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Ttme Allowed 3 hours
MaXJmwn Marks 200
Canchdates should attempt any FIVE quesl!ons The nwnber of marks earned l:y each quesl!on at the end ofthe quesl!on
Js
mdJcated
Asswne swtable data, Jjfound necessary, andmdJcate them clearly For aJr R = 0 287 kJ!kg-K, Cp = 1 005 k.J/kg-K, y = 1 4, M = 28 966 kg/kg-mole
(a)
Prove the folloWing relahons
(:),~,(:),
~d (b)
p
l:l ~"'(:),
(1 5) 3 An atr compressor iS used to fill rap1dly a3 m tank at 20°C and 1 ahn The filhng process" governed by the law pv14 = constant The kmehc and potenhal energy effects are neghg1ble The raho of the final to the 1m hal mass of aJr m the tank 1S 4 Work out the folloWing (1)
Sketch the system and hst the assumphons made
(11)
Work mput to the compressor
(1 5) (c)
Steam enters a turbme at an enthalpy of 3300 k.Jikg and a veloaty of 180 m/s The steam comes out ofturbme at an enthalpy of 2700 k.Jikg With a veloc1ty of 120 m/s At the cond1hon of steady state, the turbme develops work equal to 550 kJ!kg of steam floWing through the turbme The heat transfer between the turb1ne and 1ts surroundmgs occurs at an average temperature of 370 K The entropy of steam at mlet and e:nt ofturbme are 6 932 k.Jikg- K and 7 361 k.J/ kg-K, respechvely Neglechng the changes m potenhal energy between ullet and outlet, work out the folloWing (1)
Sketch the system and show the process on p-v and h-s d1agrams
(11)
Calculate the rate at wh1ch entropy 1S produced W!tlnn the turbme per kg of steam floWing
(1 0) (a)
The lower calonf1c value ofahqmd fuel at constant pressure 1S 44000 k.Jikg The analySiS of fuel by mass 1S 84% carbon and 16% hydrogen Detenrune the lngher calonf1c value at constant pressure, and the lower and lngher calonfic values at constant volume Take h,g for water at 25°C as 2442 k.Jikg
(1 5)
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(b)
Denve an express10n for the d1ameter of the inJector onfice to spray fuel Q 2 3 cm / eye! e! cyhnder m terms of !nJ echon pressure PnJ (kN/m ), combushon chamber pressure 2 3 pcy1 (kN/m ), denSity of fuel r:r(kg/cm ) and penod of mJechon c seconds Calculate the d1ameter of the mJector onfice of a S!x-cyhnder, 4-stroke CI followmg data
eng~ne
US!ng the
Brake power= 250 kW, Eng~ne speed 1500 rpm, BSFC = 0 3 kg/kW, Cylmder pressure = 35 bar, lnJechon pressure= 200 bar, Spec1fic gramty of fuel= 0 88, Coeffic1ent ofd!Scharge of the fuel onfice = 0 92, Dural! on of mJ echon = 3 6° of crank angle
(1 5) (c)
Explam the mechaniSm offormahon ofNO,m anSI
eng~ne
DiScuss the effect of-
(1)
compress10n raho
(11)
a1r-fuel raho
(111)
retardmg spark hmmg
(1v)
exhaust gas rec1rculat10n
(v)
temperahlre and pressure of the mlet charge on the concentrat10n of NOx m the exhaust of anSI engme
(1 0) (a)
A refngerated truck canymg foodstuff" speedmg on ah1ghway at 90 kmlh m a desert area where the amb1ent a1r temperahlre" 55°C The body of the huck may be modelled as a rectangular box measunng 11m long, 4 m W!de and 3m !ugh ConSider the boundary layer on the four walls to be turbulent and the heat transfer only from the four surfaces The wall surfaces of the huck are mamta1ned at 10 oc Assume the flow to be parallel to 11m long S!de The thermo-phySical prop erhes at the mean- film temperature of 3 2 5 oc are 3
p= 1 165 kg/m , Cp = 1 005 kJ!kg-K, K
= 2 673
X
10-2 W/m-K,
v = 16 x 10-6m2/sand Pr= 0 701 Work out the folloWing (1)
Sketch the system and show the boundaty layer development along length
(11)
Heat loss from the four surfaces
(111)
Totu1age of refngerahon needed
(1v)
Power reqU1red to overcome the reSiStance achng on four surfaces
(1 5)
(b)
A flat plate solar collector W!th no cover plate 1S used to collect the solar rad1at10n to heat water m a conuneraalmstallahon The surface enusS!V!Iy of the absorber 1S 0 12 wh1le 1ts solar absorphv1ty 1S 0 95 At a g1ven hme of the day the absorber surface temperature 1S 130 oc when the solar 1rrad1ahon" 850 Wlm', the effechve sky temperature"- 8°C and the amb1ent temperature" 27°C Assume that the heat transfer convechon coeffiaent for the calm dty cond!h on 1s g1ven by h = 0 23 (T,- Too) 48 W/m 2-K where T, 1S the surface temperature and Too 1S free- stream amb1ent temperahlre Assume steady-state cond1hon, bottom surface 1S well1nsulated and the absorber surface 1S d!ffuse Work out the folloWing (1)
Sketch the system and show the control volume
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(11)
The useful heat removal rate m Wim' from the collector
(111)
The effic1ency of collector
(1v)
Comment on the results
(1 5) (c)
For a solid cyhnder W!th umform heat generahon, denve the folloWing express10n
(1 0) (a)
In order to keep off foodstuff1n better cond!hon, a food storage locker reqmres 20 tons of refngerahon The evaporator temperature" -8°C and the condenser temperature 1s 30°C The refngerant used m the refngerahon plant" Fr-12 Th!S" subcooled by 5°C before entenng to the expanS! on valve The vapor " superheated to 6°C before 1eamng the evaporator c01l The compressor employed 1S of two cyhnder, smgle-actmg havmg stroke equal to 1 5 hmes the bore The speed of the compressor iS 900 rpm The compress10n process may be assumed to be !Sentrop! c Work out the folloWing (1)
Sketch the system and show the pro cess on T -S and p-h d1agrams
(11)
The refngerahng effect per kg of refngerant
(111)
The mass flow rate of the refngerant c1rcul ated
(1v)
The theorehcal p!Ston diSplacement
(v)
The power mput to compressor1f mechan1cal effic1ency 1S 0 9
(v1)
The co effic1ent of performance
(m1)
The bore and stroke 1f volumetnc effi aency 1S 9 0%
Use the folloWing properhes for the soluhon h, = 356 kJ/kg h, = 377 kJ/kg lm=h.=2255kJ!kg v1= 0 077m 3ikg where, 1, 2, 3 and 4 refer to ullet to compressor, outlet of compressor, eX!! ofsubcooler and cap!llaJY tub el expans10n valve ex1t respect1vely
(1 5) (b)
W1th the help of a neat sketch, d!scuss the workmg pnnc1ple of aprachcal vapor absorphon system Denve the expresS! on for 1ts coeffiaent of performance
(1 5) (c)
DiScuss the vanous loads for est1mahng the co ohng load of an aud1tonum
(1 0) (a)
What 1s the d!fference between the Bemoulh' s equahon and the steady flow energy equahon? Denve the steady flow energy equahon and reduce 11 to the Bernoulh 's equahon
(1 0) (b)
Show that for some flow, the demat10n between the compresSible and mcompresS!ble flow values of the pressure co effia en! of a perfect gas (y = 1 4) 1S about 27 5%
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(1 0) (c)
A convergent-d!vergent nozzle has an e:nt area raho of 2 Atr enters the nozzle With a stagnal!on pressure of 9 50 kPa and a stagnahon temperahlre of 3 50 K The throat area 1s 49 0 mm' Detenrune the mass flow rate, eX!! pressure, eX!! temperature, e:nt Mach number and eX! I veloc1ty for the folloWing cond!hons
(2 0) (1)
Some velo c1ty at the throat, d!vergmg sechon achng as a nozzle
(11)
Some veloc1ty at the throat, d!vergmg secl!on achng as a d1ffuser
Table below g!Ves the one-D, 1Sentrop1c, compresSible flow funchons for an 1deal gas *represents the cnh cal values at the throat where the Mach number 1S uruty
(a)
M
M'
AlA'
p/po
m,
0 308
0 326
0 936
0 9812
'"
'"
'" '"
0 528
0 8333
2 197
1 717
'"
0 0939
0 5089
In a compressor, the fncl!onal torque 1ST m the 1mpeller If the d1ameter 1S D, speed N, flmd V!Sco S!ly and denSity p, prove usmg Buckmgham' s JC-theorem of d1menS1onal analySiS that
(1 0) (b)
Determme the poS!hon 1n wlnch a sohd cyhndncal block of wood of d1ameter 0 3 m and length 0 4 m Will float m water Take sp ec!lic gram ty of wood as 0 5
(2 0) (c)
Descnb e the workmg pnna ple of a P!tot tube With the he! p of a neat sketch and explam how 11 can be used to measure the stagnahon pressure
(1 0) (a)
In an open-cycle gas turbme plant, the a1r enters at l5°C and 1 bar, and" compressed m a compressor to a pressure raho of 15 The a1r from the eX!! of compressor 1S first heated m a heat eJCchanger wh1ch 1S 75% effic1ent by turbme exhaust gas and then m a combustor to a temperature of 16 0 0 K The same gas expands m a two -stage h!rbme such that the elql anS!on work 1S mammum The exhaust gas from h p turbme 1S reheated to 15 00 K and then elql ands to 1 p turbme The 1Sentrop1c effiaenc1es of compressor and turbme may be taken as 86% and 88% respechvely The mechan1cal effiaenaes for compressor and h!rbme are 97% each The alternator effic1ency 1S 98% The output of turbo-alternator 1S 250 MW Work out the folloWing (1)
Sketch the system and show the process on T-S d!agram
(11)
The cycle thermal effic1ency
(111)
The work raho
(1v)
The spec1fic power output
(v)
The mass flow rate ofa1r
(1 5)
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(b)
A centnfugal pump 1S requued to h ft 9 10 0 ht/s of water agamst a head of 6 m wlule ruruung at 500 r p m The velocity of flow through the wheel!S 2 m/s and the manometnc efficiency " 60% The angle of vane hp W!th the direch on of mohon " 150 o Work out the folloWing (i)
Sketch an impeller of centnfugal pump and draw the veloaty In angle
(11)
The diameter of impeller
(111)
TheW!dthofimpeller
(1 5) (c)
DiScuss the factors affechng stage pressure raho m an aX!al flow compressor Draw the velocity d!Stnbuhon through a blade passage
(1 0) (a)
What 1S the purpose of steam generator control vanous methods of steam generator control
?
With the help of sketches, discuss the
(1 5) (b)
DiScuss the need of govemmg of steam turbme With the help of a sketch, diScuss the workmg pnnaple of hydro-mechanical speed govermng loop L!St the vanous speed governors used m prachce
(1 5) (c)
With the help of a sketch, diScuss the workmg pnnciple ofb01lmg water reactor and explam m bnefthe fun chon of mam elements
(1 0)
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IIIBCHANICAL BNGINBBBING Ttme Allowed 3 hours
MaXJmwn Marks 200
Canchdates should attempt Question 1 m llectton 'A' winch and TWO IBestwns from Sect! on 'C'
Js
compulsory, TWO IBestwns from lllctton 'B'
Question 1 Js ofshort answer type, hmltmganswer ofeachpart to 30words Assume swtable data, Jjfound necessary and u'!dJcate them clearly
SEC'nONA (a)
At a pomt 1n a loaded structure, a pure shear stress state of c = ±400 MPaprevaJ!s on two g1ven planes at nght angles (1) What would be the state of stress across the planes of an element taken at ±45°to the g1ven planes? (11) What are the magrutudes of these stresses?
(b)
A c01l spnng of st1ffness 'k' 1S cut to two halves and these two spnngs are assembled 1n parallel to support a heaGil machme What 1S the combmed shffness prov1ded by these two spnngs m the mod1fied arrangement?
(c)
What 1S the value of Euler's bucklmg load for an =ally loaded pm-ended (lnnged at both ends) strut of length 'I' and flexural ng~d!ty 'EI' ? What would be the order of Euler's buckhng load carry~ng capaaty of a smular struct but fixed at both ends 1n terms of the load canymg capaaty of the earher one?
(d)
Suggest most smtabl e and cheap est mat en al for the followmg
,,,
Body of screw Jack
(u)
Belts
(111)
P!Ston nngs
(!v)
fuvets
(e)
An 01! nng beanng supports a shaft of d1ameter 95 mm wluch runs at 230 rpm The maX!mum load on the beanng 1s 18 kN Detenmne the beanng character!Shc number forl/d 1 5 and absolutemscoS!Iy 0 0225 kg/ms
(f)
Menhon two best reasons why accelerometer 1S preferred over seiSmometer to measure v1brahon m mecharucal system ?
(g)
ThetiGie of cam used m cam shall of! C engmes 1S ofspec1fied contour or 11eafied mohon State 1t and g1ve reasons for your answer
(h)
A S!X cyhnder 4 stroke mulhcyhnder 1n !me engme 1S completely balanced 1n respect of rea pro cahng masses State 4 reasons font
(1)
Menhon the names of 4 plashes wh1ch are used for beanngs Gilso menhon four advantages wluch plashes offer over other matenals
6)
Explam the followmg m bnef (1)
Effect of S!Ze on the tenSile strength
(11)
Effect of surface fimsh on endurance hm1t
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(k)
What 1S the pnnc1ple of reSiStance weld!ng? Ind1cate where the reSiStance 1S maX!mum m spot weldmg operat10n
(1)
Somehmes the parhng plane between two forgmg d!es 1S not ahonzontal plane, g1ve the mam reason for th!S deSign aspect, why 1S parhng plane prov1ded, 1n closed d1e forg1ng?
(m)
What 1S permeab1hty? Permeab1hty 1S more 1mportant m the bas1c process of sand cashng than poroSity G1ve one 1mportant reason for tlns feature
(n)
Metal powders are compacted by many methods, but smtenng 1S reqmred to aclueve wh1ch property ? What 1S hot 1sostahc pressmg ?
(o)
Cast 1ron W!th 1mpunh es of carb1de reqmres a parhcular rake angle for effic1ent cuttmg W!th smgle pomt tools, what 1S the value ofth!S rake angle, g1ve reasons for your answer?
(p)
From the data of ap1lot study, the percentage of occurrence of an achv1ty 1S 60% Fmd the number of observahons for 95% confidence level and an accuracy of± 2%
(q)
A typ1cal achv1ty 1-J 1n a CPM network has acl!mty durahon (t,,) of2 51!me uruts The earher expected hme (T'E) and latest allowable occurrence hme (T'L) of event 1 are computed as 8 and 11 un1ts respechvely The correspond!ng l!mes of event J, 1 e T'E and T\ are respechvely 1 3 5 and 13 5 un1ts Fmd the three floats of the achv1ty 1-J
(r)
State any four b as1c elements of a Robot G1ve one !me statement for each
(s)
W1th the folloWing pnntf ( ) statements m 'C', express how the value x = 3 8 46 2 5 appears
,,,
pnntf("% 7 2 f', x)
(u)
pnntf("% 7 4 f', x)
(111)
pnntf("% f', x)
~d
(!v)
pnntf("% -7 2 f', x)
(t)
What for FORTRAN conunands REAL and DIMENSION are used and what are thm eqmvalentsm 'C' language? (20x2=40)
SEC:nON B (a)
A Simply supported b earn made of rolled steel Jo!St (I -sechon 4 50 mm x 20 0 mm) has a span of5 m and 1t cames a central concentrated load W The flanges are strengthened by two 300 mm x 20 nun plates, one nveted to each flange over the enhre length of the flanges The second moment of area of the JO!St about the pnnapal bendmg ax!S 1S 35,060 cm4 Calculate (1)
the greatest central load the beam W!ll cany 1fthe bendmg stress m the 300 nunJ20 mm plates 1S not to exceed 12 5 M Pa
(11)
the m1mmum length of the 300 mm plates reqmred to restnct the max1mum bendmg stress m the flanges of the Jo!St to 12 5 M Pa
(2 0) (b)
A sohd shaft 1S to transnut 300 kW at 120 rpm If the shear stress 1S not to exceed 100 MPa, find the d!ameter of the shaft What percent samng m we1ght would be obtamed 1ftlns shaft were replaced by a hollow one whose mtemal d1ameter equals 06 of the external d!ameter, the length, matenal and max1mum allowable shear stress bemg the same?
(2 0) (a)
Two gears mesh externally to prov1de veloaty raho 3 1 Both the gears have standard addendum and pressure angle" equal to 20° Detemune m1mmum number of teeth on the
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puuon to av01d mterference Instead of usmg a pm10n of these numbers of teeth another puuon havmg three teeth less than the above number 1S to be used Detemune the nummum amount of stubbmg of gear teeth m terms of module w!uch 1S to be done now for th!S puuon The velocity raho 1S to be mamtamed same
(2 0) (b)
A maclune of mass 500 kg It 1S supported on helical spnngs which deflect by 5 mm due to the weight of the maclune The machme has rotahng unbalance equal to 250 kg mm The speed of the machme 1S 1200 rpm Determme the dynanuc amphtude The dampmg factor of the ViSCOUS damper 1S 0 4 Now th!S maclune is mounted on a larger concrete block of mass 12 0 0 kg The stiffness of the spnngs 1S changed such that the stal!c deflechon 1S shll the same W!th the same ViScous damper as m earher case Detemune the change m the dynamic am ph tude
(2 0) (a)
DeSign a flat belt dn ve system for the foll oW!ng spec!lical!ons Power to be transm!lted = 100 kW Pulley diameters= 0 8 m and 1 m, respechvely Centre d! stance between the pulleys = 3 m Belt speed= 20 m/s Coefficient offnchon between the belt and pulleys= 0 3 Shp = 1 2% at each pulley Fn chon loss at each shaft= 5% Overload capacity= 20% DenSity of leather belt matenal = 1000 kg/m 3 Safe stress for the belt= 2 5 MPa Thickness of the belt= 12 to 16 mm Take mto account the effect of centnfugal tens10n Find the W1 dth and the length of the belt Draw a schemahc diagram of the belt dnve
(2 0) (b)
A shaft ABCD 1S supported at one end A and at pomt C The other end D conS! sis of a pulley wluch has belt tenSions m the verhcal d!rechon The diStance AD 1S 1200 mm AC &stance 1S 800 mm A spur gear hamng pressure angle 20°" mounted at pomt B w!uch" at a diStance 400 mm from A The diameter of pulley 1S 450 mm and that of the gear 1S 300 mm The gear 1S supphed power equal to 20 kW at 500 rpm by another gear at the top of it The tens10n on the hght S!de 1S 3 hmes the tenS! on on slack S!de m the belt The combmed shock and fal!gue factors for bend!ng moment and tors10nal moment maybe taken as 1 5 The tenSile strength of the matenal of the shaft and key 1S 700 MPa DeSign the shaft and key for the pulley assummg factor of safety equal to 5 Assume allowance for the key way for stress as 0 75
(2 0)
SEI:nON C
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(a)
A cyhnder ofhetght60 mm and diameter 100 mm 1S forged at room temperature between two flat dies Find the d! e load at the end of compresS! on to a height of 3 0 mm, usmg slab method of analySiS The )'1 eld strength of the work matenal!S given as 120 Nlmm' and the co efficient of fnchon 1S 0 05 Assume that volume 1S constant after deformahon There 1S no shckmg Also find the mean d!e pressure
(2 0) (b)
Chvonnov and Came gave rules for sohd!ficahon hme and freezmg raho for a nser Usmg these rules or othetw1se find the S!Ze of a cyhndncal nser of het ght to diameter ratio as one for a steel cashng ofS!ze 250 x 250 x 50 mm 3, when the cashng 1S fed honzontally and nser 1S a S!de one Tluckness of the cashng 1S 50 mm For steel a= 010, b = 0 03 and c = 100 ConSider it as along bar of cross-sechon 250 x 50
(2 0) (a)
Two steel sheets of tluckness one mm are welded by reS! stance proJ echon weldmg techru que A current of30,000 A for 0 005 second 1S made to flow The effechve reSiStance ofJomt can be taken as 10 0 nucro ohms The Jomt can be conSidered as a cylmder of diameter 5 mm and hetght 15 mm The denSity of steel is 0 00786 gm/mm 3 The heat needed forweldmg steel!S 10 J/mm3 Calculate the efficiency of weldmg
(2 0) (b)
Prepare part program usmg APT language for nulhng the contour shownm Fig 6(b) m a smgle pass
(2 0) C~tlO
•
T ••
1•
--'1
·~ Q
to- •oo
•
' T '"
i
iii
l:. - 1 ' 1'1.\i T ·~
(a)
Two products A and B are to be macluned on three machme tools P, Q and R Product A takes 10 hrs on machme P, 6 hrs on maclune Q and 5 hrs on machme R The pro duct B takes 7 5 hrs on maclune P, 9 hrs on machmg Q and 13 hrs on maclune R The machmmg hme available on these machme tools P, Q, Rare respechvely75 hrs, 54 hrs and 65 hrs per week The producer contemplates profit of Rs 60 per product A, and Rs 70 per product B Formulate LP model for the above problem and show the feaSible reg10n graplucally/geometncally What are the basic feaSible soluhons to the above problem? Eshmate graphically/geometncally the ophmum product nux for ma:nnuZ!ng the profit Explain why one of the vertices of the feaS! ble reg10n becomes the ophmum soluhon p omt (Note Graph sheet need not be used)
(1 5) (b)
An assembly of an eqU1pment involves the tasks A to N, the precedence tasks and processmg hmes of these tasks m nunutes are given m the followmg table ConS!denng cycle hme of 20 mmutes at any work stahon, balance the assembly !me and find the ophmum number of work stahons Also find the, Hlle hme at each work stahon
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'""' 'c
Predecessor
Duration
A
D
A
' '
'c
G
D
H
' '
'
G
K
(c)
c
,, H
M
K
N
C,M
Draw flow chart and wnte source code m FORTRAN to solve the followmg problems A rec1procahng engme has crank radms rand crank length 'I' The crank 1S rotahng With uruform angular veloc1ty 'OJ' It 1S requued to find the veloaty and accelerahon ofp!Ston at d1fferent crank p o SJI!ons Also find the p OS! I! on of crank and p!Ston at max~ mum accel erahon
and at acceleral!on nearer to zero Hmt
Ace Ofp!Ston!S
a,=r'"
'(
cos9+
"'") n
