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Dept. of Mechanical Engineering 1

ERRORS IN MEASUREMENTS

Errors in measurement systems could originate from several sources. Broadly they can

be classified under three categories viz gross errors, systematic errors and random errors.

Gross errors occur due to human mistakes in reading or calculating. Designer of

instruments to some extend can take care to avoid gross errors, but much would depend up on

interest and competence of observer. While some gross errors may be easily detected, others

may go noticed. No mathematical treatment or prediction is possible for gross error.

Systematic error may be due to instrument errors, environmental errors or observational

errors.

ERRORS IN MEASURING INSTRUMENTS

The errors in a scale and pointer type of measuring instrument can be of following

types.

1. Inherent shortcoming in instruments: - These errors may be due to construction,

calibration, or operation of the instruments.

2. Assembly errors:- These can be due to the following.

a) Displacement scale (i.e.) incorrect fitting of the scale zero with respect to the actual

zero position of the movement.

b) Non uniform division of the scale

c) Bent or distorted pointer.

Errors in this type can be easily discovered and rectified as they remain constant with

time.

3. Environmental errors:- These errors are much more troublesome than assembly errors

as these change with time in an unpredictable manner. These errors can be eliminated

or reduced by taking the following precautions.

a) Using instrument in controlled conditions of pressure, temperature and humidity in

which it was originally assembled and calibrated.

b) Automatic compensation using sophisticated devices for such deviations is also

possible and usually applied.

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4. Misuse of instruments:- A good instrument used in an unintelligent way may give error

results.

5. Observation errors:- This occur due to carelessness of operations. Parallax errors can be

taken. Digital readings also reduce such errors.

6. Loading effects:- In many measurement techniques the detector/sensor utilizes the

energy of medium, thus altering the parameter slightly to be measured resulting in

error.

7. Random errors:- These vary in an unpredictable manner and it is very difficult to list

out all the sources of errors. In this class the most common causes are

a) Friction in instrument movement

b) Backlash in the movement

c) Hysteresis in elastic members

d) Mechanical vibration

e) Finite dimensions of the pointer and the scale divisions

f) Parallax errors between pointer and the scale.

The characteristics of these errors are that they being random try to cancel each other.

The effects of external vibrations can be minimized by using shock absorbing

mountings.

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GENERALISED MEASUREMENT SYSTEM

CALIBRATION

TRANSDUCER

SIGNAL

MEASURED

ANALYSES

DRIVING SIGNAL

Sensor / Transducer: - Sensors desired input to exclusion of all others and provides analogous

output.

Signal condition:- Modifies transduced signal in to form usable by final stage. Usually increases

amplitude and/or power, depending on requirement. May also selectively filter unwanted components

and convert signals in to pulsed form.

Indicator/Recorder/Processor/controller:-Provide an indication or recording in form that can be

evaluated by an unaided human sense or by a computer or a controller.

SENSOR

TRANSDUCER SIGNAL

CONDITIONER

INDICATOR

RECORDER

PROCESSOR

CONTROLLER

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MEASURING INSTRUMENTS

1. Mechanical Instruments:- These instruments have moving parts that are rigid, heavy

and bulky and consequently have a large mass. Mass presents inertia problems and

hence these instruments cannot faithfully follow the rapid changes which are involved

in dynamic measurements. These instruments are very reliable for static and stable

conditions. But they are unable to respond rapidly to measurements of dynamic and

transient conditions.

2. Electrical Instruments:- Electrical methods of indicating the output of detectors are

more rapid than that of mechanical methods. It is unfortunate that an electrical system

normally depends up on a mechanical meter movement as an indicating device. This

mechanical measurement has some inertia and these instruments have a poor frequency

response.

3. Electronic Instruments:- Most of the present day scientific and industrial require very

fast response. These instruments use semi-conductor devices. Since in electronic

devices, the only movement involved is that of electrons. The response time is

extremely small on account of very small inertia of electrons. Another advantage of

using electronic device is that very weak signals can be detected by using pre-

amplifiers and amplifiers.

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DEFINITIONS RELATED TO MEASURING INSTRUMENTS

Some important terms used in connection with measuring instruments are

1. Range:- It represents the highest possible value that can be measured by an instrument.

It has a very important bearing on the expected accuracy of the instrument.

2. Scale sensitivity:- It has defined as the ratio of the change in scale reading to the

corresponding change in pointer deflection. It actually denotes the smallest change in

measured variable to which on instrument responds.

3. Scale readability:- In analog instruments, scale readability indicates the clearances with

which the scale can be read. Scale readability depends on numbers of graduations,

spacing of graduations, size of pointer, parallax effects, discriminating power of

observer etc.

4. True or Actual value:- It is the actual magnitude of a signal input to a measuring system

which can only be approached and never evaluated.

5. Indicated value:- The magnitude of a variable indicated by a measuring instruments

known as indicated value.

6. Correction:- It is the revision applied to the indicated value so that the final result

obtained improves the worth of the result.

7. Overall error:- It is the difference of the scale reading and the true value. It is positive if

the indicated value of the input quantity is in excess of it’s true value.

8. Dead time:- Time before the instrument begins to respond after the measured quantity

has been changed.

9. Speed of response:- It is the quickness of an instrument to read the measured variable.

10. Precision:- It is the degree of reproducibility among several independent measurements

of the same true value under specified conditions. It is usually expressed in terms of the

deviation in measurement.

11. Error calibration curve:- It is an error curve which can be used for correcting instrument

readings. The curve is plotted by calibrating the instrument against a suitable standard

at a number of points on the scale.

12. Significant figures:- It is an indication of the precision of measurement. Significant

figures convey actual information regarding the magnitude of precision.

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INPUT – OUTPUT CONFIGURATIONS OF INSTRUMENTS

DESIRED INPUT

MODIFYING INPUT OUTPUT

INTERFERING

INPUT

Figure shows a generalized input-output configuration of a measuring system.

Normally a measuring system is fed with a desired input from a sensor or transducer and

output produced accordingly to the value of the desired input. However in some cases the

output has to be modified depending on desired input and another input called modifying input.

For example mass flow is dependent on differential pressure across a nozzle but has to be

modified according to change in density of medium. This modifying input in the form of

temperature of medium would also need to be applied. In addition, there may be interfering or

unwanted inputs also like noise which we desired should not affect the output.

These inputs to a measuring system could be of three types.

1. Desired input:- A basic quantity for which instrument is specially designed and output

should respond to this input. The output would be linearly proportional to input or

S1

S2

S3

S4

SUMMING

BLOCK

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follow a certain relationship symbolized by a mathematical operator S1, defined as a

transfer function such that output = S1 x input. In case of non-linear systems, the

transfer function represented by an algebraic or transcended function. If input is

dynamic then S1 may be represented by differential equations.

2. Modifying inputs:- These cause a change in input-output relationships for desired input/

interfering input. The transfer functions S2 and S3 represent the specific manner in

which modifying input affects S1 and S4 respectively.

3. Interfering inputs:- These are unwanted signals to which the measurement system

becomes unintentionally sensitive. Measuring system gives output corresponding to

interfering input due to its principle of working and design. The interfering input could

be generated in the system or outside due to pick up of stray signals, environmental

influence etc.

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STATIC CHARACTERISTICS OF MEASURING INSTRUMENTS

In some applications, the parameter of interest is more or less constant or varies very

slowly with time. Measurements of such applications are called static measurements. A set

criteria that provide meaningful description of quality of measurements under static conditions

are called static characteristics. These criteria are a) accuracy b) error c) reproducibility d) drift

e) sensitivity f) dead zone.

a) Accuracy:- Accuracy is defined as the closeness with which the reading of the

instrument approaches true value. The true value is just impossible to be determined

experimentally. True value of a quantity can be defined as the average of a infinite

number of measured values when the average deviation due to the various contributing

factors tends to zero.

Any measurement system does not indicates true value of a loading effect, lags,

mechanical problems like wear, hysteresis, noise, pick up etc. Some inaccuracy has

thus to be accepted in measurements. Accuracy may be expressed as point accuracy or

as percent of scale range or as percent of true value. Point accuracy is the accuracy at

one point only. It does not provide information at other points on the scale or the

general accuracy. Sometimes accuracy is expressed as percentage of scale range. Thus

±1% of scale range accuracy of an instrument having scale range of 0-1000c would be

mean that instrument reading ±10c inaccurate at all the point on the scale from 0 to

1000c. Under such situation, the inaccuracy is very high at lower scale with sometimes

may be misleading. To avoid such problem accuracy can be specified in terms of the

true value of the quality being measured. Thus ±1% of accuracy of true value would

mean that inaccuracy is ±10c when reading at 100

0c and only ±0.25

0c when reading

250c on an instrument having scale range of 0-100

0c.

b) Error:- Errors are unavoidable in any measurement system. Attempts can be made to

minimize them by suitably designing the system by taking care of all sources of errors.

In order to have an overall estimate of all the sources of errors. The understanding and

through evaluation of error is essential. The accuracy of any measurement system is

measured in terms of its errors.

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Static error is defined as the difference between the best measured value and true value

of the quantity. The absolute value of error does not indicate precisely the accuracy of

measurements. The quality of measurements is provided by the relative static error i.e.

the ratio of absolute static error to the true value of the quantity under measurement.

Therefore, the relative static error is given by ratio of absolute error and true value.

When the absolute static error is negligible this means that when the difference

between the measured value and true value is negligible. Then

Relative static error = Absolute error

Measured value

The relative static error is usually expressed as percentage of the measured value.

Also true value = measured value x (1 – relative static error).

c) Reproducibility:- It represents the degree of the closeness with which a given value of a

quantity be repeatedly measured with in a close range. Reproducibility is a measure of

closeness with which a given input may be measured over and operation. An instrument

with high reproducibility has zero as negligible drift.

d) Drift:- Drift causes the measured result to vary for a given input quantity. It occurs due

to wear and tear of parts, hysteresis effect in metals, change in metals caused by

contamination or other causes, environmental factors, stray electric and magnetic fields,

thermal emf, change in temperature and mechanical vibrations, high mechanical

stresses in parts etc. Thus drift cannot be easily compensated for, but can be carefully

guarded against by care, prevention, consumption and maintenance. It is drift which

causes change in calibration of instrument.

Drift can be classified in to three categories

i) Zero drift:- It sets in when the calibration gradually shifts due to slippage, permanent

sets etc. It can be taken care of by zero drift.

ii) Span drift:- Proportional change in the indication all along the upward scale is called

span drift.

iii) Zonal drift:-It occurs only in a zone of span.

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e) Sensitivity:- It is the ratio of the magnitude of output to the input signal or the response

of measuring system to the quantity being measured.

For an instrument having linear calibration curve, sensitivity is the slope of the

calibration curve is constant over the entire range of the instrument. If the calibration

curve is non-linear, the sensitivity of an instrument should be high and thus the range

should not be high in comparison to value being measured.

Scale factor is reverse of sensitivity.

f) Dead zone:- Dead zone is the largest change in input quantity for which a noticeable

change in output is observed from zero reading. It may occur due to friction in the

instrument which does not allow pointer to move till sufficient driving force is

developed to overcome the friction forces. Dead zone is caused by backlash and

hysteresis in the instrument.

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DYNAMIC CHARACTERISTICS OF MEASURING INSTRUMENTS

The dynamic characteristics of any instrument is defined and evaluated by the

following terms:-

a) Speed of response:- It is the rapidity with which an instrument responds to changes in

the measured quantity.

b) Measuring lag:- It is the retardation or delay in the response of an instrument to

changes in the measured quantity. The measuring lag can be either of the retardation

type in which case the response of an instrument begins immediately on a change in

measured variable or of the time delay type called dead time in which case the response

of the instrument is simply shifted along the time scale.

Generally the dead time lag is very small. Instruments having appreciable dead

time are not satisfactory for measuring a variable that fluctuates rapidly. The dead time

can also be caused by a definite dead zone in the instrument as a result of friction. In

such cases, the instrument does not respond for a certain time delay and acts only when

the measured variable has changed sufficiently to overcome the starting friction. The

dead time due to this cause depends on how fast the measured variable is changing and

on the extend of the instrument dead zone.

c) Fidelity:- It is determined by the fact that how closely the instrument follows the

measured variable. i.e. it is the degree to which an instrument indicates the changes in

measured variable without dynamic error.

d) Dynamic error:- It is the difference between the true value of a quantity changing with

time. i.e. measured variable and the instrument reading if no static user is assumed.

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STUDY OF MEASURING INSTRUMENTS

1. Flow measuring instruments

a) Rotameter :-

b) Watermeter:-

2. Velocity measuring instruments

a) Pitot tube

b) Anemometer

c) Tachometer d) Stroboscope

3. Displacement measuring instrument

a) LVDT

b) Capacitance measurement trainer

4. Linear measuring instrument

a) Vernier caliper

b) Micrometer

5. Temperature measuring instrument

a) Thermocouple

b) Thermometer

c) By using RTD

6. Strain measuring instruments

a) Strain gauge trainer

b) Load cell trainer

7. Pressure measuring instruments

a) Bourdon tube pressure gauge

b) Manometers

c) Pressure transducer

8. Area measuring instruments

a) Planimeter

9. Sound measuring instrument

a) Sound meter.

10. Humidity measuring instrument

a) Psychrometer

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ROTAMETER:-

Rotameter is a particular kind of flow meter, based on the variable area principle. They provide

a simple, precise and economical means of indicating flow rates in fluid systems.

This variable area principle consists of three basic elements: A uniformly tapered flow tube, a

float, and a measurement scale. A control valve may be added if flow control is also desired. In

operation, the rotameter is positioned vertically in the fluid system with the smallest diameter

end of the tapered flow tube at the bottom. This is the fluid inlet. The float, typically spherical,

is located inside the flow tube, and is engineered so that its diameter is nearly identical to the

flow tube’s inlet diameter.

When fluid — gas or liquid — is introduced into the tube, the float is lifted from its initial

position at the inlet, allowing the fluid to pass between it and the tube wall. As the float rises,

more and more fluid flows by the float because the tapered tube’s diameter is increasing.

Ultimately, a point is reached where the flow area is large enough to allow the entire volume of

the fluid to flow past the float. This flow area is called the annular passage. The float is now

stationary at that level within the tube as its weight is being supported by the fluid forces which

caused it to rise. This position corresponds to a point on the tube’s measurement scale and

provides an indication of the fluid’s flow rate.

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One way to change the capacity or flow range of a rotameter is to change the float material,

and thus its density, while keeping the flow tube and float size constant. Floats which are made

from less dense materials will rise higher in the tube and therefore will yield lower flow

capacities for the same diameter flow tube. Floats made from more dense materials will raise

less thereby yielding higher flow capacities.

WATER METER:-

A watermeter is a device used to measure the volume of water usage. In many

developed countries water meters are used at each residential and commercial building in a

public water supply system. Watermeter can also be used at the water source, as well as

throughout a water system to determine flow that portion of the system. Watermeter typically

measure and display total usage in cubic feet, cubic meters, or us gallons on a mechanical or

electronic register. Some electronic meter register can display rate of flow as well as total

usage.

PITOT TUBE:-

It is essentially a velocity measuring instrument but can also be used for the flow

measurement of liquids and gases. Pitot tube consists of a tube of small hole being drilled in

the wall of the tube near the sealed end. For measuring the velocity of flow of any point in the

pipe or duct the tube is inserted with the drilled hole pointing upstream.

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The flowing fluid moving with certain velocity V, will strikes the Pitot tube. Its

forward motion is arrested and the impact results in the converging of kinetic energy to

potential energy. As a result of this an excess head of v2/2g is generated inside the Pitot tube. A

static pressure tapping is taken from the pipe and connected to the low pressure of the U-tube

manometer and high pressure side is connected to the Pitot tube. The differential pressure

indicated by the manometer is proportional to the velocity of flow at the tip of the Pitot tube.

Since the Pitot tube just now described contains only one tip. It is known as single tip type

Pitot tube. If the tip of the tube and the other dimensions suitably, designed then there is no

need of taking a constant in determining the velocity from the differential place respected by

the pitot tube. In other words, under such case V = √2gh .

ANEMOMETER:-

When a rotor is attached to a permanent magnet polarized at 900 to the axis of rotation,

and if the rotor is made to rotate due to the fluid velocity, the rotating magnetic field will be cut

by the pickup coil generating voltage pulses. The frequency of voltage pulses is proportional to

flow rate. Hence the measure of frequency of voltage pulses becomes a measure of flow rate.

These are used in weather stations to measure wind velocity, to measure water flow in

rivers and streams and compact models are used to measure flow in tubes and pipes.

TACHOMETER:-

Angular velocity is measured using devices called tachometers. The main parts of a

mechanical tachometer arrangement are, a worm gear cum shaft arrangement which is driven

by a speed source and a spur gear connected to the worm. The spur gear is in turn connected to

a pointer that can move over a velocity calibrated scale (dial). It is used on low speed engines,

measures between 2000 – 3000 rpm.

STROBOSCOPE:-

A stroboscope, also known as a strobe, is an instrument used to make a cyclically

moving object appear to be slow-moving, or stationary. The principle is used for the study

of rotating, reciprocating, oscillating or vibrating objects. Machine parts and vibrating strings

are common examples.

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In its simplest mechanical form, a rotating cylinder (or bowl with a raised edge) with evenly-

spaced holes or slots placed in the line of sight between the observer and the moving object.

The observer looks through the holes/slots on the near and far side at the same time, with the

slots/holes moving in opposite directions. When the holes/slots are aligned on opposite sides,

the object is visible to the observer.

Alternately, a single moving hole or slot can be used with a fixed/stationary hole or slot. The

stationary hole or slot limits the light to a single viewing path and reduces glare from light

passing through other parts of the moving hole/slot.

Viewing through a single line of holes/slots does not work, since the holes/slots appear to just

sweep across the object without a strobe effect.

The rotational speed is adjusted so that it becomes synchronized with the movement of the

observed system, which seems to slow and stop. The illusion is caused by temporal aliasing,

commonly known as the stroboscopic effect.

LVDT(LINEAR VARIABLE DIFFERENTIAL TRANSFORMER):-

Linear Variable Differential Transformers (LVDTs) are a refinement of inductive

transmitters. They contain a primary and two opposed secondary coils and a magnetic core

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connected to the sensor. With the primary energized, core displacement from a initial position

induces unequal voltages in the secondary coils. The voltage difference is a function of core

motion and can be measured directly.

High linearity and frequency response can be realized with LVDTs over specified core

displacement. Sensitivities on volt per 0.001 inch of core movement are achieved readily.

There enable use of stiff sensors to environmental effects. Frequencies for industrial

applications fall primarily in the 60-20000 Hz range, with a sensing range from vacuum to

roughly 5000psi. LVDTs are also found in instruments introducing other system parameters

besides pressure.

CAPACITANCE MEASUREMENT TRAINER:-

The capacitance between two metal plates is a function of the distance between the

plates and the overlapping area of the plates. By measuring the change in capacitance, we infer

the displacement.

VERNIER CALIPER:-

For more precision measurement of length, vernier calipers are used. The accuracy of

vernier caliper is 0.02mm. The main parts of a vernier calipers are fixed jaw, movable jaw,

main scale, vernier scale, auxiliary head, fine adjustment screw, depth gauge etc...

Least count = 1MSD – 1VSD

= 1 MSD________

No. of divisions in vernier

MICROMETER:-

Micrometer is a precision instrument used to measure the size up to an accuracy of

0.01mm. It consists of a semicircular frame having cylindrical extension at right end and

hardened anvil inside at the left end. The spindle is advanced slowly by screwing the thimble

forward. The work piece is held between the anvil and spindle, a few pressure applied on the

work. The reading of the barrel as well as thimble is noted to get the size of the work.

Least count = ____1 pitch scale division____

No. of divisions in Head scale

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Generally least count = 0.5mm =0.01mm

50

THERMOCOUPLE:-

When two wires composed of dissimilar metals are joined at both ends and one of the

ends is heated, here is a continuous current which flows in the thermoelectric circuit. Thomas

Seebeck made this discovery in 1821. If this circuit is broken at the center, the net open circuit

voltage (the Seebeck voltage) is a function of the junction temperature and the composition of

the two metals. All dissimilar metals exhibit this effect.

THERMOMETER:-

A thermometer is a device that measures temperature or temperature gradient, using a

variety of different principles. The word thermometer is derived from two smaller word

fragments: thermo from the Greek for heat and meter from Greek, meaning to measure. A

thermometer has two important elements, the temperature sensor (e.g. the bulb on a mercury

thermometer) in which some physical change occurs with temperature, plus some means of

converting this physical change into a value (e.g. the scale on a mercury thermometer).

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Industrial thermometers commonly use electronic means to provide a digital display or input to

a computer.

RTD(RESISTANCE TEMERATURE DETECTOR):-

It is also called resistance thermometer are used to measure temperature by correlating

the resistance of the RTD element with temperature. Most RTD element consists of a length of

fine coiled wire trapped around a ceramic or glass tube. The element is usually quite fragile, so

it is often placed inside a sheathed probe to protect it. The RTD element is made from a pure

material whose resistance at various temperatures has been documented. The material has a

predictable change that is used to determine temperature.

As they are invariably made of platinum, they are often called platinum resistance

thermometer (PRT). They are slowly replacing the use of thermocouples in many industrial

applications below 6000C due to higher accuracy and repeatability. Common RTD elements

constructed of platinum copper or nickel have a unique and repeatable and predictable versus

temperature relationship and operating range(R vs. T).

STRAIN GAUGE TRAINER:-

When a metallic conductor is stretched, its resistance changes due to the change in the

length and diameter (cross section) of the conductor. Hence a strain gauge measurement

transducer used to measure strain. It is a transducer because it converts information about

relative change in dimension to the change in resistance.

LOAD CELL TRAINER:-

When a steel cylinder subjected to a force, it tends to change in dimension. On this

cylinder, if strain gauge are bonded, the strain gauge (metallic conductor) is also stretched or

compressed, causing a change in its length and diameter. This change in dimension of the

strain gauge causes its resistance to change. This change in resistance (or output voltage) of the

strain gauge becomes a measure of the applied force.

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BOURDON TUBE PRESSURE GAUGE:-

When an elastic transducer (bourdon tube in this case) is subjected to a pressure, it

defects. This deflection is proportional to the applied pressure when calibrated.

An elastic transducer that is 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

intern connected to a sector and pinion as shown in diagram. To the shaft of the pinion is

connected a pointer which sweeps over a pressure calibrated scale.

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.

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MANOMETER:-

It is the most simple and precise device used for the measurement of pressure. It

consists of a transparent tube constructed in the form of an elongated ‘U’, and partially filled

with the manometric fluid such as mercury. The purpose of using mercury as the manometric

fluid is that, their specific gravity at various temperatures are known exactly and they do not

stick to the tube.

PSYCHROMETER:-

A psychrometer, also known as a hygrometer, is a device that is used to measure the

humidity in the air. A common way these devices work is by using a material that attracts

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moisture, and that changes depending on how moist it is. The probably simplest method of

these is to use a human hair. The hair will change length, depending on the moisture.

A hygrometer has two bulbs: one wet and one dry. Both bulbs are traditional thermometers,

though one is covered with a wet towel. After a period of time, the water on the wet bulb

evaporates and at that time, the temperature is measured on each bulb. The difference between

the temperatures is noted. Then each is used on a chart to find the relative humidity of that

temperature and area. A small difference between the temperatures of the bulbs shows a high

relative humidity coming from a low evaporation rate. In dry air, evaporation happens faster

showing a large difference in temperature thus giving you a low relative humidity.