of the balancing beam is
detected by LVDT located at point B.

27. • The electrical output from the transducer is amplified causing
a current to flow through the balancing coil attached to the
beam.
• At the balance position, the electrodynamic force exerted by
the coil opposes the force exerted by the bellows.
• The current required to get such a balance is taken as a
measure of the unknown pressure p acting on the bellows.
• If the loop gain is large, an extremely small deflection of the
bellows is sufficient to activate the loop and achieved the
balance condition.
• Analysis of the closed loop feedback system in terms of the
transfer function can be very helpful .

32. Transduction Methods:
( pressure to electrical output)
• Electrical pressure transducers based on the principle of
variable capacitance , resistance, and inductance have
been developed for a variety of pressure measurements,
for converting the deflections or stresses developed in
elastic elements into corresponding electrical signals.

33. Potentiometric Device:

34. • The potentiometric-type pressure transducer is one of the
earliest type of electrical pressure sensors.
• In this, a diaphragm, capsule, bellows, or bourdon tube is linked
to a free-sliding wiper contact moving on a resistive element, as
shown in Fig. 7.4.
• The wiper is driven by the elastic element in response to the
applied pressure.
• Depending upon the design of the resistance element, the
output voltage can be made linear, or any other function of the
applied pressure.

35. Advantages :
1. High range,
2. Ruggedness,
3. Simple instrumentation.
Disadvantages :
1. Finite resolution
2. Limited life
3. Large size,
4. Poor frequency response,
5. Tendency to develop noise as slider wears off,
6. Susceptibility to vibration
Typical characteristics are
– Resolution is 0.2%
– Linearity of ± 1.0%.
– Repeatability of ± 0:25%,
– Hysteresis of ± 0.5%,
all with respect to F.S.R.

36. Strain Gauge Transducer :
• In the arrangement of a bonded strain gauge device is to fix the
strain gauges directly onto the diaphragm. The range of
application of this method is limited by the non-linearity of the
strain-pressure relationship above a certain strain value.

37. • For a clamped circular diaphragm of radius R, thickness
t, and pressure difference p, the maximum radial stress
at the edges is given by

38. • Frequency (and hence low sensitivity of acceleration) and good
dynamic response Since both tensile and compressive stresses
exist on the surface of the diaphragm.
• Strain gauges can be located as shown in the Fig. 7.5(a).
Gauges 1 and 3 bonded near the periphery respond to radial
strain, while 2 and 4 near the centre respond to tensile strain.
• This arrangement yields high sensitivity and fairly good
temperature stability
• The bridge circuit for this application is shown in Fig. 7.5(b)
provides output voltage corresponding to the pressure applied .

39. Variable Reluctance Sensor:
Pressure measurements can also be carried out using
variable inductance principle, where in the reluctance of a
magnetic path is changed in proportion to the pressure.
R= L / µA

40. • An extremely compact pressure transducer with a flat stretched
metal diaphragm is shown in Fig. 7.8
• An elastic ferromagnetic diaphragm D acting as an armature is
mounted symmetrically between the faces of two circular
ferromagnetic cores with a pressure port in each section.
• Two inductance coils are wound on the central section of each
core.
• The difference in pressure between the two sections causes the
diaphragm to deflect, resulting in a change in . the air gaps
between the core faces and the diaphragm.

41. • This leads to a change in the inductance of each coil.
• The coils are connected in the adjacent arms of an ac bridge
circuit, and the bridge output is proportional to the
magnitude of the differential pressure.
Unique feature is that ·
– The dynamic response is improved by the absence of any
mechanical linkage or any other form of loading on the
diaphragm.
– The sensitivity is high
– The device is ideally suited for very low pressure measurements.
– Rugged and insensitive to vibrations.

42. LVDT Type Transducer:

43. • One of the most popular types of pressure transducers is
the Linear Variable Differential Transformer type device in
which the LVDT is used as the sensing element.
• The elastic element, normally a diaphragm is coupled to
the core of the LVDT through a suitable mechanical
linkage, as illustrated in Fig 7.9.
• On application of pressure, the movement of the core as a
result of the diaphragm deflection is sensed precisely, and
the appropriate electrical output is interpreted in terms of
pressure values.
• However, the deflections have to be kept small for
obtaining reasonable linearity in a limited size.
• The dynamic response of this device is normally limited
because of the core mass .

44. Variable Capacitance device:

45. • For the measurement of very low pressure an equally suitable
device is the variable capacitance transducer.
• In this configuration a stretched metal diaphragm is positioned
symmetrically between the two stationary plates separating two
volumes as shown in Fig 7.10.
• The capacitance between these plates and the electrically grounded
diaphragm varies as a function of the deflection of the diaphragm,
which is proportional to the differential pressure applied.
• The changes in the two capacitances can be measured by an AC
bridge, or a tuned circuit.

46. piezoelectric pressure transducer:
• Certain types of materials generate an electrostatic charge or voltage when
mechanical stresses are applied across them.
• An opposite effect is also observed when an electrostatic charge or voltage
is applied to the crystal, resulting in the mechanical deformation of the
device.
• This property of piezoelectricity has been utilised in the design of pressure
transducers, wherein the mechanical stress is generated by the diaphragm
subjected-to pressure.
• The stress distribution in the crystal will depend not only on
• the load applied but also the manner in which this is applied, and upon the
size and shape of the sensing element.

47. • The important parameters considered are
1. Sensitivity,
2. Natural frequency,
3. Non-linearity,
4. Hysteresis,
5. Temperature effects,
6. Acceleration response, and
7. Cross sensitivity.
• The performance of a crystal element depends on
1. Magnitude of the crystal's piezoelectric constants.
2. Relative permittivity,
3. Natural time constant of the material,
4. Elastic constants, density, and the change of
piezoelectric constants with temperature

48. • The most popular ones having significant values or piezoelectric
constants and sensitivity are natural quartz, Rochelle salt, ADP and
a variety of synthetic ceramic materials like barium titanate and
lead-zirconatetitanate (Materials).
• Natural quartz is the most stable device for many applications. It
has a
1. Lower temperature sensitivity
2. Higher resistivity
3. Inherently long time constant which permits static calibration.
4. Exhibits good linearity over a wide range of stress levels with very
low hysteresis.

50. Thin Film Transducers:
Why?
Answer: Conventional pressure transducers is basically a measuring
cell divided by a diaphragm to which strain gauge are bonded. A change in
pressure will cause a negative or positive deflection of the diaphragm,
producing a measurable change in resistance within the strain gauge but
such devices are prone to
 Long term mechanical instability
 Especially at higher temperature
 Affected by vibration and hysteresis
These problems can be overcome by incorporating sputtered thin
film technology

51. Thin Film Pressure Transducer
• Is a standard pressure sensor, with changes in the diaphragm
configuration.
• Basic version has diffused single crystal chemically milled,
monocrystalline silicon diaphragm with the required strain gauge laid
down by diffusing boron on to the surface.
• Gauges are electrically isolated each other form the conductive
diaphragm and configured to form Wheatstone bridge network

53. • Later version of the transducer incorporate dielectrically isolated thin film
diaphragm on which the strain gauges are electro formed using sputter
vapour deposition techniques.
• The unwanted areas are removed by sputter etching using photoresist
techniques.
• The sensor is then positioned behind a metal diaphragm and the complete
assembly is mounted within a pressure tube as shown in figure
• Entire assembly is then mounted onto a metal pressure port with associated
components designed to compensate for any difference in the thermal
expansion.

54. Digital pressure transducer:
• With the advent of IC technology and advancement in microminiaturisation
innovation, it has become feasible to incorporate the signal conditioner and
associated electronic circuitry within the body of the transducer itself.
• This has now become almost a standard practice in the design of thin film
based and surface mounted devices, leading to the development of an
accurate digital pressure transducer with a number of intelligent signal
processing features housed within a relatively small volume.

56. • The various stages built-in are the
– Pre-amplifier
– Analog to digital converter
– An output processor, controlled with a microprocessor as
illustrated in the figure above
• The final electrical output can be directly connected to a digital display
or modified to give a direct output to 0 to + /- 5 V or 4 to 20 mA.

57. END of
Module 5

58. ( Module-3 PART-B)
• Transducers/Instruments for Measurement of Level: Capacitance probes –
bare and coated capacitance probes, Conductivity probes, Float level devices –
atmospheric tanks, mercury float switch, pneumatic float switch, Optical level
switches-Noncontact level sensor, contacting level sensor, laser based level
detector, Ultrasonic level detector-On-ff and continuous, Thermal level sensors

65. Non-contacting optical level sensor.

74. THANK YOU

75. Module 4b)
1. With schematic block diagram explain electronic weighing system
2. Write short note on
a. Column types devices
b. Hydraulic l o a d c e l l
c. Absorption type
Module 5)
3. what is the importance of pressure measurement techniques. explain various elastic
elements with neat diagrams.
4. Describe the construction and working of following pressure transducers / sensors:
(i) LVDT type pressure transducers.
(ii) Potentiometer type pressure transducers
5. With a neat diagram explain the principle of working of capacitive transducer.
6. Explain the principle and working of different types of microphones used for the
measurement of noise.
7. with neat diagram and analysis explain force balance transducer
8. with neat diagram explain pressure multiplexer
9. with neat diagram explain standard dead weight tester for pressure calibration