Unit-5: Introduction to Measurement and Mechatronics

Introduction to Measurement: Concept of Measurement, Error in measurements, Calibration,

measurements of pressure(Bourdon Tube Pressure and U-Tube Manometer),
temperature(Thermocouple and Optical Pyrometer), mass flow rate(Venturi Meter and Orifice
Meter), strain(Bonded and Unbonded Strain Gauge), force (Proving Ring) and torques(Prony
Brake Dynamometer); Concepts of accuracy, precision and resolution.
Introduction to Mechatronic Systems: Evolution, Scope, Advantages and disadvantages of
Mechatronics, Industrial applications of Mechatronics, Introduction to autotronics, bionics, and
avionics and their applications. Sensors and Transducers: Types of sensors, types of transducers
and their characteristics.
Overview of Mechanical Actuation System – Kinematic Chains, Cam, Ratchet Mechanism,
Gears and its type, Belt, Bearing.
Hydraulic and Pneumatic Actuation Systems: Overview: Pressure Control Valves, Direction
Control Valves, Rotary Actuators, Accumulators and Pneumatic
Sequencing Problems.

GENERAL MEASUREMENT CONCEPTS: We know that the primary objective of

measurement in industrial inspection is to determine the quality of the component manufactured.
Different quality requirements, such as permissible tolerance limits, form, surface finish, size, and
flatness, have to be considered to check the conformity of the component to the quality
specifications. In order to realize this, quantitative information of a physical object or process has to
be acquired by comparison with a reference.
The three basic elements of measurements (schematically shown in Fig.), which are of significance,
are the following:
1. Measured Quantity: a physical quantity such as length, weight, and angle to be measured
2. Comparator, to compare the measured (physical quantity) with a known standard (reference) for
evaluation
3. Reference, the physical quantity or property to which quantitative comparisons are to be made,
which is internationally accepted
All these three elements would be considered to explain the direct measurement using a calibrated
fixed reference. In order to determine the length (a physical quantity called measured quantity) of
the component, measurement is carried out by comparing it with a steel scale (a known standard).

The act or process of measuring something a size or length or anything is defined as measurement.
Measurement is the determination of the size or magnitude that exists, by comparing the unknown
quantity with some standard quantity of equal nature.
Measurement of an amount is based on some international standards, which are completely accurate
compared with others. Just like your vegetable vendors, measurements are taken by comparing an
unknown amount with a known weight. Every measurement carries a level of uncertainty which is
known as an error. This error may arise in the process or due to a mistake in the experiment. So
100% accurate measurement is not possible with any method.
An error may be defined as the difference between the measured and actual values. For example, if
the two operators use the same device or instrument for measurement. It is not necessary that both
operators get similar results. The difference between the measurements is referred to as an ERROR.
To understand the concept of measurement errors, you should know the two terms that define the
error. They are true value and measured value. The true value is impossible to find by experimental
means. It may be defined as the average value of an infinite number of measured values. The
measured value is a single measure of the object to be as accurate as possible.
Error in measurements Definition: The measurement error is defined as the difference between the
true or actual value and the measured value. The true value is the average of the infinite number
of measurements, and the measured value is the precise value.
Types of Errors in Measurement: The error may arise from the different source and are usually
classified into the following types. These types are
1. Gross Errors
2. Systematic Errors
3. Random Errors

1. Gross Errors: The gross error occurs because of the human mistakes. For examples consider
the person using the instruments takes the wrong reading, or they can record the incorrect data.
Such type of error comes under the gross error. The gross error can only be avoided by taking the
reading carefully.
For example – The experimenter reads the 31.5ºC reading while the actual reading is 21.5Cº. This
happens because of the oversights. The experimenter takes the wrong reading and because of which
the error occurs in the measurement.
Such type of error is very common in the measurement. The complete elimination of such type of
error is not possible. Some of the gross error easily detected by the experimenter but some of them
is difficult to find. Two methods can remove the gross error.
Two methods can remove the gross error. These methods are
 The reading should be taken very carefully.
 Two or more readings should be taken of the measurement quantity. The readings are taken
by the different experimenter and at a different point for removing the error.
2. Systematic Errors: The systematic errors are mainly classified into three categories.
1. Instrumental Errors
2. Environmental Errors
 3. Observational Errors
2 (i) Instrumental Errors: These errors mainly arise due to the three main reasons.
(a) Inherent Shortcomings of Instruments – Such types of errors are inbuilt in instruments
because of their mechanical structure. They may be due to manufacturing, calibration or operation
of the device. These errors may cause the error to read too low or too high.
For example – If the instrument uses the weak spring then it gives the high value of measuring
quantity. The error occurs in the instrument because of the friction or hysteresis loss.
(b) Misuse of Instrument – The error occurs in the instrument because of the fault of the
operator. A good instrument used in an unintelligent way may give an enormous result.
For example – the misuse of the instrument may cause the failure to adjust the zero of instruments,
poor initial adjustment, using lead to too high resistance. These improper practices may not cause
permanent damage to the instrument, but all the same, they cause errors.
(c) Loading Effect – Loading errors results from the change in the measured quantity itself when it
is being measured. Instrument loading error is the difference between the value of the measured
quantity and before and after the measurement system. Ex; measuring the thickness of soft material.
It is the most common type of error which is caused by the instrument in measurement work. For
example, when the voltmeter is connected to the high resistance circuit it gives a misleading
reading, and when it is connected to the low resistance circuit, it gives the dependable reading.
This means the voltmeter has a loading effect on the circuit.
The error caused by the loading effect can be overcome by using the meters intelligently. For
example, when measuring a low resistance by the ammeter-voltmeter method, a voltmeter having
a very high value of resistance should be used.
2 (ii) Environmental Errors: These errors are due to the external condition of the measuring
devices. Such types of errors mainly occur due to the effect of temperature, pressure, humidity,
dust, vibration or because of the magnetic or electrostatic field. The corrective measures employed
to eliminate or to reduce these undesirable effects are
 The arrangement should be made to keep the conditions as constant as possible.
 Using the equipment which is free from these effects.
 By using the techniques which eliminate the effect of these disturbances.
 By applying the computed corrections.
2 (iii) Observational Errors: Such types of errors are due to the wrong observation of the reading.
There are many sources of observational error. For example, the pointer of a voltmeter resets
slightly above the surface of the scale. Thus an error occurs (because of parallax) unless the line of
vision of the observer is exactly above the pointer. To minimise the parallax error highly accurate
meters are provided with mirrored scales.
3. Random Errors: The error which is caused by the sudden change in the atmospheric
condition, such type of error is called random error. These types of error remain even after the
removal of the systematic error. Hence such type of error is also called residual error.
These occur randomly and the specific cases of such errors cannot be determined but likely sources
of this type of errors are small variations in the position of setting standard and work piece, slight
displacement of lever joints in the measuring instruments, fluctuation in friction in the measuring
instrument.

Calibration: The ability of all measuring instruments to measure accurately and reliably is to be
proved, to get meaningful results. For this, the results of measurement are to be compared with
higher standards.

The instruments, gauges to be used for measurement should be of known accuracy in order that the
results obtained are meaningful. In order to identify the errors and rectification of errors, the
instruments are compared with masters or standards. This act of comparison is known as calibration

Calibration is a process of giving a known input to the measurement system and taking necessary
actions to see that the output of the measurement system matches with its input.
Calibration is the activity of checking, by comparison with a standard, the accuracy of a measuring
instrument of any type.
Definition of Calibration: The process of comparison of a device with unknown accuracy to a
device with a known, accurate standard to eliminate any variation in the device being checked is
called calibration
So, calibration of a measuring system means introducing an accurately known sample of the variable that is
to be measured and then adjusting the readout device of the measuring system until its scale reads the
introduced known sample of the variable accurately, i.e the calibration procedure establishes the correct
output scale for the measuring system.

Why it is necessary to calibrate measuring instruments and unit gauges

 The calibration of any measuring system is very important to get meaningful results.
 In the case where the sensing system and measuring system are different, then it is
imperative to calibrate the system as an integrated whole in order to take into account the
error producing properties of each component.
 Calibration is usually carried out by making adjustments such that the readout device
produces zero output for zero-measured input, and similarly, it should display an output
equivalent to the known measured input near the full-scale input value.
 It is important that any measuring system calibration should be performed under
environmental conditions that are as close as possible to those conditions under which actual
measurements are to be made.
 It is also important that the reference measured input should be known to an as much greater
degree of accuracy – usually, the calibration standard for the system should be at least one
order of magnitude more accurate than the desired measurement system accuracy.

Steps or precautions to be observed during calibration of a measurement system:

 Specified environmental conditions are to be maintained so that similar conditions prevail when
the system is calibrated and when theca tual measurements are made.
 The device to be calibrated is checked for any physical defects.
 The standard measurement system used for calibration should be at least ten times more accurate
than the desired measurement system accuracy i.e accuracy ratio of 10:1
Calibration procedure: The procedure for calibrating instruments is of two types namely
(a) Primary calibration
(b) Secondary calibration
(a) Primary calibration
 As per this procedure, a system is calibrated against a primary standard.
 While calibrating flow meters, if the flow is determined through measurement of time and
volume or mass of fluid, then it is termed as primary calibration.
(b) Secondary calibration
 As per this procedure, a device that has been calibrated by primary calibration is used as a
secondary standard for further calibration of other devices of lesser accuracy.
 A turbine type flow meter is used as a secondary standard to calibrate other flow devices.
Secondary calibration is of two types namely
(i) Direct calibration
(ii) Indirect calibration
(i) Direct calibration
 In this procedure, a standard device is placed in series with the device to be calibrated.
 Now calibration is done by comparing readings of the two devices over the desired range.
(ii) Indirect calibration
 This procedure is based on the equivalence of two different devices adopting some similarity
concept.
 Example: Flow measurement-Requirement of similarity is „Reynold‟s number should be equal‟.
By comparing the discharge coefficient of two devices, calibration is done.
 Benefits of Calibration are as follows,
 Calibration fulfills the requirements of traceability to national/ international standards like ISO
9000, ISO 14000, etc.
 Calibration is proof that the instrument is working.
 Confidence in using the instruments.
 Traceability to national measurement standards.
 Interchangeability.
 Reduced rejections, failure rate thus higher return.
 Improved product and service quality leading to satisfied customers.
 Power saving.
 Cost-saving.
 Safety.

Measurement of Pressure: Pressure is derived from force and area. It is typically measured in
units of force per unit surface area ( P = F/A), the SI unit of measuring pressure is Pascal (1Pascal =
1Newton/mt2)

Bourdon Pressure Gauge – Working, Advantages, Application

Bourdon tubes measure gage pressure, relative to ambient atmospheric pressure, as opposed to
absolute pressure; vacuum is sensed as a reverse motion.
The Bourdon tube is the commonest pressure indicating device and also it is an elastic element type
of pressure transducer.

Construction Of Bourdon tube Pressure Gauge: The main parts of this instrument is an
elastic transducer, which is a bourdon tube which is fixed and open at one end to receive the
pressure which is to be measured. The other end of the bourdon tube is free and closed. The cross-
section of the bourdon tube is elliptical. The bourdon tube is in a bent form to look like a circular
arc. To the free end of the bourdon tube is attached an adjustable link, which is in turn connected to
a sector and pinion. To the shaft of the pinion is connected a pointer which sweeps over a pressure
calibrated scale.
The tube is manufactured by flattening a circular cross section tube to the elliptical section and
bending into the C shape. One end is fixed and connected to the pressure to be measured. The
other end is closed and connected to the linkage.
If pressure is applied to the tube it will try to straighten causing the free end to move up and to the
right, oval cross section becomes more circular, this motion is converted to a circular motion for a
pointer with a toothed quadrant and pinion linkage.
Also helical shaped Bourdon tube can be used to move the slider of a potentiometer and so give an
electrical output related to the pressure.
 Operation of Bourdon tube: The pressure to be measured is connected to the fixed open end
of the bourdon tube. The applied pressure acts on the inner walls of the bourdon tube. Due to the
applied pressure, the bourdon tube tends to change in cross-section from elliptical to circular.
This tends to straighten the bourdon tube causing a displacement of the free end of the bourdon
tube. This displacement of the free closed end of the bourdon tube is proportional to the applied
pressure. As the free end of the bourdon tube is connected to a link – section – pinion arrangement,
the displacement is amplified and converted to a rotary motion of the pinion. As the pinion rotates,
it makes the pointer to assume a new position on a pressure calibrated scale to indicate the applied
pressure directly. As the pressure in the case containing the bourdon tube is usually atmospheric,
the pointer indicates gauge pressure.
Applications of Bourdon pressure gauge:
 They are used to measure medium to very high pressures.
 For measuring high pressures e.g. in steam boilers, compressors.
 For measuring pressures in vehicles tube tire.
Advantages of bourdon pressure gauge:-
 These Bourdon tube pressure gauges give accurate results.
 Bourdon tube cost low.
 Bourdon tubes are simple in construction.
 They can be modified to give electrical outputs.
 They are safe even for high-pressure measurement.
 Accuracy is high especially at high pressures.
Disadvantages of bourdon pressure gauge:-
 They respond slowly to changes in pressure
 They are sensitive to shocks and vibrations.
 Amplification is a must as the displacement of the free end of the bourdon tube is low

Accuracy, Precision and Resolution:

Accuracy is the degree of closeness between a measurement and its true value. Precision is the
degree to which repeated measurements under the same conditions
Precision is defined as the repeatability of a measuring process or how close attempts are to each
other. Accuracy is the comparison of the result of a measurement with the true value of the
measured quantity or having attempts at the given location.
Resolution is the ability of the measurement system to detect and faithfully indicate small
changes in the characteristic of the measurement result.
Optical Pyrometers (Monochromatic –Brightness Radiation Thermometers):
Optical Pyrometer: Definition: The optical pyrometer is a non-contact type temperature
measuring device. It works on the principle of matching the brightness of an object to the brightness
of the filament which is placed inside the pyrometer. The optical pyrometer is used for measuring
the temperature of the furnaces, molten metals, and other overheated material or liquids.
It is not possible to measures the temperature of the highly heated body with the help of the contact
type instrument. Hence the non-contact pyrometer is used for measuring their temperature.

Construction of Optical Pyrometer: The construction of the optical pyrometer is quite simple.
The pyrometer is cylindrical inside which the lens is placed on one end and the eyepiece on the
other end. The lamp is kept between the eyepiece and the lens. The filter is placed in front of the
eyepiece. The filter helps in getting the monochromatic light. The lamp has the filament which is
connected to the battery, ammeter and the rheostat.

Working of Optical Pyrometer: The optical pyrometer is shown in the figure below. It consists
the lens which focuses the radiated energy from the heated object and targets it on the electric
filament lamp. The intensity of the filament depends on the current passes through it. Hence the
adjustable current is passed through the lamp.

PMMC (PERMANET MAGNET MOVING COIL)

The magnitude of the current is adjusted until the brightness of the filament is similar to the
brightness of the object. When the brightness of the filament and the brightness of the object are
same, then the outline of the filament is completely disappeared.

The filament looks bright when their temperature is more than the temperature of the source.
The filament looks dark if their temperature is less than that required for equal brightness
Advantages of Optical Pyrometer

 The optical pyrometer has high accuracy.

 The temperature is measured without contacting the heated body. Because of this property, the
pyrometer is used for the number of applications.
The classical form of this type of instrument is the disappearing filament optical pyrometer. It is
limited to temperature greater than about 700oc, since it requires a visual brightness match by a
human operator.
Monochromatic brightness thermometers utilize the principle that, at a given wavelength ʎ , the
radiant intensity (brightness) varies with temperature.
Disadvantages of Optical Pyrometer: The working of the pyrometer depends on the intensity of
light emitted by the heated body. Thereby, the pyrometer is used for measuring the temperature
having a temperature more than 700-degree Celsius. The accuracy of the pyrometer depends on the
adjustment of the filament current. Also, the pyrometer is not used for measuring the temperature of
clean gases.

Thermocouple: Definition: The thermocouple is a temperature measuring device. It uses for

measuring the temperature at one particular point. In other words, it is a type of sensor used for
measuring the temperature in the form of an electric current or the EMF.
The thermocouple consists two wires of different metals which are welded together at the ends. The
welded portion was creating the junction where the temperature is used to be measured. The
variation in temperature of the wire induces the voltages.
Working Principle of Thermocouple: The working principle of the thermocouple depends on the
three effects.
See back Effect – The See back effect occurs between two different metals. When the heat
provides to any one of the metal, the electrons start flowing from hot metal to cold metal. Thus,
direct current induces in the circuit.
In short, it is a phenomenon in which the temperature difference between the two different
metals induces the potential differences between them. The See beck effect produces small
voltages for per Kelvin of temperature.
Peltier Effect – The Peltier effect is the inverse of the Seebeck effect. The Peltier effect state
that the temperature difference can be created between any two different conductors by
applying the potential difference between them.
Thompson Effect – The Thompson effect state that when two dissimilar metals join together and if
they create two junctions then the voltage induces the entire length of the conductor because of
the temperature gradient. The temperature gradient is a physical term which shows the direction
and rate of change of temperature at a particular location.
Working of Thermocouple: If two wires of different materials A and B are connected in a circuit,
with one junction at temperature T1 and the other at T2, then an infinite – resistance voltmeter
detects an electromotive force “E” or if an ammeter is connected, a current “I” is measured, this is
called Seebeck effect. The magnitude of the voltage “E” depends on the materials and temperatures
T1 and T2.

Based on the Principle of Seebeck effect, thermocouples have made. Thermocouples are the
temperature sensors which are extensively used for the measurement of the temperature variations.
They sense the temperature and the temperature is further measured by other instruments after
sensing it. As they convert a non-electrical quantity (temperature) into voltage (electrical quantity)
so they are also known to be a transducer.

The circuit of the thermocouple is shown in the figure below. The circuit consists two dissimilar
metals. These metals are joined together in such a manner that they are creating two junctions. The
metals are bounded to the junction through welding.

The T1 and T2 are the temperatures at the junctions. As the temperature of the junctions is different
from each other, the EMF generates in the circuit.

If the temperature at the junction becomes equal, the equal and opposite EMF generates in the
circuit, and the zero current flows through it. If the temperatures of the junction become unequal,
the potential difference induces in the circuit. The magnitude of the EMF induces in the circuit
depends on the types of material used for making the thermocouple. The total current flowing
through the circuit is measured through the measuring devices.
The EMF induces in the thermocouple circuit is given by the equation

Where Δθ – temperature difference between the hot thermocouple junction and the reference
thermocouple junction.
a, b – constants

The output obtained from the thermocouple circuit is calibrated directly against the unknown
temperature. Thus the voltage or current output obtained from thermocouple circuit gives the value
of unknown temperature directly.

Measurement of Thermocouple Output: The output EMF obtained from the thermocouples can
be measured through the following methods.
1. Multimeter – It is a simpler method of measuring the output EMF of the thermocouple. The
multimeter is connected to the cold junctions of the thermocouple. The deflection of the
multimeter pointer is equal to the current flowing through the meter.
2. Potentiometer – The output of the thermocouple can also be measured with the help of the DC
potentiometer.
3. Amplifier with Output Devices – The output obtains from the thermocouples is amplified
through an amplifier and then feed to the recording or indicating instrument.
Advantages of Thermocouple: The following are the advantages of the thermocouples.
1. The thermocouple is cheaper than the other temperature measuring devices.
2. The thermocouple has the fast response time.
3. It has a wide temperature range.
Disadvantages of the Thermocouples
1. The thermocouple has low accuracy.
2. The recalibration of the thermocouple is difficult.

Torque Measurement: (Prony Brake Dynamometer)

Dynamometer: A device for measuring mechanical force, or power, transmitted by a rotating
shaft. Since power is the product of torque (turning force) and angular speed, all power-
measuring dynamometers are essentially torque-measuring devices; the shaft speed is
measured separately.
Prony Brake is one of the simplest dynamometers for measuring power output (brake power).
A Prony brake (see figure) develops mechanical friction on the periphery of a rotating pulley. It
is to attempt to stop the engine using a brake on the flywheel and measure the weight which an arm
attached to the brake will support, as it tries to rotate with the flywheel.

Prony Brake dynamometer

The Prony brake shown in the above consists of a wooden block, frame, rope, brake shoes and
flywheel. It works on the principle of converting power into heat by dry friction. Spring-loaded
bolts are provided to increase the friction by tightening the wooden block.
The whole of the power absorbed is converted into heat and hence this type of dynamometer must
the cooled.
The brake power is given by the formula
Brake Power (Pb) = 2πNT/60
Where T = Weight applied (W) × distance (l)

Elastic force meter (or) Proving Rings

When a steel ring is subjected to a force across its diameter, it deflects. This deflection is
proportional to the applied force when calibrated.

The proving ring is a device used to measure force. It consists of an elastic ring of known
diameter with a measuring device located in the centre of the ring.
A steel ring attached with external bosses to apply force. A precision micrometer with one of its
ends mounted on a vibrating reed.
It consists of an elastic ring of known diameter in which the deflection of the ring when loaded
along a diameter is measured by means of a micrometer screw and a vibrating reed.
The force deflection relation of such ring is
F = k x, where,
F = applied force,
k = ring stiffness,
x = ring deflection. Ring deflection is measured by a micrometer attached to the ring.
Operation: The force to be measured is applied to the external bosses of the proving ring. Due to
the applied force, the ring changes in diameter. This deflection of the ring is proportional to the
applied force.
At this stage, the reed is plucked to obtain a vibrating motion. When the reed is vibrating, the
micrometer wheel is turned until the micrometer contact moves forward and makes a noticeable
damping of the vibrating reed.
Now the micrometer reading is noted which is a measure of deflection of the ring. The device is
calibrated to get a measure of force in terms of deflection of the proving ring.

Strain (Bonded and Unbonded strain gauge):

Working Principle: The strain gauge working principle is based on the fact that the electrical
resistance of materials varies with deformation. A strain gauge is an example of a passive
transducer that converts the mechanical displacement into electrical quantity.
We know, the resistance of the conductor depends on the length and cross-sectional area.
The resistance
R = ρ L/A
L = length of the conductor or semiconductor element.
A = Cross sectional area.
ρ = Resistivity.

Electrical strain gauges:

A strain gauge is a sensor whose resistance varies with an applied force. The strain gauge converts
the force, pressure, tension, and weight into electrical quantity which can be measured.
The electrical strain gauges measure the changes that occur in resistance, capacitance, or inductance
due to the strain transferred from the work piece to the basic gauge element.
Based on mounting, strain gauges are classified as
Bonded strain gauges.
Unbonded strain gauges.
Bonded strain gauge:In bonded strain gauge, a fine resistance wire of diameter 0.25mm or less is
bonded or pasted on a thin flexible sheet of a paper, tissue, Bakelite or Teflon etc. and this substrate
or sheet is directly attached using adhesive to the surface of the structure whose stress or strain to be
measured. The grid of fine resistance wire is cemented to carrier. It can be a thin sheet of paper,
Bakelite or a sheet of Teflon. To prevent gauge wire from any mechanical damage, it is being
covered on top with a thin sheet of insulating material. A diagram of bonded strain gauge is shown
as follows

Working Principle: When bonded wire strain gauges are attached to the structure surface under
study and structure is subjected to a force, gauge gets elongated, hence a change in resistance occurs
which can be detected and measured by bridge circuits and can be calibrated in unit of measurement
of process variable such as force, pressure, stress etc.

Bonded strain gauges are so-called because they are attached to the elastic element surface. The
most commonly used are bonded resistance type strain gauges. They are primarily used for strain
analysis.
Wire strain gauge: The resistance element is in the form of wire foil or film of the material.
Metal Foil :The strain is detected by using a metal foil. The metal foil is pasted on one side of the
plastic The leads are soldered to the metal foil for connecting the Wheatstone bridge.

Metal Foil strain gauges exhibit a higher gauge factor than wire foil strain gauges.

Rosette Strain gauges: Rosettes type strain gauges are used when either direction or axis of
strain in a component is unknown or more than one direction are present So it cannot be measured
effectively using single strain gauge.Rosette is basically an arrangement of combining two or more
strain gauge elements in such angles and positioned so closely to measure strains of different
directions of the component. 3 element strain gauge rosette is shown in diagram
Unbonded strain gauge: In Unbonded strain gauge, fine resistance wire of diameter 0.003mm or
less is stretched between two frames using insulated pins. Here both the frames can move relative
with respect to each other and are held together by a spring loaded mechanism. Gauge wire is
connected to one arm of wheat stone bridge network. The major difference between bonded and
unbounded strain gauge is that resistance wire is not directly bonded here on the surface of the
structure under stress analysis. There can be various configurations possible when changing method
to stretch gauge wire. A diagram showing unbounded strain gauge is shown as follows

Unbonded strain gauge consists of a fixed frame and a movable frame. Movable frame is connected
to a rod or bar, which is able to move in either direction under the application of force and strain to
be measured

Working Principle: Principle of operation is similar to bonded type strain gauge. When frame is
subjected to a force, pressure, weight etc., frame get shifted slightly hence gauge wire gets
elongated, which causes a change in resistance that can be detected and measured by bridge circuits
and can be calibrated in unit of measurement of process variable such as force, pressure, weight etc.
Advantages-

 They are available in simple configuration and small size.

 They are having low hysteresis.
 Unbonded gauges can be used in high temperature installations as there is no bonding or
organic material present.
 They are used for force, strain, weight, load, pressure and displacement etc.
 They are used in accelerometers to measure acceration.

Gauge Factor is defined as the ratio of relative change in electrical resistance to the mechanical
strain. Here relative change in resistance is defined as the ratio of change in resistance produced
due to strain to its original resistance (without strained). It is also referred as Strain factor of a
strain gauge.

 According to the definition, when applied force in a solid bar of length (L) produces
change in length (ΔL) which results in gauge resistance change (ΔR) from its original
resistance (R), then the Gauge Factor can be mathematically expressed as-

.
Desirable characteristics of strain gauges:
 Strain gages should have a high value of gauge factor.
 Strain gauges should have high resistance.
 Strain gauges high resistance temperature coefficient.
 Should have linear characteristics (resistance versus strain).
 Strain gauge lead wires should have low and stable resistivity also a low-temperature
coefficient.
 If strain gauges are used frequently for dynamic measurements, the frequency response over
the entire range should be linear.
 Uses:
 Strain gauges are used in weight measurement.
 Strain measurement in concrete and metal structures
MASS FLOW RATE (VENTURI METER AND ORIFICE METER),
BERNOULLI’S EQUATION
The following are the assumptions made in the derivation of Bernoulli‟s equation.
 The fluid is ideal i.e. Viscosity is zero.
 The flow is steady.
 The flow is incompressible.
 The flow is Irrotational.
VENTURIMETER
A venturimeter is a device used for measuring the rate of flow of fluid through a pipe.
The basic principle on which venturimeter works is that by reducing the cross-sectional area of the
flow passage, a pressure difference is created and the measurement of the pressure difference
enables the determination of the discharge through the pipe.

A venture meter consists of (1) an inlet section, followed by a converging cone (2) a cylindrical
throat and (3) a gradually divergent cone.
• The inlet section of venture meter is the same diameter as that of the pipe which is followed by a
convergent cone.
• The convergent cone is a short pipe, which tapers from the original size of the pipe to that of the
throat of the venture meter.
• The throat of the venture meter is a short parallel – sided tube having its cross-sectional area
smaller than that of the pipe.
• The divergent cone of the venture meter is a gradually diverging pipe with its cross-sectional area
increasing from that of the throat to the original size of the pipe. • At the inlet section and the throat
i.e sections 1 and 2 of the venture meter pressure gauges are provided
DERIVATION
• Let a1 and a2 be the cross-section areas at inlet and throat sections, at which P1 and P2 the
pressures and velocities V1 and V2 respectively.
• Assuming the flowing fluid is incompressible and there is no loss of energy between section 1 and
2 and applying Bernoulli‟s equation between sections 1 and 2, we get,

Where 𝜔 is the specific weight of flowing fluid.

• If the venturimeter is connected in a horizontal pipe, then Z1 = Z2 ,

In the above expression (𝑃1/ 𝜔 − 𝑃2/ 𝜔) 𝑖𝑠 𝑡ℎ𝑒 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 between the pressure heads
at section 1 and 2 , is known as venture head and is denoted by h
Co-efficient of Discharge Cd=Qact/Qth
Qact=Cd Qth
Cd = Co-efficient of discharge < 1

ORIFICEMETER: An orifice meter is a simple device for measuring the discharge through pipes.
• Orifice meter also works on the same principle as that of venture meter i.e by reducing cross-
sectional area of the flow passage, a pressure difference between the two sections is developed and
the measurement of the pressure difference enables the determination of the discharge through the
pipe.

Orifice meter is a cheaper arrangement and requires smaller length and can be used where space is
limited

Where ao = area of the orifice meter

a1 = area of the inlet pipe
Cd = Co-efficient of Discharge Cd=Qact/Qth
This gives the discharge through an orifice meter and is similar to the discharge through venture
meter. • The co-efficient Cd may be considered as the co-efficient of discharge of an orifice meter.
• The co-efficient of discharge for an orifice meter is smaller than that for a venture meter.
• This is because there are no gradual converging and diverging flow passages as in the case of
venture meter, which results in a greater loss of energy and consequent reduction of the co-efficient
of discharge for an orifice meter.