ME 6504 Metrology & Measurement All Unit Notes

November 10, 2018 | Author: Kannan Kamal | Category: Calibration, Accuracy And Precision, Pressure Measurement, Amplifier, Units Of Measurement
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Detailed notes for ME 6504 Metrology & Measurement subject as per Anna Uni 2013 syllabus...

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ME6504

METROLOGY AND MEASUREMENTS

.BASICS OF METROLOGY Introduction to Metrology – Need – Elements – Work piece, Instruments – Persons – Env Environ ironme ment nt – thei theirr effe effect ct on Prec Precis isio ion n and and Accur ccurac acy y – Erro Errors rs – Erro Errors rs in Measurements – ypes – !ontrol – ypes of standards.

UNIT I

UNIT II

LINEAR EAR AND ANGU NGULAR LAR MEA MEAS SUREMENTS

"inear Measuring Instruments – Evolution – ypes – !lassification – "imit gauges – gauge design – terminology – procedure – concepts of interchange a#ility and selective assem#ly – Angular measuring instruments – ypes – $evel protractor clinometers angle gauges, spirit levels sine #ar – Angle alignment telescope – Autocollimator –  Applications.  Applications. UNIT III

ADVANCES IN METROLOGY

$asic concept of lasers Advantages Advantages of lasers – laser Interferometers Interferometers – types t ypes – %! and  A! "asers interferometer – Applications Applications – &traightness &traightness – Alignment. Alignment. $asic concept of  !MM – ypes of !MM – !onstructional features – Pro#es – Accessories – &oft'are –  Applications  Applications – $asic $asic concepts concepts of Machine (ision &ystem – Element – Applications. Applications. UNIT IV

FORM MEASUREMENT

Prin Princi cipl ples es and Meth Method ods s of stra straig ight htne ness ss – )lat )latne ness ss meas measur urem emen entt – hrea hread d meas measur urem emen ent, t, gear gear meas measur urem emen ent, t, surf surfac ace e fini finish sh meas measur urem emen ent, t, *oun *oundn dnes ess s measurement – Applications. UNI UNIT V

MEA MEASURE SUREME MENT NT OF POW POWER, ER, FLO FLOW AND TEMP EMPERA ERATURE URE

)orce, tor+ue, po'er  mechanical , Pneumatic, -ydraulic and Electrical type. )lo' measurem measurement ent (entur (enturimet imeter er,, /rifice /rifice meter, meter, rotamete rotameter, r, pitot pitot tu#e – emperatur mperature e #imetall #imetallic ic strip, strip, thermoco thermocoupl uples, es, electric electrical al resistan resistance ce thermom thermometer eter – *elia#i *elia#ility lity and !ali#ration – *eada#ility and *elia#ility.

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UNIT-I BASICS OF METROLOGY 1.1. INTRODUCTION METROLOGY

Metrology:  it is the name given to the science of pure measurement Engineering etrology: the measurement of lengths, angles, and other quantities that are expressed in linear or angular terms i! Unit e"#$reent ii! Error# e"#$reent iii! A%%$r"%y o& in#tr$ent# i'! In($#tri"l in#)e%tion

1.1.1.MET*OD OF MEASUREMENT OR CLASSIFICATION

1. Direct Direct method method of measurement measurement 2. Indire Indirect ct metho method d of measu measurem rement ent 3. Compar Comparati ative ve method method of measu measureme rement nt 4. Coinci Coinciden dence ce method method of measure measuremen mentt 5. Contact Contact and and contact contactless less method method of measureme measurement nt 6. efl eflec ecti tion on meth method od 1. Dire%t et+o( o& e"#$reent !his is a simple method of measurement, in "hich the value of the quantit# to $e measured is o$tained directl# "ithout an# calculations. %or example, measurements $# using scales, vernier calipers, micrometers, $evel protector etc. !his method is most "idel# used in production. !his method is not ver# accurate $ecause it depends on human insensitiveness in ma&ing 'udgment.

,. In(ire%t et+o( o& e"#$reent In indirect method the value of quantit# to $e measured is o$tained $# measuring other quantities "hich are functionall# related to the required value. (.g. )ngle measurement measurement  $# sine $ar, $ar, measurement measurement of scre" pitch diameter diameter $# three three "ire method etc. etc.

. Co)"r"ti'e et+o( o& e"#$reent In this method the value of the quantit# to $e measured is compared "ith &no"n value of the same quantit# or other quantit# practicall# related to it. *o, in this method onl# the deviations from a master gauge are determined, e.g., dial indicators, or other comparators.

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UNIT-I BASICS OF METROLOGY 1.1. INTRODUCTION METROLOGY

Metrology:  it is the name given to the science of pure measurement Engineering etrology: the measurement of lengths, angles, and other quantities that are expressed in linear or angular terms i! Unit e"#$reent ii! Error# e"#$reent iii! A%%$r"%y o& in#tr$ent# i'! In($#tri"l in#)e%tion

1.1.1.MET*OD OF MEASUREMENT OR CLASSIFICATION

1. Direct Direct method method of measurement measurement 2. Indire Indirect ct metho method d of measu measurem rement ent 3. Compar Comparati ative ve method method of measu measureme rement nt 4. Coinci Coinciden dence ce method method of measure measuremen mentt 5. Contact Contact and and contact contactless less method method of measureme measurement nt 6. efl eflec ecti tion on meth method od 1. Dire%t et+o( o& e"#$reent !his is a simple method of measurement, in "hich the value of the quantit# to $e measured is o$tained directl# "ithout an# calculations. %or example, measurements $# using scales, vernier calipers, micrometers, $evel protector etc. !his method is most "idel# used in production. !his method is not ver# accurate $ecause it depends on human insensitiveness in ma&ing 'udgment.

,. In(ire%t et+o( o& e"#$reent In indirect method the value of quantit# to $e measured is o$tained $# measuring other quantities "hich are functionall# related to the required value. (.g. )ngle measurement measurement  $# sine $ar, $ar, measurement measurement of scre" pitch diameter diameter $# three three "ire method etc. etc.

. Co)"r"ti'e et+o( o& e"#$reent In this method the value of the quantit# to $e measured is compared "ith &no"n value of the same quantit# or other quantit# practicall# related to it. *o, in this method onl# the deviations from a master gauge are determined, e.g., dial indicators, or other comparators.

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. Coin%i(en%e et+o( o& e"#$reent It is a differential method of measurement in "hich a ver# small difference $et"een the value of the quantit# to $e measured and the reference is determined $# the o$servation of  the coincidence of certain lines or signals. %or example, measurement measurement $# vernier calliper micrometer.

/. Cont"%t et+o(  !he measuring tip of the instrument touches the 'o$ +or material. (g- vernier caliper, micrometer, dial indicator.

0. Cont"%tle## et+o( !he measuring tip of the instrument do not touches the 'o$ +or material. (g- !ool a&ers microscope

. De&le%tion et+o( In this method the value of the quantit# to $e measured is directl# indicated $# a deflection of a pointer on a cali$rated scale. (g- pressure measurement. measurement.

1.,.Nee( &or etrology 0 !o provide provide the required accurac# at minimum cost minimi/e the cost of inspection 0 !o minimi/e 0 !o ensure ensure the capa$ilit# of measuring instruments standardi/e the various measuring instruments 0 !o standardi/e 0 !o maintain maintain the accurac# of the instrument $# cali$rating them periodicall# design the gauges, fixtures and accessories. 0 !o design 1..ELEMENTS OF METROLOGY-GENERALISED MEASURING SYSTEM ) measuring s#stem exists to provide information a$out the ph#sical value of some varia$le $eing measured. In simple cases, the s#stem can consist of onl# a single unit that gives an output reading or signal according to the magnitude of the un&no"n varia$le applied to it. 0o"ever, in more complex measurement situations, a measuring s#stem consists of several separate elements as sho"n in %igure. !he follo"ing common element 0 rimar# sensing element 0 aria$le conversion element 0 aria$le manipulation element 0 ata transmission element 0 ata processing element 0 ata presentation element

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E2:FILLED T*ERMAL SYSTEM 3OR! BOURDON TUBE 4RESSURE GAUGE 0

It is the "idel# used pressure gauge.it "as inverted $# $ourdon.

Con#tr$%tion 0 ourdons gauge consists of an elastic $ron/e tu$e of elliptic cross section $ent into a circular arc. 0 ne end of the tu$e is fixed to the frame and other end is closed and is free to move. 0 !his end is fitted to a lever arrangement consisting of a lin&, sector, pinion and a pointer.

5OR6ING D"t" tr"n#i##ion eleentpressure +capillar# tu$e 7"ri"8le %on'er#ion eleent spiral $ourdon tu$e 7"ri"8le "ni)$l"tion eleent  lin&age and gear  D"t" )re#ent"tion eleent  scale and pointer  hen the fluid under pressure enters the $ourdon tu$e, elliptic cross section of tu$e tends to  $ecome circular. ue to this, tu$e tends to straighten. !his elastic deflection of the tu$e causes the pinion to rotate through lever arrangement. !he  pointer moves the dial and sho"s the reading.

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1..MEASURING INSTRUMENTS AND TY4ES. 1. 2. 3. 4.

eflection and null t#pe instrument )nalog and digital instrument )utomatic and manuall# operated Contacting and noncontacting instrument

1. De&le%tion "n( n$ll ty)e in#tr$ent It is mechanical device .the "eight of the o$'ect is indicated $# the deflection or movement of a pointer on a graduated scale.(g- spring $alance 7 $eam $alance

,.An"log "n( (igit"l in#tr$ent !he digital instrument gives the output "hich varies in discrete steps and can ta&e onl# finite num$er of values in given range. !he output of digital instrument is generall# displa#ed numericall# as digit. (g- galvanometer 7 ammeter.

. A$to"ti% "n( "n$"lly o)er"te( A$to"ti%: !hese instrument do not depend on the operators service.(g- automated null $alance instrument 7 C8C machines M"n$"lly: !hese instruments depend on the operator9s service. (g- :athe machine

1./.4RECISION AND ACCURACY 0

!hese terms are used in connection "ith the performance of an intrument.

A%%$r"%y )ccurac# is the degree to "hich the measured value of the qualit# characteristic agrees "ith the true value. !he difference $et"een the true value and the measured value is &no"n as error of measurement. It is practicall# difficult to measure exactl# the true value and therefore a set of o$servations is made "hose mean value is ta&en as the true value of the qualit# measured.

4re%i#ion !he terms precision and accurac# are used in connection "ith the performance of the instrument. recision is the repeata$ilit# of the measuring process. It refers to the group of measurements for the same characteristics ta&en under identical conditions. It indicates to "hat extent the identicall# performed measurements agree "ith each other. If the instrument is not precise it "ill give different +"idel# var#ing results for the same dimension "hen measured again and again. !he set of o$servations "ill scatter a$out the mean. !he scatter of these measurements is designated as ;, the standard deviation. It is used as an index of precision. !he less the scattering more precise is the instrument. !hus, lo"er, the value of ;, the more precise is the instrument.

1./.1.COM4ARISON OF ACCURACY AND 4RECISION. )ccurac# is ver# often confused "ith precision though much different. !he distinction  $et"een the precision and accurac# "ill $ecome clear $# the follo"ing example. *everal measurements are made on a component $# different t#pes of instruments +),  and C respectivel# and the results are plotted. In an# set of measurements, the individual measurements are scattered a$out the mean, and the precision signifies ho" "ell the various measurements performed $# same instrument on the same qualit# characteristic agree "ith each other.

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!he difference $et"een the mean of set of readings on the same qualit# characteristic and the true value is called as error. :ess the error more accurate is the instrument. %igure sho"s that the instrument ) is precise since the results of num$er of measurements are close to the average value. 0o"ever, there is a large difference +error $et"een the true value and the average value hence it is not accurate. !he readings ta&en $# the instruments are scattered much from the average value and hence it is not precise $ut accurate as there is a small difference $et"een the average value and true value.

1./.,.F"%tor# "&&e%ting t+e "%%$r"%y "n( )re%i#ion o& t+e Me"#$ring Sy#te !he $asic components of an accurac# evaluation are the five elements of a measuring s#stem such as1. %actors affecting the cali$ration standards. 2. %actors affecting the "or& piece. 3. %actors affecting the inherent characteristics of the instrument. 4. %actors affecting the person, "ho carries out the measurements, 5. %actors affecting the environment.

1. F"%tor# "&&e%ting t+e St"n("r( It ma# $e affected $#Coefficient of thermal expansion Cali$ration interval *ta$ilit# "ith time (lastic properties 3

UNIT-7  MEASUREMENT OF 4O5ER=FLO5 AND TEM4ERATURE /.1.MEASUREMENT OF FORCE !he mechanical quantit# "hich changes or tends to change the motion or shape of a $od# to "hich it is applied is called force. %orce is a $asic engineering parameter, the measurement of "hich can $e done in man# "a#s as follo"s irect methods  Indirect methods  irect methods- It involves a direct comparison "ith a &no"n gravitational force on a standard mass, sa# $# a $alance.  Indirect methods- It involves the measurement of effect of force on a $od#, such as acceleration of  a $od# of &no"n mass su$'ected to force. /.1.1.De'i%e# to e"#$re For%e 1.*cale and $alances a. (qual arm $alance $. Jnequal arm $alance c. endulum scale 2. (lastic force meter +roving ring 3. :oad cells a. *train gauge load cell $. 0#draulic load cell c. neumatic load cell S%"le "n( 8"l"n%e# ". E$"l "r 8"l"n%e )n equal arm $alance "or&s on the principle of moment comparison. !he $eam of the equal arm $alance is in equili$rium position "hen, Cloc&"ise rotating moment H )nticloc&"ise rotating moment 2:2 H 1:1 !hat is, the un&no"n force is $alanced against the &no"n gravitational force. De#%ri)tion !he main parts of the arrangement are a follo"s ) $eam "hose center is pivoted and rests on the fulcrum of a &nife edge. (ither side of the  $eam is equal in length "ith respect to the fulcrum

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 ) pointer is attached to the center of the $eam. !his pointer "ill point verticall# do"n"ards "hen the $eam is in equili$rium.  ) rovision to place masses at either end of the $eam. O)er"tion 

 ) &no"n standard mass +m1 is placed at one end of the $eam and an un&no"n mass +m 2 is placed at its other end.  (quili$rium condition exists "hen, cloc&"ise rotating moment H )nticloc&"ise rotating moment oreover at a given location, the earth9s attraction "ill act equall# on $oth the masses +m1 and m2 and hence at equili$rium condition. 1H2. !hat is, the un&no"n force +"eight "ill $e equal to the &no"n force +"eight. 8. Une$"l "r 8"l"n%e )n unequal arm $alance "or&s on the principle of moment comparison. !he $eam of the unequal arm $alance is in equili$rium position "hen, Cloc&"ise rotating moment H )nticloc&"ise rotating moment  % x :2 H %xx :1 De#%ri)tion !he main parts of the arrangements are as follo"s ) graduated $eam pivoted to a &nife edge RYG  ) leveling pointer is attached to the $eam  ) &no"n mass RmG is attached to the right side of the $eam. !his creates an un&no"n force R%G. !his mass RmG can slide on the right side of the $eam.  rovisions are made to appl# an un&no"n force R%xG on the left side of the $eam. peration  )n un&no"n force R%xG is applied on the left side of the $eam through &nife edge REG as sho"n  8o" the position of mass RmG on the right side of the $eam is ad'usted until the leveling  pointer reads null $alance position. hen the leveling pointer is in null $alance position, the $eam is in equili$rium. Cloc& "ise rotating moment H )nticloc& "ise rotating moment %x.:1 H %. :2 %xH g.:2W:1  !hus the un&no"n force R% xG is proportional to the distance R:2G of the mass RmG from the &nife edge RYG  !he right hand side of the $eam "hich is graduated is cali$rated to get a direct measure of R% xG %. 4en($l$ S%"le3M$lti-le'er Ty)e! It is a moment comparison device. !he un&no"n force is converted to torque "hich is then  $alanced $# the torque of a fixed standard mass arranged as a pendulum. De#%ri)tion  !he scale9s frames carr# support ri$$ons. !hese support ri$$ons are attached to the sectors. !he loading ri$$ons are attached to the

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sectors and the load rod a sho"n. !he load rod is inturn attached to the "eighing platform.  !he t"o sectors are connected on either side of an equali/er $eam. !he sectors carr# counter "eighs. !o the center of the equali/er $eam is attached a rac& and pinion arrangement.  ) pointer is attached to the pinion "hich s"eeps over a "eight +force cali$rated scale. O)er"tion !he un&no"n force is applied to the load rod. ue to this force, the loading tapes are pulled do"n"ards. 0ence the loading tapes rotate the sectors.  )s the sectors rotate a$out the pivots, it moves the counter "eights out"ards, !his movements increases the counter "eight effective moment until the torque produced $# the force applied to the load rod and the moment produced $# the counter "eight $alance each other, there$# esta$lishing an equili$rium.  uring the process of esta$lishing equili$rium, the equali/er $eam "ould $e displaced do"n"ards. )s the rac& is attached to the equali/er $eam, the rac& also is displaced do"n"ards rotating the pinion.  )s the pointer is attached to the pinion, the rotation of the pinion ma&es the pointer to assume a ne" position on the scale. !he scale is cali$rated to read the "eight directl#. !hus the force applied on the load rod is measured. El"#ti% &or%e eter 34ro'ing Ring! hen a steel ring is su$'ected to a force across its diameter, it deflects. !his deflection is proportional to the applied force "hen cali$rated. De#%ri)tion ) steel ring attached "ith external $osses to appl# force. ) precision micrometer "ith one of its ends mounted on a vi$rating reed. O)er"tion !he force to $e measured is applied to the external  $osses of the proving ring. ue to the applied force, the ring changes in diameter. !his deflection of the ring is proportional to the applied force. 

 )t this stage, the reed is pluc&ed to o$tain a vi$rating motion. hen the reed is vi$rating, the micrometer "heel is turned until the micrometer contact moves for"ard and ma&es a noticea$le damping of the vi$rating reed.  8o" the micrometer reading is noted "hich a measure of deflection of the ring is. !he device is cali$rated to get a measure of force in terms of deflection of the proving ring. Lo"( %ell# ". Str"in g"$ge lo"( %ell 

 hen a steel c#linder is su$'ected to a force, it !ends to change in dimension. n this c#linder if *train gauges are $onded, the strain gauge also is *tretched or compressed, causing a change in its

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:ength and diameter.  this change in dimension of the strain gauge causes its resistance to change. !his change in resistance of the strain gauge $ecomes a measure of the applied force. De#%ri)tion  ) c#linder made of steel on "hich four identical strain gauges are mounted.  ut of the four strain gauges, t"o of them +=1 and =4 are mounted along the direction of the applied load+ertical gauges  !he other to" strain gauges +=2 and =3 hori/ontal gauges are mounted circumferentiall# at right angles to gauges =1 and =4.  !he four gauges are connected to the four lim$s of "heat stone $ridge. peration  hen there is no load on the steel c#linder, all the four gauges "ill have the same resistance. )s the terminals 8 and  are at the same potential, the "heat stone $ridge is $alanced and hence the output voltage "ill $e /ero.  8o" the force to $e measured is applied on the steel c#linder. ue to this, the vertical gauges =1 and =4 "ill under go compression and hence there "ill $e a decrease in resistance. )t the same time, the hori/ontal gauges =2 and =3 "ill undergo tension and there "ill $e an increase in resistance. !hus "hen strained, the resistance of the various gauges change.  8o" the terminals 8 and  "ill $e at different potential and the change in output voltage due to the applied load $ecomes a measure of the applied load "hen cali$rated. 8. *y(r"$li% Lo"( Cell  hen a force is applied on liquid medium contained in a confined space, the pressure of the liquid increases. !his increase in pressure of the liquid is proportional to the applied force. 0ence a measure of the increase in pressure of the liquid $ecomes a measure of the applied force "hen cali$rated.  !he force to $e measure is applied to the piston  !he applied force moves the piston do"n "ards and deflects the diaphragm and this deflection of the diaphragm increase the pressure in the liquid medium.  !his increase in pressure of the liquid medium is  proportional to the applied force. !his increase in pressure is measured $# the pressure gauge "hich is connected to the liquid medium.  !he pressure is cali$rated in force units and hence the indication in the pressure gauge $ecomes a measure of the force applied on the piston.

%. 4ne$"ti% lo"( %ell#  If a force is applied to one side of a diaphragm and an air pressure is applied to the other side, some particular value of pressure "ill $e necessar# to exactl# $alance the force. !his pressure is  proportional to the applied force.  !he force to $e measured is applied to the top side of the diaphragm. ue to this force, the diaphragm deflects and causes the flapper to shutoff the no//le opening.  )ir suppl# is provided at the $ottom of the diaphragm. )s the flapper closes the no//le opening, a  $ac& pressure results underneath the diaphragm

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 !his $ac& pressure acts on the diaphragm producing an up"ard force. )ir   pressure is regulated until the diaphragm returns to the preloaded  position "hich is indicated $# air "hich comes out of the no//le.  )t this stage, the corresponding pressure indicated $# the pressure gauge  $ecomes a measure of the applied force "hen cali$rated.

/.,.TORHUE MEASUREMENT  easurement of applied torques is of fundamental importance in all rotating $odies to ensure that the design of the rotating element is adequate to prevent failure under shear stresses.  !orque measurement is also a necessar# part of measuring the po"er transmitted $# rotating shafts.  !he four methods of measuring torque consist of  easuring the strain produced in a rotating $od# due to an applied torque  )n optical method  easuring the reaction force in cradled shaft $earings  Jsing equipment &no"n as the ron# $ra&e. Me"#$reent o& In($%e( Str"in easuring the strain induced in a shaft due to an applied torque has $een the most common method used for torque measurement in recent #ears. !he method involves $onding four strain gauges onto a shaft as sho"n in %igure, "here the strain gauges are arranged in a d.c. $ridge circuit. !he output from the $ridge circuit is a function of the strain in the shaft and hence of the torque applied. It is ver# important that positioning of the strain gauges on the shaft is precise, and the difficult# in achieving this ma&es the instrument relativel# expensive. !his technique is ideal for measuring the stalled torque in a shaft $efore rotation commences. 0o"ever, a pro$lem is encountered in the case of rotating shafts $ecause a suita$le method then has to $e found for ma&ing the electrical connections to the strain gauges. ne solution to this pro$lem found in man# commercial instruments is to use a s#stem of slip rings and $rushes for this, although this increases the cost of the instrument still further.

O)ti%"l Tor$e Me"#$reent

ptical techniques for torque measurement have $ecome availa$le recentl# "ith the development of laser diodes and fi$eroptic light transmission s#stems. ne such s#stem is sho"n in %igure. !"o  $lac&and"hite striped "heels are mounted at either end of the rotating shaft and are in alignment "hen no torque is applied to the shaft. :ight from a laser diode

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light source is directed $# a pair of fi$eroptic ca$les onto the "heels. !he rotation of the "heels causes  pulses of reflected light, "hich are transmitted $ac& to a receiver $# a second pair of fi$eroptic ca$les. Jnder /ero torque conditions, the t"o pulse trains of reflected light are in phase "ith each other. If torque is no" applied to the shaft, the reflected light is modulated. easurement $# the receiver of the phase difference $et"een the reflected pulse trains therefore allo"s the magnitude of torque in the shaft to $e calculated. !he cost of such instruments is relativel# lo", and an additional advantage in man# applications is their small ph#sical si/e. Re"%tion For%e# in S+"&t Be"ring# )n# s#stem involving torque transmission through a shaft contains $oth a po"er source and a  po"er a$sor$er "here the po"er is dissipated. !he magnitude of the transmitted torque can $e measured $# cradling either the po"er source or the po"er a$sor$er end of the shaft in $earings, and then measuring the reaction force, %, and the arm length, :, as sho"n in %igure. !he torque is then calculated as the simple product, %:. endulum scales are used ver# commonl# for measuring the reaction force. Inherent errors in the method are $earing friction and "indage torques. !his technique is no longer in common use.

4rony Br"9e

!he ron# $ra&e is another torquemeasuring s#stem that is no" uncommon. It is used to measure the torque in a rotating shaft and consists of a rope "ound round the shaft, as illustrated in %igure. ne end of the rope is attached to a spring $alance and the other end carries a load in the form of a standard mass, m. If the measured force in the spring $alance is %s, then the effective force, %e, exerted $# the rope on the shaft is given $# %e H mg  %s If the radius of the shaft is =s and that of the rope is =r, then the effective radius, =e, of the rope and drum "ith respect to the axis of rotation of the shaft is given $# =e H = s = r !he torque in the shaft, !, can then $e calculated as !H %e= ehile this is a "ell&no"n method of measuring shaft torque, a lot of heat is generated $ecause of friction $et"een the rope and shaft, and "ater cooling is usuall# necessar#.

/..MEASUREMENT OF 4O5ER  !orque is exerted along a rotating shaft. # measuring this torque "hich is exerted along a rotating shaft, the shaft po"er can $e determined. %or torque measurement d#namometers are used. ! H %.r  H 2_8! here, ! V !orque, % V %orce at a &no"n radius r,  V o"er  !#pes of d#namometers 1. )$sorption d#namometers 2. riving d#namometers 3. !ransmission d#namometers A8#or)tion (yn"oeter#

>D

!he d#namometer a$sor$s the mechanical energ# "hen torque is measured. It dissipates mechanical energ# +heat due to friction "hen torque is measured. !herefore, d#namometers are used to measure torqueWpo"er of po"er sources li&e engine and motors. Me%+"ni%"l Dyn"oeter# In pron# $ra&e, mechanical energ# is converted into heat through dr# friction $et"een the "ooden $ra&e $loc&s and the fl#"heel +pulle# of the machine. ne $loc& carries a lever arm. )n arrangement is provided to tighten the rope "hich is connected to the arm. =ope is tightened so as to increase the frictional resistance $et"een the $loc&s and the pulle#. o"er dissipated,  H 2_8!W6B !he capacit# of prone# $ra&e is limited due to "ear of "ooden $loc&s, friction coefficient varies. *o, it is unsuita$le for large po"ers "hen it is used for long periods.

E((y C$rrent Dyn"oeter

asicall# an electrical d#namometer of a$sorption t#pe, used to measure po"er from a source such as engine or a motor. hen a conducting material moves through a magnetic flux field, voltage is generated, "hich causes current to flo". If the conductor is a "ire forming, a part of a complete circuit current "ill $e caused to flo" through that circuit and "ith some form of commutating device a form of ).C or .C generator ma# result. )n edd# current d#namometer is sho"n a$ove. It consists of a metal disc or "heel "hich is rotated in the flux of a magnetic field. !he field if produced $# field elements or coils is excited $# an external source and attached to the d#namometer housing "hich is mounted in trunnion  $earings. )s the disc turns, edd# currents are generated. Its reaction "ith the magnetic field tends to rotate the complete housing in the trunnion $earings. ater cooling is emplo#ed. *y(r"$li% or Fl$i( Fri%tion Dyn"oeter

) rotating dis& that is fixed to the driving shaft, *emi elliptical grooves are provided on the disc through "hich a stream of "ater flo"s. !here is a casting "hich is stationar# and the disc rotates in this casing. hen the driving shaft rotates, "ater flo" is in a helical path in the cham$er. ue to vortices and edd#currents setup in the "ater, the casting tends to rotate in the same direction as that of the driving shafts. # var#ing the amount of "ater, the $ra&ing action is  provided. ra&ing can also $e provided $# var#ing the distance $et"een the rotating dis& and the casting.!he

AB

a$sor$ing element is constrained $# a forcemeasuring device  placed at the end of the arm of radius r. /..FLO5 MEASUREMENTS !he flo" rate of a fluid flo"ing in a pipe under pressure is measured for a variet# of applications, such as monitoring of pipe flo" rate and control of industrial processes. ifferential  pressure flo" meters, consisting of orifice, flo" no//le, and venturi meters, are "idel# used for pipe flo" measurement and are the topic of this course. )ll three of these meters use a constriction in the  path of the pipe flo" and measure the difference in pressure $et"een the undistur$ed flo" and the flo" through the constriction. !hat pressure difference can then $e used to calculate the flo" rate. %lo" meter is a device that measures the rate of flo" or quantit# of a moving fluid in an open or closed conduit. %lo" measuring devices are generall# classified into four groups 7ent$ri Meter enturi tu$es are differential pressure producers, $ased on ernoulli9s !heorem. Meter )n rifice flo" meter is the most common head t#pe flo" measuring device. )n orifice plate is inserted in the pipeline and the differential pressure across it is measured.

A1

4rin%i)le o& O)er"tion !he orifice plate inserted in the pipeline causes an increase in flo" velocit# and a corresponding decrease in pressure. !he flo" pattern sho"s an effective decrease in cross section  $e#ond the orifice plate, "ith a maximum velocit# and minimum pressure at the venacontracta. !he flo" pattern and the sharp leading edge of the orifice plate "hich produces it are of ma'or importance. !he sharp edge results in an almost pure line contact $et"een the plate and the effective flo", "ith the negligi$le fluidtometal friction drag at the $oundar#. Ty)e# o& Ori&i%e 4l"te# !he simplest form of orifice plate consists of a thin metal sheet, having in it a square edged or a sharp edged or round edged circular hole. !here are three t#pes of orifice plates namel# 1. Concentric 2.(ccentric and 3. *egmental t#pe !he concentric t#pe is used for clean fluids. In metering dirt# fluids, slurries and fluids containing solids, eccentric or segmental t#pe is used in such a "a# that its lo"er edge coincides "ith the inside $ottom of the pipe. !his allo"s the solids to flo" through "ithout an# o$struction. !he orifice plate is inserted into the main pipeline $et"een ad'acent flanges, the outside diameters of the  plate $eing turned to fit "ithin the flange $olts. !he flanges are either scre"ed or "elded to the pipes. A('"nt"ge# 1. It is ver# cheap and eas# method to measure flo" rate 2. It has predicta$le characteristics and occupies less space 3. Can $e used to measure flo" rates in large pipes Liit"tion# 1. !he venacontracta length depends on the roughness of the inner "all of the pipe and sharpness of the orifice plate. In certain case it $ecomes difficult to tap the minimum pressure due the a$ove factor 2. ressure recover# at do"nstream is poor, that is, overall loss varies from 4B to DB of the differential pressure. 3. In the upstream straightening vanes are a must to o$tain laminar flo" conditions. 4. !he orifice plate gets corroded and due to this after sometime, inaccurac# occurs. !he coefficient of discharge is lo". Rot"eter !he orifice meter, enturimeter and flo" no//le "or& on the principle of constant area varia$le pressure drop. 0ere the area of o$struction is constant, and the pressure drop changes "ith flo" rate. n the other hand =otameter "or&s as a constant pressure drop varia$le area meter. It can $e onl# $e used in a vertical pipeline. Its it is simple in construction, read# to install and the flo" rate can $e directl# seen on a cali$rated scale, "ithout the help of an# other device, e.g. differential pressure sensor etc. oreover, it is useful for a "ide range of variation of flo" rates +1B-1. !he $asic construction of a rotameter  is sho"n in figure. It consists of a vertical pipe, tapered do"n"ard. !he flo" passes from the $ottom to the top. !here is c#lindrical t#pe

A2

metallic float inside the tu$e. !he fluid flo"s up"ard through the gap  $et"een the tu$e and the float. )s the float moves up or do"n there is a change in the gap, as a result changing the area of the orifice. In fact, the float settles do"n at a position, "here the pressure drop across the orifice "ill create an up"ard thrust that "ill $alance the do"n"ard force due to the gravit#. !he position of the float is cali$rated "ith the flo" rate.!he ma'or source of error in rotameter is due to the variation of densit# of the fluid. esides, the presence of viscous force ma# also provide an additional force to the float. A))li%"tion# 1. Can $e used to measure flo" rates of corrosive fluids  2. articularl# useful to measure lo" flo" rates A('"nt"ge# 1. %lo" conditions are visi$le 2. %lo" rate is a linear function +uniform flo" scales 3. Can $e used to measure flo" rates of liquids, gases and vapour 4. # changing the float, tapered tu$e or $oth, the capacit# of the rotameter can $e changed. Liit"tion# 1. !he# should $e installed verticall# 2.!he# cannot $e used for measurements in moving o$'ects 3. !he float "ill not $e visi$le "hen coloured fluids are used, that is, "hen opaque fluid are used. 4.%or high pressure and temperature fluid flo" measurements, the# are expensive 5.!he# cannot $e used for fluids containing high percentage of solids in suspension. 4itot t$8e )n o$struction t#pe primar# element used mainl# for fluid velocit# measurement is the itot tu$e. 4rin%i)le Consider %igure "hich sho"s flo" around a solid $od#. hen a solid $od# is held centrall# and stationar# in a pipeline "ith a fluid streaming do"n, due to the presence of the $od#, the fluid "hile approaching the o$'ect starts losing its velocit# till directl# in front of the $od#, "here the velocit# is /ero. !his point is &no"n as the stagnation point. )s the &inetic head is lost $# the fluid, it gains a static head. # measuring the difference of pressure $et"een that at normal flo" line and that at the stagnation point, the velocit# is found out. !his principle is used in pitot tu$e sensors. ) common industrial t#pe of pitot tu$e consists of a c#lindrical pro$e inserted into the air stream, as sho"n in %igure. %luid flo" velocit# at the upstream face of the pro$e is reduced su$stantiall# to /ero. elocit# head is converted to impact pressure, "hich is sensed through a small hole in the upstream face of the pro$e. ) corresponding

A3

) common industrial t#pe of pitot tu$e consists of a c#lindrical pro$e inserted into the air stream, as sho"n in %igure. %luid flo" velocit# at the upstream face of the pro$e is reduced su$stantiall# to /ero. elocit# head is converted to impact pressure, "hich is sensed through a small hole in the upstream face of the pro$e. ) corresponding *mall hole in the side of the pro$e senses static pressure. ) pressure instrument measures the differential pressure, "hich is proportional to the square of the stream velocit# in the vicinit# of the impact pressure sensing hole. !he velocit# equation for the pitot tu$e is given $# A('"nt"ge# 1. 8o pressure loss. 2. It is relativel# simple. 3. It is readil# adapted for flo" measurements made in ver# large pipes or ducts Di#"('"nt"ge# 1. oor accurac#. 2. 8ot suita$le for dirt# or stic&# fluids and fluids containing solid  particles. 3. *ensitive to upstream distur$ances. /./.TEM4ERATURE MEASUREMENT !emperature is one of the most measured ph#sical parameters in science and technolog#K t#picall# for process thermal monitoring and control. !here are man# "a#s to measure temperature, using various principles. %our of the most common are echanical +$imetallic strips  !hermo 'unctive +thermocouples  (lectrical resistance thermometer  Me%+"ni%"l Te)er"t$re Me"#$ring De'i%e# ) change in temperature causes some &ind of mechanical motion, t#picall# due to the fact that most materials expand "ith a rise in temperature. echanical thermometers can $e constructed that use liquids, solids, or even gases as the temperaturesensitive material. !he mechanical motion is read on a ph#sical scale to infer the temperature. Biet"lli% #tri) t+eroeter  !"o dissimilar metals are $onded together into "hat is called a $imetallic strip, as s&etched to the right.  *uppose metal ) has a smaller coefficient of thermal expansion than does metal . )s temperature increases, metal  expands more than does metal ), causing the $imetallic strip to curl up"ards as s&etched.  ne common application of $imetallic strips is in home thermostats, "here a $imetallic strip is used as the arm of a s"itch $et"een electrical contacts. )s the room temperature changes, the $imetallic strip $ends as discussed a$ove. hen the $imetallic strip $ends far enough, it ma&es contact "ith electrical leads that turn the heat or air conditioning on or off.  )nother application is in circuit $rea&ers 0igh temperature indicates overcurrent, "hich shuts off  the circuit.  )nother common application is for use as oven, "ood $urner, or gas grill thermometers. !hese thermometers consist of a $imetallic strip "ound up in a spiral, attached to a dial that is cali$rated into a temperature scale. T*ERMOCOU4LES 3T+er[email protected]$n%ti'e te)er"t$re e"#$ring (e'i%e#! !homas Qohan *ee$ac& discovered in 1A21 that thermal energ# can produce electric current. hen t"o conductors made from dissimilar metals are connected forming t"o common 'unctions and the t"o 'unctions are exposed to t"o different temperatures, a net thermal emf is produced, the actual value $eing dependent on the materials used and the temperature difference $et"een hot and cold  'unctions. !he thermoelectric emf generated, in fact is due to the com$ination of t"o effects- eltier effect and !homson effect. ) t#pical thermocouple 'unction is sho"n in fig. 5. !he emf generated can  $e approximatel# expressed $# the relationship-

A4

here, !1 and !2 are hot and cold 'unction temperatures in ?. C 1 and C2 are constants depending upon the materials. %or CopperW Constantan thermocouple, C 1H62.1 and C2HB.B45. !hermocouples are extensivel# used for measurement of temperature in industrial situations. !he ma'or reasons  $ehind their popularit# are- +i !he# are rugged and readings are consistent +ii !he# can measure over a "ide range of temperature +iii !heir characteristics are almost linear "ith an accurac# of a$out B.B5. 0o"ever, the ma'or shortcoming of thermocouples is lo" sensitivit# compared to other  temperature measuring devices +e.g. =!, !hermistor. T*ERMORESISTI7E TEM4ERATURE MEASURING DE7ICES OR Ele%tri%"l re#i#t"n%e t+eroeter

4rin%i)le o& o)er"tion  ) change in temperature causes the electrical resistance of a material to change.  !he resistance change is measured to infer the temperature change.  !here are t"o t#pes of thermoresistive measuring devices- resistance temperature detectors and thermistors, $oth of "hich are descri$ed here. Re#i#t"n%e te)er"t$re (ete%tor# ) resistance temperature detector +a$$reviated =! is $asicall# either a long, small diameter metal "ire +usuall# platinum "ound in a coil or an etched grid on a su$strate, much li&e

4re##$re t+eroeter  ) pressure thermometer, "hile still considered mechanical, operates $# the expansion of a gas instead of a liquid or solid. !here are also pressure thermometers that use a liquid instead of a gas  *uppose the gas inside the $ul$ and tu$e can $e considered an ideal gas. !he ideal gas la" is  H m=!, "here  is the pressure,  is the volume of the gas, m is the mass of the gas, = is the gas constant for the specific gas +not the universal gas constant, and ! is the a$solute temperature of the gas.

A5

*pecific gas constant = is a constant. !he $ul$ and tu$e are of constant volume, so  is a constant. )lso, the mass m of gas in the sealed $ul$ and tu$e must $e constant +conservation of mass.  ) pressure thermometer therefore measures temperature indirectl# $# measuring pressure.  !he gage is a pressure gage, $ut is t#picall# cali$rated in units of temperature instead.  ) common application of this t#pe of thermometer is measurement of outside temperature from the inside of a $uilding. !he $ul$ is placed outside, "ith the tu$e running through the "all into the inside.  !he gauge is on the inside. )s T increases outside, the $ul$ temperature causes a corresponding increase in pressure, "hich is read as a temperature increase on the gauge. /.0.Reli"8ility: It is the a$ilit# of a s#stem to perform and maintain its function in routine circumstances. Consistenc# of a set of measurements or measuring instrument often used to descri$e a test. /..C"li8r"tion : Cali$ration is the process of determining and ad'usting an instruments accurac # to ma&e sure its accurac# is "ithin the manufacturer9s specifications. /..Re"("8ility: It is the ease "ith "hich the readings in an instrument can $e read. %ine and "idel# spaced graduations +lines improve the reada$ilit# of the instrument. ,-MAR6S HUESTION AND ANS5ER  UNIT I 1. Di#ting$i#+ 8et>een line #t"n("r( "n( en( #t"n("r(.

s.no 1

,. .

.

/.

line #t"n("r( en( #t"n("r( hen the length is measured $et"een t"o hen the distance +length is measured $et"een t"o lines it is called line standard. surfaces +or faces it is called end standard. (g- !he protot#pe meter and imperial #ard (g- *lip gauge. , 5+"t yo$ e"n 8y #en#iti'e o& " e"#$ring in#tr$ent. !he ratio of the magnitude of output signal to the magnitude of input signal. De&ine #y#te error "n( %orre%tion Error: !he deviation $et"een the results of measured v alue to the actual value. Corre%tion:  !he numerical value "hich should $e added to the measured value to get the Correct result. Di&&erenti"te 8et>een )re%i#ion "n( "%%$r"%y. A%%$r"%y   !he maximum amount $# "hich the result differ from true value. 4re%i#ion  egree of repetitiveness. If an instrument is not precise it "ill give d ifferent results for the same dimension for the repeated readings. 5+"t "re t+e i)ort"nt eleent# o& e"#$reent# I . easurand 2. =eference 3. Comparator 

A6

0. 5+"t i# e"nt 8y noin"l #ie "n( toler"n%e Noin"l #ie:  *i/e o$tained through measurement "ith permissi$le error. Toler"n%e: the difference $et"een allo"ed highest value into the allo"ed lo"est value . De&ine re"("8ility "n( re)e"t"8ility. Re"("8ility:  it is the ease "ith "hich the readings in an instrument can $e read. Re)e"t"8ility:  it is the a$ilit# of an instrument to repeat the same results for the same measurement . De&ine leg"l etrology. :egal metrolog# is part of etrolog# and it is directed $# a 8ational rgani/ation "hich is Called `8otional service of :egal etrolog#`. !he main o$ 'ective is to, maintain uniformit# of  easurement in a particular countr#. . De&ine #t"ti% "n( (yn"i% re#)on#e. St"ti% re#)on#e:  )n instrument "hich are used to measure an unvar#ing process conditions. Dyn"i% re#)on#e  !he $ehavior of an instrument under such time var#ing inputoutput condition is called d#namic response of a instrument. 1?. Gi'e "ny &o$r et+o(# o& e"#$reent. 1. irect method. 2. Indirect method. 3. Comparison method. 4. Coincidence method. UNIT II 1. What are the various types of linear and angular measuring instruments? Line"r - i. ernier calipers ii. icrometers iii. *lip gauge or gauge $loc&s iv.Comparator  Ang$l"r:  +i )ngle gauges +ii *ine $ar "ith slip gauges +iii )utocollimator +iv )nglede&&or  ,. 5+"t i# %o)"r"tor Comparators are one form of linear measurement device "hich is quic& and more convenient for  Chec&ing large num$er of identical dimensions.

. 5+"t "re t+e So$r%e# o& error in #ine 8"r# 1 (rror in distance $et"een roller centers. 2 (rror in slip gauge com$ination. 3 (rror in chec&ing of parallelism. 4 (rror in parallelism of roller axes "ith each other.

. 5+"t i# e"nt 8y >ringing o& #li) g"$ge It is nothing $ut com$ining the faces of slip gauges one over the other. ue to adhesion propert# of slip gauges, the# "ill stic& together. !his is $ecause of ver# high degree of surface finish of the measuring faces.

/. 5+"t "re t+e liit g"$ge# 1. lug gauges. 2 =ing gauges. 3 *nap gauges 0. De&ine inter%+"nge "8ility. ) part "hich can $e su$stituted for the component manufactured to the same shape and dimension is &no"n as interchangea$le part. !he operation of su$stituting the part for similar manufactured components of the sa me shape and dimension is &no"n as interchangea$ilit#.

. *o> t+e e%+"ni%"l %o)"r"tor >or9# !he method of magnif#ing small movement of the indicator in all mechanical comparators is

A>

effected $# means of levers, gear trains or a com$ination of these elements.

. 5+"t "re t+e "('"nt"ge# o& e%+"ni%"l %o)"r"tor 1 It is usuall# ro$ust, compact and eas# to handle. 2 !here is no external suppl# such as electricit#, air required. 3 It has ver# simple mechanism and is cheaper "hen compared to other t#pes. 4 It is suita$le for ordinar# "or&shop and also easil# porta$le.

. 5+"t i# e"nt 8y le"#t %o$nt it is defined as the difference $et"een the values of a main scale division and vernier scale division. 1?. 5rite t+e le"#t %o$nt '"l$e o& 'ernier %"li)er= i%roeter= "n( (i"l g"$ge "n( 8e'el )rotr"%tor. 7ernier %"li)er:  B.B2mm Mi%roeter:  B.B1mm Di"l g"$ge:  B.B1mm Be'el )rotr"%tor:  5 minute

UNIT III

1. State any two application of laser in machine tool metrology. i )ircraft production and ship$uilding ii to $e c hec&ed for predetermined straight line. iii !o $e chec&ed for flatness of machine surfaces 7 chec&ing squarness

,. Mention "ny &o$r "('"nt"ge# o& %ol$n ty)e CMM. i uic&er inspection ii )ccurate measurements iii (asier osition iv =eduction of good part re'ection.

. 5+"t "re t+e "('"nt"ge# o& l"#er inter&eroeter i It is ideall# suited for measuring linear positioning, straightness in t"o planes. ii :ong covering range and high sensitivit#. iii 8oncontact measurement is possi$le. iv Jse of single photo detector per measurement axis.

. 5+"t i# CNC -CMM !he computer numerical control +C8C s#stem is used "ith C for the measurement of complicated parts. !he inaccuracies are automaticall# corrected $ # the C8C

/. N"e t+e ty)e# o& "%%$r"%y #)e%i&i%"tion $#e( &or CMM i easurement accurac#- )xial length measuring 7 volumetric length measuring. ii )xial motion accurac#- :inear displacement, straightness, perpendicularit#, pitches etc.

0. 5+"t "re t+e %+"r"%teri#ti%# o& l"#er i onochromatic light source ii irectional possi$ilit# iii Coherent light ra#s

. Li#t "ny &o$r "))li%"tion# o& %o)$ter "i(e( in#)e%tion#. AA

i Chec&ing tool accurac# ii chec&ing tool "ear iii monitoring manufacturing process iv )ssisting qualit# engineers and machinist.

. De&ine M"%+ine 7i#ion. achine vision can $e defined as a means of simulating the image recognition and anal#sis capa$ilities of the human s#stem "ith electronic and electromechanical techniques. . 5rite t+e "))li%"tion o& inter&eroeter . i :inear measurement ii )ngular measurement

1?.5+"t (o yo$ e"nt 8y "lignent te#t on "%+ine tool !he alignment test is carried out to chec& the grade of manufacturing accurac# of the machine tool.

UNIT I7

1. 5+"t i# )rogre##i'e error in #%re> t+re"( !he pitch of the thread is uniform $ut it is longer +or shorter to its nominal value and this is called progressive error.

,. De&ine L"y. Mention "ny &o$r o& it# ty)e. :a#- irection of the bpredominate surface patternb i 0ori/ontal la# ii ertical la# iii =adial la# iv Circular la#

. 5+"t i# e"nt 8y 8e#t #ie >ire in #%re> t+re"( "n$&"%t$ring est si/e of "ire is a "ire of such diameter that it ma&es contact "ith the flan&s of the thread on the pitch line

. De&ine t+e ter %on#t"nt %+or( o& ge"r Constant chord is the chord 'oining those points, or opposite faces of the tooth.

/. De&ine (r$n9en t+re"( < 4erio(i% error. Dr$n9en t+re"(: !his is one, having erratic pitch, in "hich the advance f the helix is irregular in one complete revolution of thread. 4erio(i% error: !he periodic error repeats itself at equal intervals along the thread

0. St"te t+e et+o( $#e( &or %+e%9ing ge"r toot+ )ro&ile. i ptical pro'ection method ii involute measuring machine.

. 5+"t i# ge"r r$no$t !otal range of reading of a fixed indicate r "ith the contact points applied to a *urface AD

=otated, "ithout axial movement, a$out 3 fixed axis.

. 5+"t i# #e%on("ry tet$re o& #$r&"%e !he irregularities o$tained $# first and second order of irregularities are called secondar# texture.

. 5+"t i# e"nt 8y o($le oduleH pitch circle diameterW num$er of teeth

1?.De&ine Me"#$reent o& Str"ig+tne##= Fl"tne## < Ro$n(ne##. Str"ig+tne##: !he shortest distance $et"een t"o points. Fl"tne##: !he minimum distance $et"een t"o planes "hich cover all the irregularities of  the surface. Ro$n(ne##: It is a surface of revolution "here all the surfaces intersected b$# an# plane  perpendicular to a common axis in case of, c#linder and cone.

11. De&ine )it%+. !he distance measured parallel to the axis from a point, on a thread to the corresponding next point. UNIT-7 1. 5+"t "re lo"( %ell# )re devices for the measurement of force through indirect methods.

,. 5+"t i# >or9ing )rin%i)le o& t+ero%o$)le hen t"o metals are 'oined together it "ill create an emf and it is primaril# a function of the 'unction temperature. . Mention t+e )rin%i)le in'ol'e( in 8iet"lli% #tri). Is $ased on change in dimension . De&ine &or%e= tor$e < )o>er For%e: !he mechanical quantit# "hich changes or tends to change the motion or shape of a $od# to "hich it is applied Tor$e: !orque can $e defined as a measure of the tendenc# of a force to rotate the $od# on "hich it acts a$out an axis. 4o>er: %orce "ith respect to !ime /. Li#t t+e in#tr$ent# $#e( &or e"#$ring te)er"t$re

1. echanical +$imetallic strips 2.!hermo 'unctive +thermocouples 3.(lectrical resistance thermometer  0. 5+"t "re t+e (i&&eren%e 8et>een ori&i%e "n( 'ent$rieter #.no Ori&i%e eter 1 :oss of head is small 2 8o "ear and tear 3 Initial cost is more 4 =equires more space . St"te "ny &o$r in&erenti"l ty)e o& &lo> eter# enturi meter, orifice meter, rotameter, pitot tu$e. . St"te "ny t>o )rin%i)le o& &or%e e"#$reent

DB

'ent$rieter :oss of head is more ore "ear and tear   :o" initial cost =equires less space as compared "ith venturimeter  

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