gate chemical engineering 1995
TRANSCRIPT
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IGATE - 1995
1ul 1
CHEMICAL N G I N R ~
: : : = : = : : : : = = : : : : : . J
SE TION··
(
1
Mlll ka)
Choose the
ro r
rerl
an
swer a
nd
' indica
te
the
co
n-esponding capital l
et
ter
A.
8, C oo 0 in
your answe.o·
book.
(23
X
1=23
l'he
tank ofmn ln» I)
~
ts
3 o
a.
l i
b I
C-
2
d 3
2 The angle
between 111
o
·vec tors
il 7-k and T+/+ lk is
3,
-
1
.5.
a ll
b. 300
c. 45°
d.
( ll
Dunng
coking
of
coal.
tba
nsh conJent
(percenlllge)
;1
i
ncre ses
b. decreases
c
re
mains
constant
Joggong
os
.a
techmque
by
11hooh diiTerenl
pa
rticles can be
n. Sepurat
ed
by particle
size
b.
separ ed br
par1ic
le
den
sity
c. separ
ated by
panicle shape
d.
mixed
A panicle attains its temtinal s
etUing
velocit)
w1Jeo
a.
force + drag
force
= buoyanC)
force
b
gra1
It)'
force -
drag force
=
bu
oyancy
force
c, buovancv
force+ dmg
force
= Gravct)
'
Co
ree
d drag Ioree
= y
force
for un Ideal Ouid no
11
tha-
Reyl)old
s
number1s
a. 21
)()
b t O(I
c t.ero
d.
infinity
7. A
flu
id merw· mi ll is USed for
a curhng
b
gnnding.
c. wlrs
grinding
d. crush
i
ng
Fo r an tdenl mixed
now
react
i
on (CSTR)
~ t e
exit ngedistrib
uti
oo E(
ll
is
gil'eo
b,v
a. a dirac dellll function
b. a
step
fLmcuon
c a
ramp functi
on
d,
none
of
he
abo ve
The con
version
ru1d res
1deoce tu11e
data
are
collected
for zero order
liqutd
phase
reach
on
ln
n
stirred
tank reactor. hicb oi
the
following will ben straight line
a.
X
rsr
b
x-
1
I n r
c.
Y,,/ 1 - .\' t r
d.
X,,
(I
- X
1
)1 'ST
I C
The dtmenstons
of
mte
co
nstant t·
or
reactton 3A -+
B are
g m o l ~ t n t n .
Therefore
the
~ a c t i order is
a. (I
b. I
c. 2
d 3
t
A
l iiSI. orde.r-
reactton
A S occurs in
an
isothennal
porous
catalyst
pellet
of
spherica l
shape
. If
the
concentrauon
of A
at the
centreof the
pellet ts
much less t
han
~ u n
at
~ 1 e
e.
\1emal
surface, the process is
limited by
n. doffusion 11
i
thin
the
pellet
b.
reacto
on
c. external mass transfer
d noneof
he
above
12. A i d i ~
transfonned into vapour
without
going tb.rough tl1e Liquid
ph.ase al
a.
t
ripl
e
point
b
botling point
c.
below
trip
le
poont
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13.
d. a)WDY•
Al Ihe ln
vcn<ion
point. the
J o u l ~ >
nwmpson codliciem
is
.
< ~ .
posito
ve
lJ, negotlv<>
c zero
14
-
ll
te enorgy of g•s mol
cc.
u[I:Jl
ls
lS
.
zero at
t
. U C
b.
213
•c
c.
J
IJO
"C
d.
-273
(
l'llc b·au.rcr fuuctiou ilr a PD u M l J is
n. 1 - r ;> )
b.
K
(l
-1/ t"> )
.:.
K
r
nJ )
cl
,
16.
TI
1e offilct inlroduced
by
propo
rti
ou:tl
contro
ll
er wi
th gain K, in
r
osporun>
off
'
mt
order syst
em
""""
he reduc.ld
i>)'
n. n:duomg volue ofK ,
b, int
r<xlucjng jntegrul C lotrol
.:. introduc
ing de
rivative
.:antral
d. none of the above
17
. Bode diagram' nre gener>l
cd friJ
rn ouiJ)Ut
rcspot
15c of
" SIStcm
~ j c . : ~ Lu
which
o>fU1c
following
input
••
impul ;e
b.
"'"P
.:.
romr
d. srm"oid
nl
IS.
TI
1e
root locu•
me01od. •
po le
of
•
lrOD$ cr
li
metion
('l(s) 1S the va lue nl' 8 l
hr
"hich
G(s) illll>ro>cbes
•• -1
b. 0
c.
d. .,.,
19
. Gas chromatography Is used for
ll c; 1suromc:ut of
a. lcmpernturc
b. i ' I : . ~ U f e
c. nccnl.r:l lion
d.
Uow rotc
20. Ac<ordins to Dod. st.bllity
l'ntcroon. •
5Ybletn il> u n ~ t n b l e i the open fpop
frequen;:.y
respon,e
ex:htbits
-an
amplitude
2 1.
22.
lnC1
r.otio exc.:eding unit) at f r e q u ~ c
y
for
'
vhic
h
h ~ s e lAg is
•· o•
b. 45"
c. 90"
d. 180"
Tbe respvnse of hvo t•nks of •:om
c:-s
h e
uud
rosillllJJCC
h\
series
~
a. un
der
duntt>cd
b.
co
lically damped
c.
rwer
d.Jmpe
d
d.
none
1>1
tho ul
)(>V<
Th.: lranYdt fuuctiou ot' u p
un:
doaJ Lllru:
system with dead
t d is
l
d. e t l
23,
The
l-ime . o o n s o f ~ lir.;t
order pm"ess
wiU1 r ~ s i s l o o c e R >Od c>pocitanteC I
a.
R • C
b. R • C
· Rt
d. ltR C
i
e
1
1
•J,f
0
i 1•\f
~ I
( •] : fJf{
*
«l
Ch
o >'ic
lh r
'o rr
c.:
t
~ l r
nnd lndi
eQf<•
lh<
t ~ l lett•r . \. R. c. D
.:ase nu1y
be
in
yuur
answer
book
24.
25.
26.
(J.9 X 2 •
J8)
A function I(X) ~ 12.t · x
1
hos maximum
voluu n :<. -
•. -2
b. 0
"· 2
d. ru
I
.
lim
.\'
om- - =
o - 1 .\ '
b
I
"· 0
d.
-1
'l'he second order e r i e ~
e ' < p ~ n s i o n
for a function llx) - x·
al
x
• t
is
a. x
b. I x=-
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'
.
'
. 1
x •,.-
27, The •veroge va
lu
e
or li•n
t ti1m Hl'J - ._.
in
the interva I () x
2 ;,
b. 2
c. 4
tL
a
28. An
o:vaporator
wh1Je
l:tlncentroting an
nqUQCJus solution from
lO lo 4 ( ) ~ . wli<4
c:Voporntos
30000 Kg of wnter. The
amoun
t of
solid•
h:m4led
bv
th
esvs
tem In
Kgls · ·
-
4\)CIO
b, Q ) )O
c. 46 10
d : ; ~ t t l
29
. 1000 KM of wet
~ o l l d ~
a ~ to
h.:
li·om
60°6
to
2 ~ ~ moisture (by \Ieight). ·
n,e
- i ~
uf moistun: n.moved in Kg i>
520
b. 200
i:.. 400
d.
500
30. A umin2 that C O ~ oboy$ pcrfcot
gas
low.
calculate the density
of
O ~ fin Kg/
tn
> at
· c atod
2 atm
.
.
I
b 2
c. 3
d..
4
3 I. Pure
0
ml1tcd with ::tir to p r o d u « an
"nrich
ed
a
ir
contolninj 50 volume ••
'rhe rolio of moles of air
lO 11.•ed
c•
•. 1,72
b. \).;Sll
c. o.s.
tl
0.2
32, Hyd r3ulic mtan m
e t < : t
tor tlow l.hn)t.tgh
packed
bed
of
$pherical
a 1 1 l d ~ of
$1'7.
o,
with porosity
t :
:L D
1
'
• 6 1-c::
b. D I 1 .:c
6 ..
.,_ n 21-><
d.
1:
. ]
E
3
uf1
113. Use
of
R.1>chig ring• in place of crushed
swne as
pacldn.g
in
packed
heds
(other
Ulings b c i n ~
~ a m e )
a. inereasds ptessu ' drop. im:.re.1ses
urfilt C aro s
b. increase·
c s s u
drop . dacrcases
o n
:
c
c
area
c.
c l e c r e 3 ~ e •
pressnre
llr<>p
,
in¢re:tM><
' n e c orea
d.
d e < : r e a $ ~
pressuro: tlrop.
decreases
r f i ~ c -
al'da
34. A Jtospeusiou o( uniform [Ja<ticlelltU. watet
at a
co
ncentration
of
500 l<g
of
so lido per
cubic meter of r r y t• sett ling in a tank:.
D ~ > i t y of l
lte
part
Mes
h 2500 l{g m and
terminal Wlodt_y o f ~ sluglo purliclo i
20
cmis. Wh
at
will be the scllli
ng vel
ocit
y
of
' ' ' P ' ' - ~ I o n
Richardson
and
~ i d i
nd
ex
is
4.1\.
a. 2\ cm/s
1> J4.,;
t:.
7,16 cutis
d. 3.58 " tn/S
35.
Bed
prossure
drop
in an I1ir OuiJl
ze
d bed
ofcl\IJJiysl·p•tticles 1p -
2000Kwm
3
• Dp
0.05 em)
of 60 em
bdd depil1 nnd
bed
J'Of<lSity ur 0.5
exp
ressed
in
Um or Water
tUlDilOtnti\CI')
is
I t 9
b.
GO
c.
d.
30
36. .-\ pilot lUll¢ indieot<•
S
CJII
of
\ ~ a l c r
~ n m c r ) wh
en it i•
being uaed for
m
o a ~ u n
g vei<Jdty QF ;oir. l
ne
veluc.it)• of
air in mrs
s
a. 5
b.
t4
.1
c., 56.22
d. 28.2
37.
In
tli>Lillati
on
wlt.:re-
q
deline<l
Ue
rnolCli of liquid
fl
ow ill l.he slrippitljl
scclion per molo qf food introduced. for
s n t u r ~ t e d l
iquid
feed
a. q > I
h.
q
I
<:.
tl
= I
d.
q= ll
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3
8.
In
go,•
liquid
oonuct
operolion tlte
numl>e<
o de;
•
l•l•
gesl'-' - .r. ) (.1) - .\ , ) T h i ~
is tru" wheu the sU'fppiog,Lictor S is
a. S > 1
b.
s
<. 1
.: S • l
tL
.S
=
oc
39.
For
abstlrbmg a spnringly sotublt gas
in
•
liquid
gll l
' ide
tud>IS
t r ~ o s f c r
~ o c O i c i L n l
<hould
be:
im;nr.rscd
b. lic1uid moss trnns
tcr
coefficiem
should
be
increased
c:. liquitl i d e o n m s ~ tr;tnsfer coetncient
Nhould be
e : c r c ; a ~ c d
,1
m••• U ' 3 n ~ O F
r o d l i ~ i c : n l s
must
b c - ~ c p l
COtlSIOlnt
·
l11
c
.rotc
c:o
nsllml
of
•
chcmJ<:a
l n:oction
increoses
by
100 l,imcs when tltc
temperature is mcreased from 4{)0 K
to
500
K.
Assumiug tmndlion
m l ~ U u ~ o r y iA
\'ll lid,
Otc,•aluo ofEIR
is
L
89l 7
K
b
92
1
0K
c.
8764 K
d. 8621 K
-11 A closed s t c m
is coo
led c v ~ b l
y
lr
om
1
oo
•c to
5o
•r . If
no
work
ia
d
om: on
the
VS1¢tn
a. its intem•l enerl y
(L)
decreases. and
its entropy (S) increases
b. t:
•nd
S boUt de.::tea'"'
c. U
dcctL'li.C'S
but S
L
constnnl
d.
is
oonstnnt but S ,clect-.:oses
42. Idunlify
lUI
uubountlcd
iupuL
frvm
four
1" 1ul'<
whose
lnm
slet filn
ction5 ore
giwn
llclow
a. I
h
,,,
I'S
2
t l II(S
1
-
I \
..J3 Makh the ilems ln the left colunui
wiOt lh
e
oppropdM
e
it.mts
In
0 110
rigltl
eo
l
umn
(I) 1 - x•
m1
(A) limt u·0 .D
E.
(13)
noollnco
.rO.D.E.
(C) liu'"'r b r o k ~ X
D) llOnlln<iw'
•lg.:bra.ic
oqll.'ltioo
l u(1
14
.
1-®tch the item&
n
the Je
ll
column with tbc
Appropriateitemllln the
right
« ~ h u n n
(I
) dyldx - Sy = 0. y O )=y.
(J
I) 5
= O. y(t)) =
y.,
A) y : Y• + sx
(B)
y = ya-Sx
(C')
y
=
~ > <
(D)
y
:
y,.c'"
-IS M ~ i d t the
items in
the tell column wi th
th
e
appruprialc ill: ns
in ilic
i ~ l l < : < ~ l u l l J J L
(1)
o a ~ J >
y l i o rdonuiog
(II)
•
mok
e
puint
A) fti b
llpe.:d diesel
B)
korQ8cnb
(
C)
, g o s o I n ~
(D) ommaliC l
-16. l'vl.itlctl UtQ itoms in
tbc
~ t l columo wi
th
Ihe
appropriate
items m the
ng.hl
column.
(I) solulropic
sy>
timl
(II ) e
qu
ilibrium moi.jlurc Cllnlont
( i\)
cryslollfzttlion
(B) distill;1tion
(C) edrm:Lotl
('B) dl)ting
-17,
Ma lch
the
it
ems in
the tell column
with the
appropriate items
in Ihe righ
t
rotumn.
{I) vonturintell:l
fl
) wei
g.'IS meter
(A)
s
ta
tic
he.1d
) l:llergy
(C)
volumolrlc displocemeal
(d)
ftuict drng foroe
-lg
, Fill io t
he;
hl"nk.
9
(4 1= 4)
a. ltl 1>rocoss heal exchangers
s
team
is
~ r t e O\'er
1C3Jil..
h. H O JiaS lll
m o ~ . : r n t
l l t t =
usually
in
the s
ido
of
shell and
tube c x ~ h o n g c ~
AI higher
pressure.. it i. 5.-cll. i l( fluur}
to
put gas in
the
e. 1
niten
ius equolion dcscribin& the
e
ff'
eet of temperatJJJ\': on rote c o n s
~ n t
is
d. In an .1git
at<ld
vess .J.
ballJ<:S
ate us«
to
supprc
s.
Tho
r:uc o
jn
cn:aso o number o ba
c
h:
ria
under certAi
n c
Qnditio
ns
is
propo
t1 ionol
to
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50
5 1.
52.
the num bcr ,,,.
ha
otena. tr the 11 1l111her
dClu
bl
es in 4 hows,
hnw much
iOCI> Il1<:
io1
number
of
b3Ctcria can
be
ex
pected 111\c
r
IJ
hours?
(5)
Metlumul os produ<etl
by
the re.1ctiou-of
CO woth
CO H
1
- Clf,Oli
Onh J j ,;, of carbon-
m o
d c - c
o \ l c n n g
1 \ll reactor co nven
ed
to nJcthao\ol The
methanol f o r m ~ d is ~ o n d o u s e d and
rccovcred complc1<'1) . Titc unrcnctcd CO
und
li: ure reuycled back to
fM
r
•'tlc
tllr.
The ILc<l will contnln ll1 and CO In Ute
mtih of I. l ur 32(l(J of md h11MI
pmduc<-d.
ua
lou
lnll.'
.
(5)
(II Ke molelhrol'fresh bed.
(ii) Kg
mulclhr
or
re
cycle
J l
ts.
Mol
wt u r C J -
~ O 32
Culculote lh•• surfltlle vo lume mean
diameter for l
it
o lb llowon g purt
ic
ulmo
ma te
ri
a
l.
Sh
ow
demiled
ca
lculaaions.
(5)
-j;,.,
.,
. ;C.
r.tns
of paniclei in cbc:.d.Dp.. 1DJ
, J
(;I
+ l$1
u
.
. -3S2 + 1?6 :n s
.:]
..
-h
-
-
15
-
, 1+
. .
15
Pa
n
-
;Q
m n
the hent lnm>ior llrcd for am
a n g e
to coo l nn organic liq
ui
d (tom
ltl5 ·c to 5tl C. 'l'be boo iquid will llow '
11
ru
k
of IH.IXIII K aod
will
he oonled
hy u
si
og ettcul;lling fo
ul
w• ter cQolnuung
>UDJ<' snlL (ho cuo lmg
WH
ICr wi ll
c ~ V O
&I
~ t l
C. [I is proposed 10
us
c one
sh
ell pass
nnd
h v ~ > lttbe pnss exchanger for tire obol'e
duiy
(5)
Couliug \\afc:r i n l ~ lt 111
f'<lnt
lun: -
25°C
llc
nt Cllpacitv lor water 4.2
KJ /Kg. C
l l c ~ t capaci
ty
lor lot liquid =
.2
.84
K.f/
K L
C
the temper:tllll'e u o r r ~ o l i o n li1r
I
he
d e ~ i g n will 11, >.5
53 .
3o
T
l 'he
l(:c<lmtneotdc-d
o•·
cm
ll heat
lrunsfer
coeOid
co
n
II
will 1)6
IiilO
Whn
1
C
Fo r " first t.lrd(·r rcao.'
llOn
laking Jllaoo in un
isothermal ·
Hatch
rcnctor_ so•. ol' liquod
e : ~ e t u u is couwrtod lo ~ r o d u c t 111 15
111i
nu ll.,.
Cnlculate ~ c c vd oclly
r<
luirf;<l
tu ae
ht
evc sume ~ ~ o n in u plug flow
roacmr and 111 a ba
ck:mi11
flow reactor
(5)
SI CnON·B
PlY
MAIUC.a QUI STIONS 14-73)
55.
56.
57
l'lnd < . . ~ e e n values nuJ e)eenvectors of
mn lrl'\
[ ~ ~ J
l l
t.: Or
<ll
aualnts
>f
a
tluc
ga5
os
co1
127"A>
1 7.1%
N
80.2%
Ikteru.ili1c ilic pc.
recnt
C X l l c s ~
Dlf
u;-k:d t
Ue cornbusuou. Tit' ultroJA<tt pt ._t l in
Oe
gns
is ooutn'bu t.:d
by rur onlv
l>tJn> CO
is mixed
wi th 1 ( ~ ) %
~ c e , ; s
air
nnd b
urn t..
Only
CJ% of CO
bu
ms.
The
1'1 3Ctauts l'C ut j
oo•c.
utlli Ue jllUdUC(S are
ut
.:31)(1°C. C ~ t l c u l u h : i t ~ auoo ullL nf h.::.l
:lddcd
) f
fll111111
'
cd
pet
Kg llm
le
ol'
co
r :<J
to the renetor
Data: Mean molal specific heats bctWOOil
5
°C and T"C
(gtVCll
be low) m
KJ/Kg. milk. "
K '
Cu• T= IOO"C T""JII0°C
(;0 2Y.22 30(11
Cf.l1 <377
0: 29, \4 311.99
N
1
29.
17
2VM
Stnud<od b
ent or
fo nnntion ttl 25"
<.:
in
IU/K( mole
IS
co -11052+
CO:
.j')35
1.J
Bltumuwus con
l
WiUl
u
cakln lic \'ttlue or
201)(1 1 KJ/Ke
ts-
used
for generating
stc:m1
in a boiler how ruuch coal has to
be
bnru l
i
ll
;enc:rak 1MW
of
ct l
c
f t l l?.tlic
oc
ncy ol'
b t L S l l • m is II.75 How rnuch rnr
is
nccclod
j
5()0/o)
t:XI:CSS
ni
IS lO
be: used.
8/20/2019 GATE Chemical Engineering 1995
http://slidepdf.com/reader/full/gate-chemical-engineering-1995 6/7
8/20/2019 GATE Chemical Engineering 1995
http://slidepdf.com/reader/full/gate-chemical-engineering-1995 7/7
w w
w . e x a
m r a c e
. c o m
67
68.
69
1 )
Cip.:.'tation with .2.5 times
the
mwlmwfl
solvent rate.
A coWJtercwnnl
pla,te
absorber is tQ be
installed fru scrubbi:n& ·of wt alr
mh.'tUre
ccntaini.ng.S
percent ammonia by vcil ume.
l
he scrubber JS fed with
water
containlng
Q.002
.
mole
Nli3 per ruole
of w·ater
. TI.te
scrubba1g water
IJows
ala
rate
of 1.0
fll"le
watet
per n 1 o l ~ ais:. It
is n e c e s ~ a r y to
absorb 85 percent of
the
ammonia• 'l"'lenl
i:o. llie
gas by operating d1e absorber at
2o•c.
K =O
SO
m<ll N/ 1
1
/ molair
m
o.l
NH
1
1mo/ H O
c, tculate lhe concentratiou of 1 in
Ut
e
,,)llgontg li
quid
and estimate 11llllber
of
sl,ages ·necessruy for this operntion
'
T'lie
mte
or
a homogeneOilil liqulJ jlhase
reaction
is
given as
- YA
=
KC A Thi$
re-action lakes
place with 50%
t X > n v e r ~ i o n
in
a back JUix reactor. What will be Ute
co1
1v
er.sion i f
his
re-a.ctoc iJ 1eplacoo
by
a
bigger one. which. •i t
bnle$
larger. ALL
o1l1er conditiomr remain unchangl'd,
.Liqui
d A
dccomj)Oi'esm.
a batch
reactOF
by
a s
eco
nd oroer kmetics.
If
50,o of A
is
C(lnverted: iJ
,
a
Jjve IJUllUte. w ~
how I i
r
would lake to
reach
conversion,
a l e ~ a t e l h ~ change in onttopy when one
grSJ11 of
ce
i i i
o•c
is converted
i11l
o stearrt
at
c Lutiilll1heal
o
ffU$ion
ofice = SO
callg
.
Latent
heat
of vaporization
= 5·
40
cal/g and mean
specific l
tea
t of wat('[
between o•c
and
too•c= l.
When
u
1 e r m o m e t • ~ at
3o
•c is
phwedina
1vater
bath
at 90•C dte ini1ial rate
of
rise
itt ltennruncteJ' tetnperatul:e is found to be
2"C/se<J. Wlm t is
tl1e
lime C\1f1Simlt of lhe
t : h . ~ r . t n o r t J <
assunlillg
it
is a fust order
dl;>vice
wi
th tmil
y
st-eady
sl;lt'e
guin /
W)W
will
thermometerreact a'fter ,,nemln.ute7
II.
first
or
der
S)' 'tem
wil
h
I J ] l l i ~ e r
1\mction
o.
=
Y(&yX(S)
=
1/(S+l) is b ~ d e d to
iU]lut X(t)
=
t Perive Ute
expressi011
for
change m
output Y(f) tlS a
±imc
tion of ime .
7L
71
,
7J.
1 nf 7
Wllllt
is
tho maximum
ajtd muwnurn
d i f f e r e n ~ »
between
mput
and output? t
what time does
Uus
dillerence occur'?
A
nm
p
rder
reaction A B
is
being
carried out in a ·stirred lank
re
• ctor. Tile
feed slream
containing
reacl,an
t
A at
ooncentra6on CAOis bcing
fed
nt
oo
nslanl
rate
F
1 to
Ole
reactor. The
vo
hune
and
tewpe.raturc of tl
te. reactor are constant
Drui ve a. tnmsft>J
' ftu
totiotl relafu1g
concentration ofA
in
lite product
stream to
c t m ~ l l l ~ t a t i o n Of A
in
01e fee<Lotreillll .
Ao Jll
itu
de
Julio corrusponding tcr
cr6s'sover lfet
tu
ency
of
I 0 radlsoo
foe u
1'rt1CeSS is fi' '
' J to be
Q,1
a, What s the ult±mate gahl?
b.
Wlli\1
lhe veriod
of
s ~ l a i n e d
oscillationo corresponding to ullimat·e
giDn1
c. If a PI'O JOrtiooal coiJu·oller Is to be
l i S e ~
what
is tJ,e value
o
fw
o
por
bo
nal
gain you. would : C C ~ J n n
The
l
l"
<lll&fer limction of a
1 1 r o ~ e s s
llll a$urillg
devi
'
ct>,
Cl)lib"OUm' 3Jid Cilllll'o l
valve, fl'spectively
iS
gi•'<'n by
K
G
y=
( , VG =J,G, =K A.= l
~
The rool lpcus
diagram
of
the
~ ; J ~ s l e m
is
givenin figure 2.
a. Identify l@ Uons
Qf
pl'm\$ A and
S.
b. At X. = 1, the rooll
of
the syoiem are
lo
cal\.'d
at point C.
IdentifY
1he location
ufpoiJLtC.
c. Determine lhe value
e>f
J :t
. --
-..
-
~ --.
..
• · =
.
-
,