Time Allowed : Three Hours

~if; f.!! <'fl('1 i "1"1 f.!! £1 f{ II

P"'f-~-l

MECHANICAL ENGINEERING Paper-I

P"'f--q"';f ~ T fVliT ~ #; 3l'ft ~ if wff PiAfRf(i;m ~ ~ FAI'I~oi<n W

jC-DRN-N-OFFA I

~ 3i<t>. 250

Maximum Marks . 250

'!Yf arro (8) TJV"f ciT f.CIVif if ~ JR ff niH 1fif fff;tT r:;ct .-iit'ift ~;f'f ~ if ~ ~ t 1

rrfterreff or;T '!Yf '1i<f r;v;f'f <f; 3D( ~;f t I

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vrit'f; 1JV'1 /'lf71T <f; 3f<t> 1JV'7 <f; 3l'fr if fl!Wr ff I !Jitw-tf'if if ~ 1fTUf11 if 3D( fffiiRT 3fTCfVlT'fi t niH 7.Ti! ~ (Question-cum-Answer) ~ if ~ ~ 'IT ~ 'P'G7 3fTCfVlT'fi ~ I ~ 7fr!)l11 oF 31rfTCfT 3RT 1fTUf11 if f'fR2t rfit ;miT or;T 3f<t> '1iff ~ ~it I ~ ""'Z'"

'IV~ ~ ~ 'Ftf 'lfr 9/'fif><-4 1 /l{ if>'t rrt t. ~ ~ ~ it wnr <nt 1

arrffl/fil'lifRlll( ;;ri( q;eff 'lfr 3fTCfVlT'fi if, 9~'fif1( <f; f'ffi: ~ FfT'1 'IT !t ~I 3Rf!1T ~

'1 if;f 'IT l'd~RJ<n ~ <f; Wlffiii'P ~ ~ ifit I r;v;f'f <f; 3D( ~ fiRm:r if fTrr ~it I '1iff W 7R 1JV'7 <f; 3D( or;7 'lfr fi'mft if ffrlTr ~

1R1fi'r m 3D( 3/ifffl; ~ if ~ JR it' 1 Jn(-~ if m 'AT liT 'AT * Jtvr 3f1T( ~ ff nr ::ITt/~ ~ ~ it <t>TC rn 'Wft t 1

QUESTION PAPER SPECIFIC INSTRUCTIONS

Please read each of the following instructions carefully before attempting questions :

There are EIGHT questions divided in Two Sections and printed both in HINDI and in ENGLISH.

Candidate has to attempt FIVE questions in all.

Question Nos. 1 and 5 are compulsory and out of the remaining, THREE are to be attempted choosing

at least ONE from each section.

The number of marks carried by a question/part is indicated against it.

Answers must be written in the medium authorized in the Admission certificate which must be stated clearly

on the cover of this Question-cum-Answer (QCA) booklet in the space provided. No marks will be given for

answers written in medium other than the authorized one.

Wherever any assumptions are made for answering a question, they must be clearly indicated.

Diagrams/Figures, wherever required, shall be drawn in the space provided for answering the question

itself

Unless otherwise mentioned, symbols and notations carry their usual standard meaning.

Attempts of questions shall be counted in chronological order. Unless struck off, attempt of a question shall

be coumed even if attempted partly. Any page or portion of the page left blank in the answer book must

be clearly struck off

I

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'

~--&

SECTION-A

Q. !(a) ~ClPil'1 m'fil 1.1;9i 'fi11T, ~ r<fi 1.1;9i ~"t an.f~f11ifll< ff!Ris< "CIT·~ B"CIT fci<l!ii<W:n "CIT i I W fcl1 m I (a) it ~ Tfi.IT ~, ~ ffi Rls < <f; -cR" <f; ~ 1.1;9i ~ A "CIT,

. ~~m ~ ~ 2 r <tt ~ "CIT, 1.1 r ~ <tt 1.1;9i ~ <f; mq <fm ~3TT ~ 1 ~ ~ 9iT 'fiTC ft<rr ;;mn i, m 'fi1lT <tt ftqfij c 9iT ~ m qffi 9iTVT e 9iT ~ ~. "fii. fcl1 ~ ffl Ris < <fi 'lW< ~ ~ ~ 1

A particle of mass m is resting at point B. on a smooth semicircular cylinder of radius r,

tied to a point A vertically above the centre of the cylinder at a height of 2 r, with a string

. of length 1.1 r as shown in Fig. I (a). If the string is cut, find the angle 9 defining the

position C of the particle where .it jumps off the cylinder. 10

A

~ l(a)/Fig. l(a)

Q. !(b) 1.1;9i ~ "CIT ~ m !(b) it ~ ~ ~ 1 ~ ~ BC it 40 MPa 'fiT. t m, m ~ AC "CIT ~ ~ if!lT iiTm ? ~ AB ~ ~ m, m 9iT"l 9 'fiT '1ftmtlT

. if!lT i ? ~ "CIT. ~ ~ ~ if!lT t ? .,

Stresses at a point are shown in Fig. !(b). What is the shear stress on plane AC, if ton

plane BC is 40 MPa ? What is the magnitude of angle 9 if AB is a principal plane ? What

is the maximum shear stress at the point ? 10

t

100 MPa

~ l(b)/Fig. l(b)

2 **

A

60MPa

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Describe different crystal systems in Materials. 10

Q. l(d) 30 Gffl 'C!Tffi \!,'fi fqfA!l1 80 Gffl 'CI'ffi fl'niT q,l '<l'ffi'ffi ~I fl'niT 'llt qf{,g~ifll 20° GT<f 'fllur,

12 mm ~aft\ 10 mm ~ ;f; mt~ gfM>·N ~ 1 ~ 'tft! 'llt ~. rn 'fiT~ aft\ ~ 3f1'YTII ~ ~ I

A pinion having 30 teeth drives a gear having 80 teeth. The profile of the gears is involute

with 20° pressure angle, 12 mm module and I 0 mm addendum. Find the length of path

of contact, arc of contact and contact ratio. 10

Q. I (e) 7 6 kg ~ ~ '111 'llt .rnR ;f; ~ \!,'fi V!IT1' ~c: mr 3lCn1fur fil;'1:( iilffi ~, oil 'GT ~

~ if ~ ;f; 3lTtl111 '1>1 17.2 mm ~ t:m iR 3.2 mm 'ifl\ ~ ~ 1 .rnR '1>1 '111: ifl'"liP!ll'i

'11: "{'@ lf!!T ~. oil ~ 7.5 N/mm 'llt ¥.ID 'llt ~I ~ 'lfl'1'it ~ f'l; ~ an9' ~ ;f;

mt~-mt~ qf{qRfu mot ~. f.rrrhul ~

(i) ~~

(ii) 3lCn1fur aft\ 311ql1Ht1 ~ 'llt ~ 'fiT 3f1'YTII

(iii) 3lCilifur ~ 'fiT 3!TCI'iff <!iffi I

The vibrations of a machine of mass 76 kg are damped by a viscous dashpot which

diminishes amplitude of vibrations from 17.2 mm to 3.2 mm in two complete oscillations.

The machine is mounted on four springs each of stiffness 7.5 N/mm. Assuming that the

damping force varies as the velocity, determine :

(i) the damping coefficient,

(ii) the ratio of frequencies of damped and undamped vibrations, and

(iii) the periodic time of damped vibrations. 10

Q. 2(a) tRffiT ~ ;f; GT<f offi'f if ~ aft\ '!ft:rl11< ~ ;f; ~ ~ c~cq-1 ~I Jq(liffi

~ 'fiT ~«1"11(1 m ~. ~ 1:((1'lft:uft. Rlfl9s< if '!ft:rl11< am-~ ~ 'fiT

f.rrrhul ~. ~ m ~ fil; Rlfl9s< Pt~1RIR~t1 f<ffini'l' 'C!Tffi \!,'fi tRffiT ~ GT<f offi'f

i :

OD-315 mm -xfim : 2.8 mm I ftm ~11 '1>1 ~ ~ aft\ ~ f'l; f€f\9s < if

tfl1'!1""l! ffi"''' '11: GT<f I .4 M P a ~ I

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· Derive expressions for longitudinal and hoop stresses in a thin walled pressure vessel.

Using the above expressions, determine hoop and longitudinal stresses in a household

LPG cylinder, assuming it to be a thin walled pressure vessel with following dimensions :

OD - 315 mm thickness : 2.8 mm. Take end caps to be flat and the pressure in the

cylinder is 1.4 MPa at room temperature. 20

Describe Austempering of steel with help of ITT diagram. 10

Q. 2(c) ~ ~ ~ ~ ~~!HIIIIil 311~ ('1i'Tffi3R) qi') f.1~1f\1f@d ~ "ft <fffi"dT ~

.~ ofi ~~ 120° ~1" ofi ~. '1i'Tffi3R ~ m>ifm omr ofi m!:f 20 mm 'P'T "«T C!'F

'!ffil: 'P't m ~ iifTd1 ~ 1 ~ ~1" ofi m 30° ofi ~. ~an: m 'fi«<T ~ 1

~ ~1" ofi m 12oo ofi ~. '1i'Tffi3R ~ ~ .mr ofi m!:f m oFt am: ftomq;

iifTd1 ~I ~ ~1" ofi m 90° ofi ~ '1i'i'ffi3R ~ iifTd1 ~I ~ 9\t ~"fdlf ~ 25 mm

~I

A cam drives a flat reciprocating follower in the following manner :

During first 120° rotation of the cam, the follower moves outwards through a distance of

20 mm with simple harmonic motion. The follower dwells during next 30° of cam rotation.

During next 120° of cam rotation, the follower moves inwards with simple harmonic

motion. The follower dwells for the next 90° of cam rotation. The minimum radius of the

cam is 25 mm.

Draw the profile of the cam. 20

Q. 3(a) ~ V'r:rc '!il 750 3!R<ft1:(11 'R 2 kW 9iT ~ '!>\11 ~I V'r:rc ~ Am C if, "'T

~ ~ "fr 300 mm 3fc11T t "ffiT s3lT ~I 300 mm C!lm 3l\l: 150 mm C!lm 9\t ~ f\Hf.'l~i

B m D 'R m!:fd ~. ~ 1il> m 3(a) if fumm lf!lT ~ 1 ~ ~ 1il> ~11 RHf.1Jii·

'R '!G,c:T (f1T1f 3;!P:fm ~ I ~11 f~nf-1 <iT ofi ~ '!G,c:T ~ 9iT 311'1Td" 3 ~ I ~ {f.j ~1· m V'r:rc ofi "lT<: '!il 'l'if{~ ~ 1 <i<P1" . m $1" if ~ Wft1 m m ~ 'flll1ff:

. Kb = 1.5, Kt = 1.0 ofi "if{l(if{ ~ I

V'r:rc ofi C(9i<il1111 C!lm 9iT f.ruhuT ~. 1Ift 311~ o1"1" ~ 110 MPa m 311~ 3T1!1M"T ~ 65 MPa if I (V'r:rc C!!ffi '!il 5 mm ofi m<rr11 if ~ I)

4

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A shaft is to transmit 2 kW at 7SO R.P.M. The shaft is supported in bearings A and C,

300 mm apart. Two pulleys of 300 mm diameter and ISO mm diameter are located at B

and D as shown in Fig. 3(a). Assume that the belt tensions are vertical for both pulleys.

Ratio of belt tensions for both pulleys is 3. Neglect weight of pulleys and shaft. Take

. combined fatigue and shock factor in bending and twisting equal to Kb = l.S, K1 = 1.0,

respectively.

Determine uniform diameter of the shaft if allowable tensile stress is II 0 MPa and

allowable shear stress is 6S MPa. (Take shaft diameter in steps of S mm.) 20

i I I I I I I I

-+t I I

120mm

B i 300mm~

I

0 ; 150mm~

I I I I I

I I I -I 180 mm ---+\60 mmi+-

~ 3(a)/Fig. 3(a)

1

I I

Q. 3(b) ~ w2f 'fl:!T ~ ~ 7 <D ~ "II'PR't <F oftTf ~ ~ 1

What are polymeric materials ? Distinguish between two polymer types. 10

Q. 3(c) ~ ~ <F 9ill\1·i'i ~ ~ <F '!iR'1!, ~ 'liR <rR-~ f.'l~'iRI~ct <F ~ a~ict<lfilifi

~ :

~ <lT'i"-<ft!IT{ qftlt>l'l"l <f; ~. 'liR <rR-~ 10 kNm ~ IS kNm cr<t> l!>'f'MI'i ~

~ 'fiPCIT ~I ~ <i"TG 3!Tit qft'fil101 <f; 1m( Cffi" a~qftqRfct ~ ~ 3ih: (!<! <lT'i"-<ft!IT{ qft'fii'IOI

if c:(ifi<:1111'1 ~ ~ "'G ""!>{ 50 kNm tn iiiTc!T ~I W'f; <i"TG, ~ qft'fii1UI <fi 1m( Cffi" a~qftqfifct

~ ~ I ~ 1J'f'T{ <rni ~l f\ ( 1/.ll iiiTc!T ~ I

~ ~ f.f1:m <rR-~ li'rn ~. 300 311<cfic:('"l ~ m ~. 2200 kg/m2 <F ~<l.ll'll'i ~

~ <f; lf\11 { q; ~I \1 <fi "ffit!, "'iffi<fi ~ I

f.ruhul ~ :

(i) li'rn <F "!lUI <rR-~ 'fiT ttft'1luT

(ii) li'rn ~ vWffi

(iii) ~ 'fiT m J"Cillqii'i 1

5

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Because of nature of its operations, the load torque of a machine is intermittent as

follows:

During its three quarter revolution, the load torque increases uniformly from 10 kNm to

15 kNm. Thereafter it remains constant for half revolution and then decreases uniformly

in three quarter revolution to 50 kNm. After this for one revolution it remains constant.

Thus the cycle is repeated.

The machine is run by a constant torque motor running at a speed of 300 rpm, in conjunction

with a flywheel of mass moment of inertia of 2200 kg/m2•

Determine-:

(i) Magnitude of mean torque of motor

(ii) Power of the motor

(iii) Speed fluctuation of the system. 20

Q. 4(a). ~ W ~nl'fll( V'ttR -q"( 3 kN-m <FT ~ ~ 3ih: 1 kN-m <FT Of\'! ~ WIT '§;3TT ~ 1

V'ttR 'liT "fl'li'l w:rm 'if <r"fll!T ;;rAT ~. ~ fffil: cry= 480 MPa 3ih: ty = 265 MPa ~ I

m <ll'ffi <FT, f.HRIR'it~ <FT ~ttlAI\1 ~ ~ Yfl:'fl\11 ~

(i) ~ 9fll'11•!! "\!UT1 ~ ~

(ii)~~~~l

A solid circular shaft is subjected to a bending moment of 3 kN-m and a torque of

1 kN-m. The shaft is to be made in carbon steel· for which cry = 480 MPa and

ty = 265 MPa.

Calculate shaft diameter using :

(i) Maximum normal principal stress theory

(ii) Maximum shear stress theory. 20

Q. 4(b) ~c 'if!IT 'iffit ~ ? ~ qltf'fl<"l ~ m fil;m %IT ~ ? ~iT <F f<t;;tf "q'l\

311,~ 'FT ~ ~I

What are composites ? How are they classified ? Mention any four applications of composites.

10

Q. 4(c) ~ 3lfuilfili'fl m ");'1'filtl fl'l<:r\ 3lih.9 m 4(c) 'if fu9T<rr 1Tl:rT ~I <itfll"fl • B-C,

"iffif'l V'ttR 'it '¥. ~ fiR A -q"( ~'l m "<F fffil: 'lf!U ~ I • C or;g: • E '<F

'fl1!1 'li'fl1 '§;3TT ~, am • B • D "<F 'fl1!1 'li'fl1 ~, un f¥'1 V'ttR "<F 'fl1!1 ~ "<F

mu '¥T ~3TT ~ 1

~ ~ if GhiT '1ft ~ m Tb = 27, Tc = 30, Td = 24 am: T. = 21, 'ffi 'iJT\1"fi am: "CJ1ft:rcr.

mit '1ft -mlif '<F 311,-qm 'FT f.r~ ~ I

6

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An epicyclic speed reduction gear schematic is shown in Fig. 4( c). Compound wheel

B-C is free to rotate on pin A connected to driving shaft. Wheel 'C' meshes with fixed wheel 'E' and wheel 'B' meshes with wheel 'D' keyed to driven shaft.

If number ofteeth on wheels are Tb = 27, Tc = 30, Td = 24 and Te = 21, determine the ratio of speeds of the driving and driven shafts. 20

Driving Shaft

A

B

c

n D E

m- 4(c)/Fig. 4(c)

~-<{

SECTION-B

Driven Shaft

Q. 5 (a) 'lNi'f fYlmt 3ffi: rffi fYlmt q\T ¥>fT ~ 3ffi: "l'('q."C(\1.1:(11., <t> I il f~s 3ffi: ~ ~ffi <fi ~ ~('! ~ ORR "<t>Cf-r ~ CIIF 'I'~ I

Compare flank wear and crater wear and draw tool life versus cutting speed curves for H.S.S., Carbide, and ceramic tools. 10

Q. 5(b) '~ 3f'11:f!Q' q\T '1ft~ ~I mq tft flli;)ll .. l( fil> ~ ~ <fi ~ 'fiTlf m 31qqr 't>3'R 'fiTlf m 'fiT 'fl:fT ~ lffirr ~ 1 'fl:!T, ~ if, ~ ~ 3f'1'ml' >I'T'{!

'f>{'fT . ~ q i (9 "1~ ~ liTcrr ~ ?

Define 'Grinding Ratio'. Also explain what is meant by a grinding wheel acting soft or acting hard. Is it always desirable to obtain a high grinding ratio in practice ? I 0

Q. 5 (c) 'l(<t> <Ftl'fi if TlcfT ~ ('f]llCf ~ 'fiT 3TUI"!f'l fil;<:rr 3ih: 'S!ft1 I 00 ~ ~ ~ ~ 3ih: f.1>:i?roT ('f]llCf 3ih: Ri Lfict<tl ('f]llCf <fi ~. f.'! ~1 fftRCI<t <fi a~, 'l(<t> 'fioft~ '1f!!1 :

f4Lfict<tl ('f]llCf F = 1500 + 120 X

~ 3000 I ., '" '1 vI ('f]llCf C = --

X

"''l?1 X ~ ~ ~ I

7

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<:Tl? ~ ~ r r 'f<!T ~ -;;IT "T'JCil ffiTR[ ~"ffO'f 'li1: '{ifr ~, ? m- "C('fi m ~ 1f{ ~"ffO'f

"TTciT ffill(f ~ ~ ? .

A coJnpany studied the cost data on quality and found a relationship between the percent

defective and the cost of control and cost of failure per 100 parts as under :

Cost of failure F = 1500 + 120 X

3000 Cost of Control C = X

where X is percent defective.

1 f

What is the percent defective which minimizes the quality cost ? How much is the

minimum quality cost per hundred parts ? ' 10

Q. S(d) "C('fi ~ ~ <F fffil: ~ ~~ fclf.1'1fa1 ~man <F fffil: f.1tra" aiT\ ·~ l'fliffi ~ ~

lf{ ~ :

AA.~ ~. mmr~ (<i.) qfl::q(ff mmr~ (<i.)

A 1,25,000 f 50 '

B 2,00,000 40

c 2,50,000 20

(i) ~ ~~tllfVId 3T8C1~ "~!fit qq 8000 ~ liT"'D t "ffi fllm ~m 'lit ~on i;ff'ff ~?

W <mf 'lit lJI'fl <Fi ~ ~ ~ ~ I

(ii) ~ B q>i[ r<f>'llltiCI~I ~ ?

(iii) ~ <Fi ~ 'R fVl:!ulT ~ I

Fixed and variable costs for three potential manufacturing facilities for same product are

shown below : .-

Mfg. Facility Fixed Cost/Yr. (Rs.) ' Variable Cost/Unit (Rs.)

A 1,25,000 i 50

B 2,00,000 • 40

c 2,50,000 20 .

1-

(i) If the expected output is to be 8000 units per year, which facility should be selected?

Explain with the help of a graph.

( ii) When is option B economical ?

(iii) Comment on choice of the options.

8

**

10

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\

Q. 5(e) l:;'f.-6t. lffilrr 3it;rm if ~ WIT iff, ~ iff aih: 3l'j)'fj_<1~ ~ (f;i'f <f; ~ ~ ~I

Differentiate between open loop, closed loop and adaptive control systems used in NC

machine tools. 10

Q. 6(a) -wrr am: ~ e:J>-.i!ll 'R, 3lf{ -c;tr.an. ~ <fi .:J>ctlfil<t>, 311mftt; 3lllll'!, ~ am: e~ISUJtll

"'fiT hill~ ?I ~I 'fliT "ifiTtUT ~ ~ ll:ifi-'l~ ft~ISUJ>tll <tiT ~-'left ft~ISUJ>tll -ij '"1m ~

~ ;;rmr ~ 7

According to the ISO system, sketch the basic size, deviation, and tolerance on a shaft and

hole assembly. Why uni-lateral tolerance is preferred over bi-lateral tolerance ? I 0

Q. 6(b) 1l:<t> hill~ ?I <t\l m -ij, ~ f.rB'f\1JT lffilrr'l ({it.~.) 'l<A" \"1\Z ~ 1 ~ MN

am: ~ qfht~lilc( 'fl!T-'fl!T ~ 7 {it.~. <fi mr ~ 'fiSC <t\l ~ "<t>T quf, ~ 1 "ttW

~ ~ -aT'1 li!irq'1;'f ~]5 '!GT!if <fi '11l1 ~ I

Explain with the help of a sketch the Electric Discharge Machining (EDM) process. What

are its advantages and limitations ? Describe the nature of the surface obtained by EDM.

Also name any three important electrode materials. 20

Q. 6(c) mtli-mtli 't<.'ll~,j'f <f; mr tffi'ifi1T 3!l<!f ~ (1fr.1:(.~.) <tiT \"1\Z ~ am: ~ 3{1,~ afh: qfhi'lli Fm 'R "'i'f'<lf ~ I

Explain with neat sketches the Plasma Arc Welding (PAW) process and discuss its applications

and limitations. 20

Q. 7( a) iJ;q."f 31TC1:('li. ' if ~ ~ GT ~ m <fi ~ ~ l:fiT:r ~ filfulli ~ I 1l:ifi

h'll~?l <t\l m "ft ~ ~ G<: ~ <t\l ~ ~, fimr (~ ~ lt~) ftli;)ii .. C( I mq ~ '1J;q:f3lll: 1:('li.' fimr <f; GT ffi~ am: <lR li(';rq~of 3{1,~ "'fiT ~

~I

List five distinct methods used to obtain high energy rates in HERF. With the help of a

sketch explain the spark discharge method of High Energy Rate Forming. Also mention

two advantages and three important applications of HERF method. 20

Q. 7(b) Wffl f<Rim <f; ?J>f.'llliG~I ~ "'fiT ifi!1'1 ~I ~ ~ lfi m<:Ufi if 12 ifiTif ~ q\1

~ ~ 'ltc«ff ~ afh: fTAif if 3l'ffu <fi "ftW ~ ~ lfi WI 20 fTAc: <f; 'tlili-ifili'l

9

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~ ~ m ~ ~ m-~qffi -ij ~ ~ n<rr ·'PI ~"11~1 ~· ~ 1 n<rr

~a1c!T, ~ ~ 3it<: fil<fifiUIC\1 ');i:ii'\iii'\i 'PI 4nM11 ~ :

'iiflf m<r ~~m<r ~

A - 10

B A 6

c B 8

D A 6

E B 12

F E ! 10

G F 4

H G 12

I F 2

J F 8

K G g

'[ L H, I, K 14

· State the basic principles of plant layout. Table below lists 12 work-elements along with

their immediate predecessor elements and duration in minutes. Design suitable line consisting

of appropriate work-stations assuming a cycle time of 20 minutes. Compute the line

efficiency, balance delay and smoothness index :

Work Element Immediate Predecessor Element

A -B A

c B

D A '

E B

F E

G F '

H G

I F

J F

K G

L H, I, K . '

Use the least-number- of predecessors rule.

10

**

Duration

10

6

8

6

12

10

4

12

2

- 8

8

I4

20

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Q. 7 (c) ~ qf{q $1 <tcRT '!>! l1R11 ~ f<f; "ClTA"T it 1JTfcf cn:rn '1ft 3!1 q Q!Ffi(j I '!>! ~ Tf1l; fit> cflli"l "" ( ~ ofi m!:! f.l<l>c '!>! tr.iu ~ 1 ~ 3T1,m< ftrOO m-~ <f; f.1~1R1~t1 ~ ~ fil;l:( Tf1l; ~ :

~ ~ffi 1'1 H'l CT<I1: ~~~ km

I 100 1500

2 !50 2000

3 120 1700

4 80 1100

5 90 1200

6 180 2700

(i) ~ 'R 31Tmfuf, ~ cn:rD 3ih: ~ Tf1l; kms ofi o\Tq tr.iu (~) f~

~ 1 «<? "W'-B<iu ~ ~ ~ ?

(ii) ~ ~ it 9(qlfVId kms <flti'f 32,00,000 llT, "ffi c:TlliT '1ft lfi"ir '!>! ~1,'Wf ~I

A transport company assumes that the requirement of tyres used in vehicles are closely

related to number of kilometres driven. Accordingly, the following data covering the last

six months have been collected as follows :

Months Tyres Used Thousands of km driven

I 100 1500

2 150 2000

3 120 1700

4 80 1100

5 90 1200

6 180 2700

(i) Establish the relationship (linear) between the required tyres and kms driven based

on data. How good is the co-relation ?

(ii) If expected kms drive in a month is 32,00,000, forecast the demand for tyres. I 0

Q. 8(a) "tf<!; .~ 'R" ("~"R" ~ CWI") oFt (1·if>~Y'11 oFt Wf1T "[4f.1yfol miTU'f 3Ml"''11"

(~f.1tf><tilfl:•1 fumf t&.'i''T) oFt ~11 <i': mq ~ 1

II

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~ illT<f ~ m ~ 'fiT ~ffil'fli'f 'li«fT ~. ~ 2oo ~ "B11f ;;00 ~ 1 ~ '1il ~

<f; ~ ~ ~ <f; J~GI~'1 .i'(. 60 llr"'iY 9ft ~ M ~I ~ 9il ~ 'fil<f-"f?:ffi"

. '(fi!' "i't ~ 3ft\ ~ ~ '1il 'lT'ffi m i'! 120 mz- \91ffi ~ 1 w:rll ~ ~. ~ mz-6 ~ 9ft -qfir 1f\ ~ ~ I

(i) IDr <fi ~ ~ ~ 9ft if<olrr 'fiT Gf<'lii'1'1 ~I

(ii) IDr if. ~ l'fli'f\l;"'~ 'ft!T ~ ?

(iii) ~ ~ '1il '11{~ * ~ ~ 3ft\ 'fil<f-1liffi ifll1' ~ 4o mz- 'll{ m-r iiflll;, m 'fl".lT ~ 9ft if<oqr 9il . ifll1' ~ ;;rr tl'f\m. ~ ? if'! IDr i'( l'fli'f\l;ill fi);o-fi itlft ?

Compare the concept of 'Just-in-Time' with that of 'Manufacturing Resource Planning'.

A work centre uses Kanban containers which hold 200 parts. To produce enough parts to

fill the container 60 minutes are needed. Moving the container to the next work-station

and return of empty container takes 120 minutes. There is overall demand rate of 6 units

per· minute.

(i) Calculate the number of containers needed for the system.

(ii) What is maximum inventory in the system ?

(iii) If the setup and runtime to fill the container is reduced to 40 minutes, can the

number of containers be reduced ? How much Wil.l be the inventory in system then?.

20

Q. S(b) ''mf;i:! eiR""l<t>~lll f.rl:i?roT i'! ~·' ~ 'ft!T w:m1 ;;nm ~ ? W iiT6 9il ~ '111 \mQm ~

mtfi ~ ~ 3ft\ 'flltj"'OI ~ ~ ~~· q;l ~ J<li~{Oj'f mmt el'fiHI~~ I

fll~'11ftR9t~ ~ ~ 3ft\ 5 of; ~ 3Wf!tT 'fiT ~~'11\'l ~ SO:. X 3ft\ R of; ~

f.rl:i?roT <nf \tim: ~ I <nf ~ ~ ~ flli mlil1 ~ if ~ 3Ttflff ~ ~ I

~mr

X R

~l\1"11 ~ 2 ~ n

d2=R/cr' 1.128

c2 =cr/cr' 0.5642

1 2 3 4 5

5.004 5.204. 5.014 5.008 5.009

0.02 0.08 0,03 0.05 0.04

3 4 5 . 6

1.693 2.059 2.326 2.534

0.7236 0.7979 0.8407 0.8686

12

**

6 7 8 9 10

5.016 5.030 5.010 5.016 5.010

0.09 0.04 0.04 0.05 0.07

7 8 9 10 11

2.704 2.847 2.970 3.078 3.173

0.8882 0.9027 0.9139 0.9227 0.9300

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What is understood by "process is under statistical control" ? Explain clearly with the

help of diagrams, illustrating out of control situations.

Plot the control charts of X and R, using the following sample data and a sample size

of 5. From the chart, find out whether the process is under control.

Subgroup No. I 2 3 4 5 6 7 8 9 10

X 5.004 5.204 5.014 5.008 5.009 5.016 5.030 5.010 5.016 5.010

R 0.02 0.08 0.03 0.05 0.04 0.09 0.04 0.04 0.05 0.07

The factors for estimating cr' from R and cr from statistical tables are reproduced below :

Number of 2 3 4 5 6 7 8 9 10 II observations n

d2 = R/cr' 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078 3.173 c2 =ala, 0.5642 0.7236 0.7979 0.8407 0.8686 0.8882 0.9027 0.9139 0.9227 0.9300

20

Q. 8(c) "C('!l Fclf.'lliful Wwr GT ~<t>R-q<t> Jq<:<t>(f A aftr B i( ~ 'flt't if>'T m W ~I ~ A if>'T "ffi"I1"0 <i 30,000 t ~ ~ B if>'T "ffi"I1"0 <i. 50,000 t I ~ Jq<:<t>(f A aTtr B

~ ~ ~ .q--qf if ~ f.rffl 3lN <f; ~Plm: <i. 10,000 3itt <i. 15,000 ~ol '1'>'T

~tl

'li('lffi ~ ~ ~ ~ '1'>'T "ffi"IIC[ 12% lJfft qll[ t, f.ruhur -~ ~ G)-;ff if ~ '1\"r"'im -,Jmq<:<f>={ ~'ll UTRT ~I Wffl ~ ~ "d"Ylllll· 'fiT ~~'"1111 ~I.

A manufacturing organisation is considering investment in two alternative equipments

A and B. Equipment A costs Rs. 30,000 while the equipment B costs Rs. 50,000. The

expected yearly net income for the first five years from these equipments are Rs. 10,000

and Rs. 15,000 for equipments A and B respectively.

Assuming the cost of capital as 12% per annum, determine which equipment should

be selected. Use net present value approach. 10

13

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cs 1~/-·i·~\ "''''1ffi. ~~~ .. -- · · :' -lol,<..•.d. 0 ,lfiV .,

Q i f?4 Cfi $:•f\ f.l Q {\ (51~ -l:Bf-11)

w-J-l:Bf ~ut ~ ~

(;m t.l ~ 'l'f f.l"'l~fula f.Rm <i\ 'f'T'l1 ~ ~ )

G113uil il ¥J .:me m fu( 1""[1.( ~ it fRt ~ ~ G1:ii il .,q ~ 1

3Uil ~<m <i\ ¥J "!l'r.J m ~ "3<1\ t.J ~ I

C-DRN-N-OFFB

~~:250

m <=i&n 1 3itt 5 ~ ~ <M owt) m i\ "i\ ~ ~ "i\ 'fill -"i\ -'fill ~ m ~ eft:! m ~ "3<1\ ~I ~ m /'IWT ~ ful( f.i'«! ~ ~ oo fu( 1""[1.( ~ 1

-srru ~ ;m "3B1 ~ l11111'l il fffiY -.rR ~. fum~ ~ m-'1'1 il m-r 1f!ll t, :>fR ~ l1TI1Ill 'Ill "\'11!

~ m -B0-"3<1\ ("if<lo -a\ o 11; o) ~ ~ ~ q>; f.lfu! ~ q>; ~ <!RT ~ 1 ~ l1TI1!ll ~ 3ffilfut; 3P!

mfi l11l1lll il fffiY 1""[1.( "3<1\ '11: qi\{ ~ ~ ~ I ~ ~ "\11l<l ~ q;){ 'l'ftffiUTT <lit ;;rm:,, "3WliT ~ m ~ <IRT ~~ ~ ~ m, 311&;fu! "3<1\ ~ ful( fu( 1""[1.( ~ il tt ~~ ~ 3ltt ~ ~ ~ 3l~ ~. ""' (jqi 3P!'1IT " <!>01 1f!ll m 1

l1T-i\ ~ >l"ll"T"ffi "<litlJURl sl>lilj<AR <lit~ I 3lifu<f; ~ "i\ fu( 1""[1.( m ~ "3<1\ <i\ >fl t!P«<T <!\ ~ ~ "Jil 'll1lT '!

1f!ll m I ffi-B0-"3<1\ ~ i\13l<'ft ~ 1""[1.( qi\{ '[IJ 3l~ '[IJ ~ 'IWT <i\ ~: <m: ~I

MECHANICAL ENGINEERING (PAPER-II)

I Time Allowed : Three Hours I I Maximum Marks 250 I

QUESTION PAPER SPECIFIC INSTRUCTIONS

(Please read each of the following instructions carefully before attempting questions)

There are EIGHT questions divided in two Sections and printed both in HIND! and in ENGLISH. . Candidate has to attempt FIVE questions in all. Question Nos. 1 and 5 are compulsory and out of the remaining, THREE are to be attempted choosing at least ONE question from each Section. The number of marks carried by a question/part is indicated against it. Answers must be written in the medium authorized in the Admission Certificate which must be stated clearly on the cover of this Question-cum-Answer (QCA) Booklet in the space provided. No marks will be given for answers written in medium other than the authorized one. Wherever any assumptions are made for answering a question, they must be clearly indiCated. Diagrams/figures, wherever required, shall be drawn in the space provided for answering the question itself. Unless otherwise mentioned, symbols and notations carry their usual standard meanings. Attempts of questions shall be counted in chronological order. Unless struck off, attempt of a question shall be counted even if attempted partly. Any page or portion of the page left blank in the Question-cum-Answer Booklet must be clearly struck off.

1 [P.T.O.

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!

GIUS-A / SECTION-A

1. (a) v;q; <iiRf 'Glli if "3i'i!T 480 'C 'R mll otft ~ 3fu: 40 • C 'R ~ 3ffift ~ I >ffir 'illli 1Wfi <lit 1@ifi 0·0785 kJ /kg K ~ omft ~I >ffir 'Glli ~ ;;rR ~ "if>T'f 'liT f.tlffiu! ~I In a Carnot cycle, heat is received at 480 •c and rejected at 40 •c. The entropy of the sink increases by 0·0785 kJ /kg K per cycle. Determine the work done per cycle. 10

(b) ~ <:~ llt ~ 1l;<j; ~-'Glli fm ~ re ;f;\ ~ <:&R!T llc ~I~ fm <fTil Tmin i 3fu: <:6'1 'fil\l if TJlf <!if.t 'R 3B'1iT <fTil Tmax ~I ~ Wf\s;r 3fu: mRUT it Wr1; Gl'! ~ r P it, eft

!!"H 4><.1 llc . 11 t • T max if; Wr1; -.ftl!l 'l<!l it;ft .? Tmin

An open-cycle gas turbine plant with turbine effidency llt has a compressor of efficiency llc· The minimum gas temperature is Tmin and after heating in the combustion chamber, its temperature is Tmax. If the pressure ratio for compression and expansion is r P, what should, be the limit for the product

Tmax? llc "llt · --Tmin

Neglect pressure losses and assume that working substance is a perfect gas.

(c) v;q; 300¥ fm if, ~\11%<1 W'fi if; Wr1; f.'l8~fuld ~ ~ ~ :

Py=~M2_Y-l X

Px Y + 1 Y + 1

~ x 3fu: Y W'!i -a~ 3fu: <lTG ;f;t ~ ~. Y f<llm! "3l'I!Tm 'liT~ i 3fu: M ~ ~ ~I

Derive the following expression for normal shock in an ideal gas :

Py=~M~-y-1 Px y+1 y+1

:r where x and y are conditions before and after the s~ock, y is ratio of specific

10

heats and M is Mach number. ' .10

(d) G'r.i\ wg; <ro<11: ;f;t Jf\'1;;\'lidl (l(fqfufMl) C[K'ff v;q; !'«K'!T ~ 'lfu:l\l'li ~ ~) af\'1;;\'lictl~ 0·8 3fu: 0·5 ~<it~~ it <ft'! 3fu: ;ffi; WTRR m W:n omrr ~ 1 "'@it 92%

<fi!i "3i'i!T 3RR01 G< <it 'f;l'l <!if.t it Wr1; ~ 'lfu:l\l'li ;f;\ 3f\'lof<!>dl 'liT f.tlffiuT ~I A thin radiation shield having equal emissivities on both sides is introduced parallel to and in between two large planes with emissivities 0·8 and 0·5 respectively. Determine the emissivity of the radiation shield to reduce the heat transfer rate by 92% of the original. 10

2

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(e) ~ 1ITl ~ ~ ~ omtl 3fu: 1furt\ '1!il ~ ~ ~: 1·25 m 2 3fu: 0·25 m 2 ~ 1

~<fit~ 10 em 3fu: ~~<fit~ '<ll<'l'lidl 50 Wfm K ~~ '1!il 'R 100 •c ([It{ 3MR ~ ~' ~ il B ~ ~ 3RRUl "l!ft'l'l ~I ~ ~ 'fi1 ~ ~I The outer and inner surfaces of a thick hollow cylinder have areas 1·25 m 2 and 0·25 m 2 respectively. The thickness of the cylinder is 10 em and the thermal conductivity of the cylinder material is 50 W jm K. Find the radial heat transfer through the cylinder for 100 ·c temperature difference at the surfaces. Derive the formula used. 10

2. (a) ~ ~i'41'11tft ~ WIWI; (lJ~silil>R•1 't('R ~) q;J 3 m 3 ~ 'fi1 1 bar 3fu: 30 ·c 'R il9ft B 'R ~ ~ ~ ~ f;;<rr ;;mn ~I ~ 'f;l '5ISf;J! pv1

'4 = const. ~ s:RT f.l<iful m ~I •

3i"lf ~ JMq '1\lR~ ~ 'ifR ~ ~I ~ il ~ ~ ~ ~ 'R ~ ~ q;J

~ 4 t1 PiR~flsct ~ ~:

A reciprocating air compressor is used to flll rapidly a 3 m 3 tank at 30 •c and

1 bar. The filling process is governed by pJ4 = const. The effects of kinetic

energy are negligible. The ratio of the final to initial mass of air in the tank is 4. Work out the following :

(i) <i'! q;J ~ ~ 3fu: f.rillur 3WI<R ~I

Draw the system and show the control volume.

List the assumptions made.

liiiJ 'I:IR '1lif:r<l; <:1d<ll 90% m, m WflS<li "" ~ 'ffil f<RRT o1rrr? What would be the work input to the compressor, if mechanical efficiency is 90%?

(b) 1200 r.p.m. 'R ~ !;3ll ~ ~ ~ '!!'ffi ~ q;J 800 m 3 /min lRR '-f;«ff t I ~ 0·84 <fit ldli«<Tcft <:1d<ll ~ ml!! 1 bar, 30 •c -6 4·8 bar (f<f; Wftfu! <fit omft ~ 1 ~ ~ ~ f.rrfq- (~) 'R ~ ~ 31'\1: 80 mjs ~ ~ ~ 'fi1 ~ <ml 31GitilfdctllRT on WlictT t 1 ~ <fit omt\ ~ '3Wii\ >fuRl ~ B G1!fl\ % I ~ ~ (@!G m) 'fi1 0·9 llRT on ~ %1 ~ ~ ~~'R 0·9 ~ <m<R%1 A centrifugal compressor running at 1200 r.p.m. delivers 800 m 3 /min of free air. The air is compressed from 1 bar, 30 •c to 4·8 bar with isentropic efficiency of 0·84. The impeller blades are radial at outlet and the flow velocity of 80 mjs may be assumed constant throughout. The outer radius of the impeller is twice the inner. The slip factor may be assumed as 0·9. The blade area coefficient is equal to 0·9 at inlet.

(i) ~ ~ ~ ~ 3fu: f.rrfq- ~ f:f<!;)uj ~ 3fu: '5ISf;J! 'fi1 ~ T-s ~ 'R ~I

Draw inlet and outlet velocity triangles for the impeller, and show the process on a T-s diagram.

20

3 (P.T.O.

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. {ii) ~ ~ G~ 95% it, m ;;nqm; ~ W'ffi <!il 4f1:'ht-H ~I Calculate the input power needed, if mechanical efficiency is 95%.

(iii) ~ 3ft\ f.t*r 'R ~ 01ffil <A ~ ~I

Calculate the impeller diameters at inlet and outlet.

(iv) ~ 'R ~3ft\~(~)~ 'h1uit <A 4f1:'h<:'H ~I

Calculate the impeller and diffuser blade angles at inlet.

(c) 500 kg/min <lit~ B ~ili64H i'l<'! if; <iQll <fi1l 'R, ilT"' ~ ~ fi1f.l4f4'1 ~ it 355 K tR

~ <Rm% 3ft\ 'ffl mn it "'T<lT %, ~ 'ffl 3600 kg/min <lit~"' <i1Rr "R1 B i6l it omrr % ;;ft 2 86 K 'R w:rRR-];lq]Q ~ fi1 A~ f4 'I <lit ~ ~ it ~ <Rm % I <10 ~ 'i'fffi! gl(

1if; B4!! ~ 3'RRUI ~ 475 W Jm 2 K%, i'l<'f <lit :!lf ~ (~ t\<:) 600 kJfkg K %, m 25 mm ~ Olffil, 2 mm ..ntT 3ft\~ 4·87 m <lit f<!;q.ft ~<lit~ irft? ~ W<A "R1 ~ 'liT 2 m/ s B ~ ~ it'll %, m ~ '!TID ofi't m '1'!1 irft? "R1 if; ~ c p 'liT 4·18 kJ /kg K 3ft\ "R1 if; 'R(<I 'lit 1000 kg{m 3 ~I

The vapour, at the saturation temperature of an oil flowing at the rate of 500 kg/min, enters a heat exchanger tube, at 355 K and condenses while it is cooled by water flowing at the rate of 3600 kg/min entering the concentric tube of a parallel-flow heat exchanger at 286 K. Assuming overall heat transfer coefficient of 475 Wjm 2 K, latent heat of oil as 600 kJfkg K, calculate the number of tubes required of 25 mm outer diameter and 2 mm thick with a length of 4·87 m. What will be the number of tube passes, if cooling water velocity should not exceed 2 mfs? Take CP for water as 4·18 kJ/kg K and

20

density of water as 1000 kg/ m 3 . 1 0

' 3. (a) ~<lit n fu<ffi'l fuftr <A~ 'fi<'t g{( f.ikl~Rsio mi!<:'il 'R f.t~ ~<lit G~ 11 if;~~ ~l.l~~: ~ 'R(<I p, ~ ~ jl, ~~OJ, fm <A 01ffil D, ~ Q

Using Buckingham's 1t theorem method, derive a relation for the efficiency 11 of a fan which depends on the following parameters : 20

Mass density p, Dynamic viscosity jl, Angular velocity OJ, Diameter of the rotor D, Discharge Q

(b) G't <'fl'<lt '«<<'fi ~ A 3ft\ B, 31WT -31WT ~ ofi't <A\ ~, 'ffiiR if; 01ffil 12 mm 3ft\ ~ 1 m <fit, ~ ~ '!lJ if; WI ~ ~ ~, f.rn'liT <fi1l 100 •c 'R <Rl1l; BID Tf':IT ~ I ~ if; '!lJ

, 20 ·c "' ~ ~ ~ B M g{( ~ 1 <fl1l ilm io W~ ~ <fit ~ io W~ -WI ~ "' 'll'IT

Tf':IT 1if; 3lTl.TR '!!! B ~ sr;<m: 15 em 3ft\ 7 · 5 em ~ 'R ~ A 3ft\ B if; ~ <fi1l 'ffiiR 21 I <lfu A <fit mlf!fi <!>fOi;r Wffil% ~ ~ "lliil'hdl 60 W Jm Kit, <it~ B <fit~ "lliil'hdl

'1'!1 irft? an~ <fit ~ ~I "!Tf.tt; 1if; ~ if; ~ 31'ffid ~ ~ ('h«l~H <t>10Cf;i11Q:l) 5 Wjm2K~I ~A 3ft\ Bio~~ 3i<RuT <fil~<A ~~~~

4

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Two long slender rods A and B, made of different materials having same diameter of 12 mm and length 1 m, are attached to a surface maintained at a temperature of 100 ·c. The surfaces of the rods are exposed to ambient still air at 20 •c. By traversing along the length of the rods with a temperature sensor, it is found that the surface temperatures of rods A and B are equal at positions 15 em and 7·5 em respectively away from the base surface. If material of A is carbon steel with thermal conductivity 60 W /m K, what is the thermal conductivity of rod B? List the assumptions made. Assume that the average convection coefficient for air is 5 W Jm 2 K. Find the ratio of rate of heat transfer for rods A and B. 20

I c) ~ t<l; X ili 3l"'Gl: fffi <Ji\ ~ f<mq llT'IT 'R eft ;;mft t or<! <l'li f<l; GTil 1 00 kPa ~ i'IT'!

330 K H) "'T''l ~ 3R t<l; Y i'\ t<l; X i'\ '1it fffi ili 'lffi 'liT 5 ~ 'R WIT ;;mrr t ~ GTil

~ 500 kPa oT ;;mrr % ~ i'IT'! ~ 900 K oT ;;mrr % I 31<1 Gf.:il ~ X ~ Y <it ~ <iG 'ffi'<! <'fT<'ft 'l<'fi ili WI ~ WIT ;;mrr % I ~ llR'R <rffi\ ~ f<l; fffi ~ % ~ ~ 'ffi'<! <it <1<!

<l'li 1iffi Wrr ;;mrr % or<! <l'li f<l; € IUlliH0\!!1 'ltf WI o1<f\ t Gf.:il ~ il; ~ 'liT ~, €1Rli<'H"".JI i'IT'! ~ GTil ~~I t<l; 3>"'11?iftrn ~I fffi il; iW(, ~ R = 0·296 kJjkg K

~ Cu = 0·75 kJ/kg K.

A certain amount of gas is filled in a tank X until its pressure is 100 kPa and temperature is 330 K. In another tank Y, 5 times the weight of gas in X is filled raising the pressure to 500 kPa and temperature 900 K. Both the tanks X and Y are now connected through a tube having a valve which is closed. Assuming the gas is ideal and if the valve is opened till equilibrium state is achieved, find the ratio of the volumes of both tanks, equilibrium temperature and pressure. The tanks are insulated. For the gas, take R = 0·296 kJjkg K and Cu = 0·75 kJ/kg K. 10

4. (a) J::'! N2 ~ 'I"<R'fi cft<m <'fT<'ft 20 mm O!ffi! <Ji\ 'l<'fl i'\ 77 K 'R >rim 'li"«fi% ~ 3Jqfti1frli1 ~ ~ 'lO<fi %I 'l<'fl it ~ 'l!l <Ji\ 3RioT"hi11 0·02 %I W 'l<'fl <it 50 mm '~fuRl O!ffi! <Ji\ ~ 3R 'l<'fl, ~ >furt\ 'PJ <Ji\ 3RioT"hi11 0·05 %. ili 3l"'Gl: ~: ("hToflf{"h<.'11) 1.<9 WIT ;;mrr %I ~ 'l<'fl il; >furt\ 'PJ "<'fi't 300 K 'R <AT\; WT ;;mrr % ~ ~ il; oft"! il; ~ <it "@R'ft <fi1: Wrr ;;mrr

% I 'l<'fi <Ji1 llfl'r ~ ~ 'R J::'! N 2 IDU WI "J>Ufl 'liT fumur ~ I ~ Gf.:il '[!il 'R 3f€%i11 0 ·02 <m'fl 'I"<R'ft cft<m <Ji\ ~ ~ ~ <it '~fuRl ~ ~ 'lfWil ili «fhihftoq ~: ~ Wrr "'T'!, <i\ 'f<'ll <Ji1 llfl'r ~ ~ 'R J::'! N 2 IDU WI "J>Ufl it "l1"fi'm<l '!ftr<R 'liT q fti'h<:14 ~ I

Liquid N2 enters a thin-walled 20 mm diameter tube at 77 K and flows steadily. The outer surface of the tube has an emissivity of 0·02. This tube is placed concentrically in another tube of 50 mm inner diameter, whose inner surface emissivity is 0·05. The inner surface of the outer tube is maintained at 300 K and the space in between the tubes is evacuated. Determine the heat gained by the liquid N2 per unit length of the tube.

5 (P.T.O.

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If a thin-walled radiation shield with emissivity 0·02 on both sides is inserted midway concentrically between inner and outer tubes; calculate the % change in heat gained by liquid N2 per unit length of the tube. 20

(b} 1% "R'ft ~ 3Rl: 0·5 kg/s <liT~ -B ~ ~ 1% <m'! ~. 180 ·c ~'"" <R ~ <iif.t 3ffi: 80 ·c ~ '"" <R 'ilfOl: ~ lffi'fi 1'flf i'm1 am, 30 ·c -B 6o ·c <f'fi 1'flf f<Rr omrr t 1 <m'f 3ffi: fm1 <liT ~ ~ (('ilfB[q;ili ~) 4·186 kJ/kg K 3ffi: 1·08 kJ/kg K ~I 1@ft it .~ 3ffi: 20 •c ~ 'lfmT ~ trtmft <fl'l ~ ~ ~ ~ it ~ 'f;l qf<ilii'H ~I

A fluid flowing in a tube at the rate of0·5 kg/sis heated from 30 •c to 60 •c by hot gases entering at a temperature of 180 •c and leaving at 80 •c. The specific heats of the fluid and gases are 4·186 kJ/kg K and 1·08 kJfkg K. Calculate the change in entropy and increase in unavailable energy for ambient temperature of surrounding of 20 •c. 20

(c) 1% ~ ~-'qil; i\tr ~ rn it~ 1 bar, 288 K ~ ~ <R<it t 3ffi: ~ 2 bar <f'fi

Wfifur Wn Offill t I ~ 'lTG ~ ~ 'li~ it ~ <iif.t "B ~ ~ it 1'flf Wn Offill t, ~ ;rui!il 1 1oo K ~ '"" (f'fi 1'flf f<Rr omrr t 3fu: m <ro ·~ it ~ <R<~t t 3fu: <~ 1wi•kll<~ Gl'l

<f'fi fcl~lf<o iRft t I ~ 3fu: ~ <liT l."t~~'fFii!i G~ Sfitm: 87% 3fu: 88% ~I ~ 'li~ (~) 3fu: ~ fclf.lqfil~, ~<liT G8.1<il 0·97 t1 ~ 'li~ it Gl'l mf.l 0·4 bar t1 ~ aiU ~ ~ 350 MW t1 ~ 'f;l ~ l!R 42 MJ/kg tll!R ~ Cp.;, = CPgas

= 1·005 kJ/kg K 3fu: y = 1-4 ~I

In a simple open-cycle gas turbine plant, air enters at 1 bar, 288 K and is compressed to 2 bar. It is then heated in the regenerator before entering the combustion chamber where it is heated to a temperature of 1700 K and theri enter~ a turbine and expands to atmospheric pressure. The isentropic

' efficiepcies of compressor and turbine are 87% and 88% respectively. The combustor and heat exchanger efficiencies are 0·97 each. Pressure loss in the combustor is 0·4 bar. Power developed by the turbine is 350 MW. Calorific value of fuel is 42 MJ/kg. Assume cp.;, = CPgas = 1·00.5 kJ/kg K andy= 1·4.

(i) <i:!"" Sfilmff 31iW ('R'il Sf4!1'Tl!) ~ 3fu: T-s 31iW 'R M ~~I Draw the system flow diagram and show the processes on a T-s diagram.

(ti) ~3ffi:~<li't~~~~~l Find out the mass flow rate of air and fuel.

(iii) q;W~~~I Find out the work ratio.

(iv) ~ G8.1<il ~~I

Find out the thermal efficiency.

(v) ~ ~tl'! 13'«1 ~~I Find out the specific fuel consumption.

6

10

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~-8 I SECTION-S

5. (a) ~ 3'®<! ~ C xH y i\; Wol i\; "3i<ITG1 qrr f.t"1~ ful d ~ ~ ;hrr f'f> ~ 3ffim ~ IDU ll1'!1

1Jln ~ :

C02 = 8·0%, CO = 0·9%, 0 2 = 8·8%, N2 = 82·3%

X afR y i\; liT'iT, ~-~tl'l ~ afR ~ ~ ~<lit Sifd~lddl qrr f.ttlttuT ~I

The products of combustion of an unknown fuel C xH y have the following composition as measured by an Orsat apparatus :

C02 = 8·0%, CO = 0·9%, 0 2 = 8·8%, N2 = 82·3%

Determine the values of x and y, the air-fuel ratio and % of excess air used. I 0

Determine the expression for the ratio of chimney gas temperature to outside air temperature in terms of mass flow rate.

(c) lifdfsMI ~it~ ~it, 'Ill'! qrr 01'! 34 kPa (v9

= 4·65 m 3fkg) ~ aiR~ ;;rn (~ ~) 0·95 ~I 36000 kgfhr <lit ~ <:1: i\; ~' ~ 950 kW ~ q;\<ft ~I ~ 3600 r.p.m. 'R 'ffi<IT ~aiR~ qrr WT, ~ WT qrr 0·72 ~~I~ aiR~ Gh'l ~ i\; f.rfo! <!?tui 20• ~ I ~ ~ 'R '11~ ~ O!ffi'l afR ~ <lit ~ ~ ~I

At a stage in a reaction turbine, the pressure of steam is 34 kPa

(v9 = 4·65 m 3 /kg) and dryness fraction is 0·95. For a flow rate of 36000 kg/hr,

the stage develops 950 kW. The turbine runs at 3600 r.p.m. and velocity of flow is 0·72 times the blade velocity. The outlet angles of both stator and rotor blades are 20•. Determine at this stage the mean rotor diameter and height of

10

blades. 10

(d) ~ <'M:JMI~ li'fi •Mifol'h ~ '11: ~ M on~ t ~ rn ~ "$!q; ('FR) ~ ~ >n•flfolq; ~ i! ~ m on m ~I ~. 'l'i\ I ~ Gh'f ~ ij ~ ~ 'hl~l

Mechanical air-conditioning can be used in all geographical locations, whereas desert air-coolers can be used only in some geographical locations. Explain why. Show the processes involved in both these equipments. 10

(e) q;qu ~ <ri'R ~ i\; ~ $1 ~ llfiRtq <l1'l'f; i\; ~ i\; <r.!l<l = 'lll! (t!\l 'lll!) "" ~ "'hB! 3>64111fd<no: (l!lli'isl~~f'i<n<'fl} ~ ~~ ~ll\lll~~. 'l'i\1

It is thermodynamically advantageous to employ a heat pump rather than employing a direct electrical resistance heater for a room air heating application. Explain why. 10

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6. (a) T% 2-* ~ ~ 'liT ~ l!R 44000 kJ /kg i!> ~ ~ i!> m~ 20 'C i!; tlfllPl (!]q

(~ ~) 1R 'ltl1d"' foti<rr 1fiiT I f.'I101Wiful~ ~ 'liT-~ ~ ~ ~ 3it\ "WI; ~. ~ 3it\ "WI; ~ G:~ 'liT qfl:ifi<o;H ~ w.n ~ W'f'!-'Br .~ : ~ -.m: = 20 em; *--.m: ~ = 1·3 : 1; \9011:,; 500 r.p.m.; "WI;~ ."''ffi

= 120 em; ~ "''ffi = 3 em; f.'r<R1 "WI; 1fR = 460 N; ~ MEP = 2·8 bar; ~

13'1<1 = 3·7 kg/hr; ~ WI<R 'jf('f G1: = 456 kg/hr, 27 'C i!> (j]q ~ i!> WI;

~,;){141l< it • "'i«ft ~ ~ fffi 'liT (1]11 320 'C 3it\ ~ ~ ~ fffi 'liT (j]q

220 'C; "5l"1'l1l1 G1: 8 kg/mini!> WI ~<-1IM1l< 'jf('f it (j]q '[f.a 8 'C%

1 A 2-stroke oil engine was subjected to a test at room temperature of 20 'C with

I fuel oil of calorific value 44000 kJ /kg. Calculate the indicated and brake

. power·, mechanical and brake thermal efficiency, and draw the heat balance

'

sheet using the following data :

Cylinder bore= 20 em; Stroke-bore ratio= i-3 : 1; Speed = 500 r.p.m.;

Brake drum diameter = 120 em; Rope diameter = 3 em; Net brake load

= 460 N; Indicated MEP = 2·8 bar; Oil consumption = 3·7 kgfhr; Jacket

cooling water rate = 456 kg/hr with a rise in temperature of 27 'C;

Exhaust gas temperature entering calorimeter is 320 'C and leaving

220 'C; Temperature rise in calorimeter water is 8 'C with a rate of flow

8 kg/min

(b) : T% ~ fffi ~ (GT)-111'l ~ (ST) ~it, fffi ~ (GT) it~ 'liT~ it 11l'l

q;) 7J1f "'fiB it ~ foti<rr 'i1T<!1 %, ;;@ 1R fffi it ~If.! ofi't 3Wt ofi't 'If<! ~ ;;mf\ % I G T 'liT <:1<1

~ 8%, ~ (~) ~ (j]q IS 'C%, ~ '<ijfi (j]q 800 'C il ~it~ fR:r. (1]11 "'liT ~ 800 'C "iii( ~ % 3it\ fffi ~ it 100 'C 1R ~ Rih<"lol %I 11l'l

~ (ST) it 11l'l ~ 60 bar 3it\ 600 'C 1R i (h = 3656·2 kJfkg, s =

7·166 kJ/kg K) 3it\ ~ Gl<! 0·05 bar % (h1 = 137·8 kJfkg, h19 =

2423·8 kJfkg, s1 = 0·476 kJfkg K, s19 = 7·92 kJfkg K) I "¥f ~ ~ 190 MW i!> ~ ~ 3it\ 11l'l ofi't ~ "5l"1'l1l1 G1: W.fl ~ ~ ofiT "Wf!l T] 'liT qfl:ifi\'11 ~I

'I><"Rl ~ fo!; "@:ft ~ ~ %1 "Wf!l ~-~If.! ~ '1'<1 %? l!R ~ CPgas =

1·11 kJfkg K 3it\ CP. = 1·05 kJfkg K W.fl fffi 3it\ ~ i!> ~ y 5f>lm: 1·33 3it\ a1r

• 1·4 i I ~ "5l"1'l1l1 1R ~ ofiT ~ "5l"1'l1l1 G1: "'liT ;r,iR~ ~I ~If.! 'liT ~ l!H '

I 43·3 MJ/kg %1

· In a combined gas turbine (GT)-steam turbine (ST) plant, the exhaust from GT

is used to heat steam in boiler at which a further supply of fuel is burned in the

gas. Pressure ratio of GT is 8, inlet air temperature is 15 'C, maximum cycle .. temperature is 800 'C. Combustion in boiler increases the gas temperature to

800 'C and gas leaves the boiler at 100 'C. The steam inlet in ST is at 60 bar

and 600 'C (h = 3656·2 kJ/kg, s = 7·166 kJfkg K) and condenser pressure

8

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is 0·05 bar (hf = 137·8 kJ/kg, hfg = 2423·8 kJfkg, sf = 0-476 kJfkg K, sfg = 7·92 kJ /kg K). Calculate flow rate of air and steam required for a total power output of 190 MW and the overall 11 of the combined plant. Assume that all processes are ideal. What is overall air-fuel ratio? Assume CP = 1·11 kJ /kg K gas and CP . = 1·05 kJ /kg K, and y for gas and air as 1·33 and 1-4 respectively. a>r

Neglect mass flow rate of fuel on the airflow. Calorific value of fuel is 43·3 MJjkg. 20

h = CPm xDBT +2500w

"'Ii CPm = ~ ~ f<rim "W1i = (1·005 + 1·88w), w = f<lfm 3ffi\m kg/kg~~, "~<'~ il; ful( 0 •c 'R h fg = 2500 kJ /kg 'R =>itt DBT = ~-Of<'<! (!lll 1

Show that the enthalpy of humid air per kg of dry air is given by

h = CPm x DBT +2500w

where C Pm = humid air specific heat = ( 1·005 + 1·88w), w = specific humidity kg/kg of dry air, hfg = 2500 kJ/kg at 0 •c for water and DBT = dry-bulb temperature. 10

7. (a) {i) ~ il; ~ <:!'! ~ (fst>fl'h<1 Wm l;fu31'\) il; ful( 1:("'1> ~~~I ~ ij 31<ffitH (~)<Iii~ "if>i <'IT! ~I

Derive an expression for critical pressure ratio of a nozzle. Explain the phenomenon of choking in the nozzle. 10

(ii) 1:("'1> '1T'! ~ ~ ~"'l~fuid "fSSi q;r ~<mil~ : '1T'! ~ f.rm 150 bar, 550 •c (h = 3450·4 kJfkg, s = 6·523 kJ/kg K); 40 bar '11: 550 •c 0'1> -r-r:(!lll (h = 3560·34 kJ /kg, s = 7·235 kJ /kg K); 0·1 bar'R~ (hf = 191·8 kJfkg, hf

9 = 2392·05 kJ/kg,

sf= 0·649 kJ/kgK, sfg = 7·5 kJjkgK)

~ "5fslil'!1 "'hi ~ ~ ~, ~ ~ "hl<i'h "<R '1T'I <Iii "Tffi1, "fSSi <;1\{(11 :om '1T'I m G\ ~kWh lffi'l'! ~I A steam power station uses the following cycle :

Stearn boiler outlet 150 bar, 550 •c {h = 3450-4 kJ /kg, s = 6·523 kJ /kg K); Reheat at 40 bar to 550 •c (h = 3560·34 kJfkg, s = 7·235 kJ/kg K); Condenser at 0·1 bar (hf = 191·8 kJfkg, hfg = 2392·05 kJfkg,

sf= 0·649 kJ/kgK, sfg = 7·5 kJfkgK}

Assuming ideal processes, find quality of steam at turbine exhaust, cycle efficiency and steam flow rate per kWh. 10

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(b) · v;<fi <lldlj'li<il~ Wti il, ~ ~ v;q;q; ~·~~~'liT 4500 crnrn ~ '!i«fT t ;;i\ . 'I1R iii ~ 40 'C DBT, 27 'C WBT '1\. 20% (lf;;fi ·~ ~ 25 'C DBT 3fu: 50%

RH '1\ 80% ;F:qftti'1fto ~ Wn %1 ~ ~ ~ (~ ~) <) 13 'C '1\ ~'ITO\ f.l<h<i!dl ~I ~ ~ 'I1R 3fu: <lil\l ;o;arr <i!f.tr 'liT qftih<i!'l ~ :

I I

<mT DBT WBT RH fcrfm!~ ~w (•q (•q (%}

(kg/kg 'U"'fi ~) (kJ /kg 'U"'fi ~)

<mt't~ 40 27 P.2 85

<lil\l ~ 25 50 10·0 50·8

ADP 13 100 9A 37·0

The air handling unit in an AC plant supplies a total of 4500 crnrn of dry air which comprises by weight 20% fresh air at 40 'C DBT, 27 'C WBT and 80% recirculated air at 25 'C DBT and 50% RH. Air leaves the cooling coil at 13 'C saturated. Calculate total cooling load and room: heat gain : 20

Condition DBT WBT RH Sp. humidity Enthalpy (•q (·q (%} (kg/kg of dry air} (kJ /kg of dry air}

Outside air 40 27 17·2 85

Room air 25 50 10·0 50·8

ADP 13 100 9·4 37·0

(c) 1

f.lRRli'Ga ~ v;q; 4-$, 4-~ ~ t.R iii ~ il ~ :

~ O!ffil = 36 ern;$= 40 ern;~= 315 r.p.rn.; ~ MEP = 7 bar;

W.. m = 250 kW; ~tl'l 19'«1 = 80 kg/hr; ~ l!R = 44 MJ/kg; ~ 19'«1

= 30 kg/min; ([]q il 38 'C <tT ~iii WI~·~~ = 90 kg/min; f.l<m:r Tm ([]q = 324 'C 3fu: mi!Ff ([]q (~ ~) = 45 'C; CP . = 1·005 kJ /kg K,

"" cP = 1·05 kJfkgK, cP = 2·093 kJfkgKif.iof;rnfrmil~'lil~ gas steam

G1'l 0·03 bar 3fu: ~tl'l il ~ 13% H2 . .

~ <:8.1<1!, ~ ~ T(, W.. ~~f'hih ~tl'l 19'«1 ~~I tW iii 3lTm1: '1\ t.Ff iii~ ;o;arr g;<il'! -'1'1 ~I

The following data refer to a 4-stroke, 4-cylinder diesel engine :

Cylinder diameter= 36 ern; Stroke= 40 ern; Speed= 315 r.p.rn.; Indicated MEP = 7 bar; Brake power = 250 kW; Fuel consumption = 80 kg/hr; Calorific value= 44 MJ/kg; Air consumption= 30 kg/min; Cooling water circulated = 90 kg/min with rise in temperature 38 'C; Exhaust gas temperature = 324 'C and Room temperature = 45 ·c kJ /kg K; CP .

, ~r

= 1·005 kJ /kg K, cP = 1·05 kJ /kg K, cP · = 2·093 kJ /kg K. In gas steam

exhaust gases, partial pressure of steam is 0·03 bar and fuel contains 13% H 2 •

Find mechanical efficiency, indicated thermal T(, brake specific fuel consumption: Draw· heat balance sheet for the engine in hourly basis. 10

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8. (a) (i) ~ R12 <ffi'l ~ ~ 35 •c am -15 •c ~ ~ tR ~ 'li«<T ~I <i'l <lit COP am "llf<r Col "5i"WR (Uiil"i{~H) ~ fu1( HP 'f;l f.\tffiul ~ :

31fclrrfr 20 K 40 K

t hf hg Sg ·h s h s I"C) lkJ/kg) lkJfkg) lkJ/kg K) lkJfkg) lkJ/kg K) lkJ/kg) lkJ/kg K)

35 69·5 201·5 0·6839 216-4 0·731 231·0 0·7741

-15 181·0 0·7052 193·2 0·751 205·7 0·7942

An R12 simple saturation cycle operates at temperatures of 35 •c and -15 •c. Determine the COP and HP per ton of refrigeration of the system: 10

Superheated

20 K 40 K

t hf hg Sg h s h s I"C) lkJ/kg) lkJ/kg) lkJ/kg K) lkJ/kg) lkJ/kg K) lkJ/kg) ikJfkg K)

35 69·5 201·5 0·6839 216·4 0·731 231·0 0·7741

-15 181·0 0·7052 193·2 0·751 205·7 0·7942

fiiJ ~ ;ng am 11fto ;ng ~ <'lldl:!'tii'1'1 ~~oft'! f<lm ~~ Differentiate between summer and winter air-conditioning processes. 10

fbJ m WI-~ ~ ~ <'ll'l c:ey (t!;f?h~~~<) o'rn ~, 3'%l c:l'! <A ~ 31'Wn3il ii WITf! (11~1::<~o: WI-~ o'rn ~ 1 ~ <FiT ~? WI-~ am Gl'l-~ ~ WITfi\ ii G1'l

am WiT ~ ~ "" ~ ~~ Even though velocity-compounded impulse turbines are less efficient, in the initial stages of high pressure turbines are normally velocity-compounded. Why? Plot the variation of pressure and velocities in velocity-compounded and pressure-compounded impulse turbines.

(c) ~ 'liT'! ~ Wf:! ~ ~ ~ ~ 'R '<l<'fdT ~ 1 'liT'! ~ ii 6 MPa, 450 •c 'R

m W ~ (h = 330 1·8 kJ /kg, s = 6·7193 kJ /kg K) am ~ ii 20 kPa 'R Jdi!rn it "ffifi ~ (hf = 251-4 kJ/kg, hfg = 2358·3 kJ/kg, vf = 0·001 m 3 f)<g, sf

= 0·832 kJ /kg K, s Jg = 7·0766 kJ /kg K) I 'l\Uf ~ ~ (CIR\ tm) ~ 'llf q;f.l ~ ~' 'lT'! ~ WITfl ~ 0·4 MPa 'R f.l"fififu Wn om!!~ (hf = 604·74 kJfkg, vf

= 0·001 m 3 /kg, hfg = 2133·8 kJ/kg, sf = 1·7766 kJfkg K, s 19

= 5·1193 kJ /kg K) I 'lT'fi 'l\Uf ~ ~ ~ ~ J::<'l ~ ~ ii 'IW\ f.\<!;ffin ~I T-s ~ 'R

~ m ~am f.t<RI ~~/kg 'll'l, ~<A~ am~ G~ ~ ~~

10

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A steam power plant operates on ideal regenerative Rankine cycle. Steam enters the turbine at 6 MPa, 450 •c (h = 3301'8 kJ/kg, s = 6·7193 kJjkg K) and is condensed in the condenser at 20 kPa (h1 = 251·4 kJjkg, h19 = 2358·3

kJ /kg, v f = 0·00 1 m 3 Jkg, sf = 0·832 kJ /kg K, s fg = 7·0766 kJ /kg K). Steam is

extracted from the turbine at 0'4 MPa (h1 = 604·74 kJfkg, v1 = 0·001 m 3 /kg,

h19 = 2133·8 kJjkg, s1 = 1·7766 kJfkg K, s19 = 5·1193 kJfkg K) to heat feedwater heater. Water leaves feedwater heater as saturated liquid. Show the cycle on T-s diagram and find net work output/kg of steam, the boiler and thermal efficiencies of the cycle. 20

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