4th Semester (Dec-2015; Jan-2016) Civil Engineering Question Paper

1. USN O6MAT41
Max. Marks:100
(07 Marks)
(06 Marks)
isv:r'cos20_ rcose+2.
(07 Marks)
: 1, i, -1 on to the points
(07 Marks)
(07 Marks)
Fourth Semester B.E. Degree Examiii , Dec.201" 5lJan.20l6
Engineering Mathematics - IV
Note: Answer any FIVE full questions, selecting
atleast TI,VO questions from each part.
b.
b.
c.
c.
(.)
o
o
c.
;
'o
o
!
3v
;va
;il
ioo
.E cq3 ri'
oY!
oE
-0
3s
@:;
oO
'==
E
50i
dd
>P,6
d-
-? o)
oP
o-X
oi.
a.v
6:
,C)
utE
6=
!o
5.e>'!oo-cbQ
O=
-c. E
E>
^O
L'<
* a.l
o
o
Z
F
o,
PART _ A
I a. Use Taylor's series method upto 4th degree terms find y at the points x : 0.1 given that :
dv))
f=^-+Y-'Y(o)=l'
By Runge - Kutta method of order four, solve
y(0.4), taking step - length h:0.2.
c. By using the Milne's predictor - Corrector method, find an approximate solution of the
.dv1 -
equation
#=*'-r, at the point x : A.4, given that y(0) : 1, y(0.1) : 0.9051,
Time: 3 hrs.
3a.
h.
4a.
(06 Marks)
dv /-Y
the equation ]l with y(0) - I, for
ox y+x
(07 Marks)
y(0.2) :0.8212, y(0.3) :0.7492. Apply corrector formula twice.
2 a. If (z) : u * iv is an analytic function, then prove that :
r^ -2 r^ t2
ffrtrr,l]
.ffrEr,t
)
=lrr,tl'
Find the analytic function (z) :u * iv, whose imaginary part
Find the bilinear transformation which maps the points z
w : i, 0, -i, respectively. Hence find the image lzl < l.
State and prove Cauchy's integral formula. (06 Marks)
Expand f1z1= . -3-asLaurentseriesvalidfor:i) 1< lrl<2 11)lz- 1l> 1.
(z-t)(2- z)
(07 Marks)
State Cauchy's residue theorem. Using this theorem evaluate , t--1 , dz, where C is
i z(l- 4z')
lzl: r-
Prove that Pn (x1=-l l.[.' - l)" ]. where n is a positive inreger.
lf-2n dx
n '
Express (x) : 3x3 - x2 i 5x - 2 in terms of Legendre polynomials.
(06 Marks)
(07 Marhs)
Obtain the series solution of Bessel's differential equation in the form y: AJn(x) + BJ,(x).
(07 Marks)
I of2
b.
c.

2. PART _ B
O6MAT4I
5 a. Fit a parabola y: a-f bx + cx2 by the method of least squares to the following data:
(07 Marks)
While calculating the correlation coefficient between x and y from 25 pairs of observattons,
a person obtained the following values. Xxi : 125, Zxi2 : 650, Xy, : 100, tyi2 : 460,
Ixiyi : 508. It was later discovered that he had copied down the pairs (8, 12) and (6, 8) as (6,
14) and (8, 6) respectively. Obtain the correct value of the correlation coefficient. (07 Marks)
In a bolt factory there are four machines A, B, C, D manufacturing respectlely 20oh, l5oh,
40Yo of the total production. Out of these 5oA, 40 ,3oh,2oA are defective. if a bolt is drawn at
random was found defective, what is the probability that it was manufactured by A or D.
(06 Marks)
A pair of coins is tossed. A random variable X represents the number of heads turning up.
Find the discrete probability distribution for X. Find its mean and variance. (06 Marks)
2o/o of the fuses manufactured by a firm and found to be defective. find the probability that a
box containing 200 fuses contains i) no defective fuses ii) 3 or more defective fuses iii) at
least one detective fuse. (07 Marks)
c. The mean weight of 500 students at a certain college is 50 kgs and the standard deviation is
6 kgs. Assuming that the weights are normally distributed, find the number of students
weighing i) between 40 and 50 kgs and ii) more than 60 kgs. (07 Marks)
Explain the following terms :
i) type I and type II errors ii) null h-vpothesis iii) level of significance. (06 Marks)
A coin was tossed 400 times and the head turned up 21.6 times. Test the hypothesis that the
coin is unbiased at 5o/o level of confidence. (07 Marks)
c. A certain stimulus administered to each of 12 patients resulted in the following change in
blood pressure '. 5,2,8, -1, 3,0, 6, ), l, 5,0, 4 (in appreciate units). Can it be concluded
that, on the whole, the stimulus will change the blood pressure? Use t6 65(1 l) : 2.20t.
(07 Marks)
8a. The joint probability distribution of two random variables X and Y is given below :
Find:
i) Marginal distribution of X and Y
ii) Covariance of X and Y. (06 N{arks)
Define a stochastic matrix. Find the fixed probability vector of the regular stochastic matrix.
[o 1 ol
ttP=l 0 0 11. (07Ntarks)
lY, Y, ol
A psychologist makes the following assumptions concerning the behaviour of mice
subjected to a particular feeding schedule. For any particular trial, S}oh of the mice that went
right on a previous experiment will go right on this trial, and 60oh of those mice that went
left on the previous experiment will go right on this trial. Suppose 50% of the mice went
right on the first trial. Find the predictionofthe psychologist for the next twotrials. (07 Marks)
+**jr*
2 of2
b.
c.
6a.
b.
a.
b.
b.
x: 0 I 2
a
J 4
v: 1.8 1.3 2.5 6.3
v-+
*J
a
-J +2 4
1 0.1 0.2 0.2
f
J 0.3 0.1 0.1

3. x-8 _ y+9 *
b.
b.
()
oo
o.
.o
:c
.JP
!o
=-a=
u!o
6+
oo>N/
.Y
-6dt
3ar
F.v
^:
o'j
AE*,O
@L:
5-
?'o
>,4-
"no.ic
ii=
=9
=tuVL
o
^nlr<
-61
o
-7
(n
o
c"
USN
3a.
4a.
a. Frove that div(curlA) = g.
))
b. Find div F and curlF where
c. Show that the vector fr = 13*'
+
suchthat p=grad$.
F = V(x3 + yt + z) -3xyz) .
-2yz)i+ (3y' -2zx) j+ (322 - 2xy)k
MATDIP4Ol
(07 Marks)
3), B: (i. 1, 1),
(07 Marks)
(06 &Iarks)
{07 Marks}
z -10 and
3-t67
(CI7 Marks)
(05 N{arks)
{07 Marks)
is irrotational and find $
Zx-y -z*6 =0 .
Find the image of the point (l , -2,3) in the plane 2x -t y -z:5.
Find the shortest distance between the lines
x-15 _y -29 :r-5
B -5
Find the constant 'a' so that the vectors 2i- j+ k, i + 2j-3k and 3i + aj + 5k are coplanar.
[- ]: + + +r -[*: ,r
(o6Marks)
Frovethat la+b. b+c. c+ al:21 a,b.c l. (o7Marks)
L]L-]
Find the unit normal vector to both the vectors 4i- j+3k and -2i+ j-zk. Find also the
sine of the angle between them. (07 Marks)
A particle moves along the curve x:t3 +1, y =t2,2:2t* 5 where t is the time. Find the
components of its velocity and acceleration at time t : 1 in the direction af 2i + 3j + 6k .
(06 Marks)
b. Find the angle between the surfaces x'+y2 +22 =9 and x=z1t +y'-3 at the point
(2, -1,2). (07 tl{arks)
c. Find the.directional derivative of O = xy' +yz3 at the point (1, -2, -1) in tlie direction cf the
normal to the surface xlogz - yt = -4 at (- 1 , 2, 1 ). (07 Marks)
ff*^4r
Fourth Semester B.E. Degree Examina ec.2015|Jan.2016
Advanced Mathematics - ll
Time: 3 hrs. Max. Marks:100
Note: Answer any FIYE full questions.
I a. Find the direction cosines of the line which is perpendicular to tnie lines with direction
cosines (3, -i, l)an(-3,2,4). (05Marks)
b. If cos c{,, cos p, cos y are the direction cosines of a line, then prove the following:
i) sin2 cr +sin2 B +sin2 y = 2
i, cos 2cr + cos 2p + cos 2y = -1
c. Find the projection of the line AB on the line CD where A: (1,2,
C : (0, 0, 1), D : (2,3,0).
2 a. Find the equation of the plane through (1, -2, 2, (-3, l, -2) and perpendicular to the plane
I of2
(07 N{arks)

4. 6 a. Find: L
b. Find: i)
c. Find: L
cos 2t
cos' t),
at - cos
{cos t
L{e-'
Icos
r
cos 3t) .
ii) L{te-'sin 3t}.
MATDIP4Ol
(06 Marks)
(07 Marks)
(07 Marks)
(06 Marks)
(07 Marks)
(07 Marks)
II
I
I
I
I
I
I
I
I
l
l
l
btl
-t
7 a. Find: [
{
4s+5
(s-l)2(s+2)l'
Find: i) t-.-'J =
t*2 I.' [s' - 4s + 13.J
Find: L- J . ' I.
Is'(s+1)J
8 a. Using Laprlace transforms, ,o1r. -d'{ -2+* y = e" with y(0) : 0, y'(0) : 1. (10 Marks)
ox ox
b. Using Laplace transformation method solve the differential equation y"+ 2y'-3y =siflt,
Y(0)=Y'(0)=0. (l,Marks)
b. ii)ri"'[x)]
***<r<*
2 of2

5. USN
4a
b
7a.
b
5a.
b.
c.
5a.
b.
t0cY !c'{42
(lS Marks)
(tS Marks)
(06 Marks)
(10 Marks)
(84 [4arks)
(06 Mari<s)
(t0 Marks)
V//C ratio? (ls Marks)
(18 Marks)
GS 10262-
(12 Marks)
(0E Marks)
o
o
o
L
p-
c3
d
a
o
o!
6.)
ox
J?
d9
+h
.=+
d<'
;:b4
Io
o(
'Pts
V)-
u2
ad
KY
OU
_!
oo=
>F
,G
-z' ts
o!a4
io+a-C6
E=
2j
aa
9E
AEd-l
rrO
>a (H
^^o
'-a
A!Y
i>
v!
;>,
(r<
-. a.l
o
a
?
!
Fourth Semester B.E. f)egree Examin .20115/Jan"2015
Goncrete Technology
Time: 3 hrs. Max" I4arks:i00
Note: l. Answer FIItE full qwestions, selecting
at least TWO questions f,rom ewch part.
2. Use of IS 10262-2009 is permiwed..
PART _ A
a. Explain with flow chart, the cerrent manufactured by wet process. (tr0 Marks)
b. List the different laboratory tests conducted on cement. Explain any one of them in detail.
(tr0 Marks)
a. Explain the role/effect of fine and coarse aggregates in concrete. (10 Marks)
b. Write a note on "mechanical properties" of coarse aggregates. Explain the test for
detennination of aggregate impact value as per 152386 part IV - 1903. (10 Vlarks)
a. Define the term "Workability." List the factors affecting workability of concrete and
methods of measurement of workability. (10 Marks)
b. List the various stages/process of production of quaiity concrete. Explain in brief. (10 Marks)
. Discuss the role of chemical admixtures and mineral admixtures in cernent concrete.
Write short notes on: (i) Rice husk ash, (ii) Air entering agents
PART _ B
List the factors influencing strength of concrete.
What is the relation between:
i) Compressive strength and tensile strength of concrete as per IS456-2000
ii) Cube strength and cylindrical strength of concrete. {04 Marks)
Explain in brief the principles of flexural/modulus of rupture testing of concrete under third-
point loading rnethod.
Mention the different modulii of elasticity of concrete.
What are the factors affecting shrinkage and creep of concrete?
Write short notes on:
i) plastic shrinkage
ii) drying shrinkage
Define the term durability. What is its significance and its impact on
Write shoft notes on:
i) Sulphate attack and its control
ii) Freezing and thawing and its remedial measures
a. Discuss the steps involved in Indian standard method of concrete mix design
1 982).
b. List out the variables in proportioning of concrete mix design.
*****

6. USN 10cv43
,/
Fourth Semester B.E. Degree fxifid ec.20l5lJan.20l6
HL
o>
Es
oX
HX
0 (g * 1m [r5.Y..4./' r-rts.vzuJ,,
; Ei b. ql;ffi the maximum slope and maximum deflection for the beam shown in Fig.Q2(b).
H E ffinjusate beam method. Take E : 2xl0s N/rnm2, I : 40x 106 mma. (10 Marks)
EE n&
E F 3 . ffitate Castigliano's First and second theorems. (04 Marks)
$E - *ilS Using Castigliano's theorem compute the deflection at the mid-point of simply supported
E *. A[-*-
' beam of span 'L' and flexural rigidity EI, carrying a point load 'W' at the midspan.
ISO c. Determine the vertical and horizontal deflection at 'c' of the beam shown i,, li!.tli:i
6 {- Take E :200 GPa and I: 80x106 mma. (10 Marks)
-.: c.i
o
o
z
!
a
E
q)
o
od
E
6
CI
d)
0)
!
ER
EE
sq5
EE
=ra
60 ,,
!: ca
.=N
d+
g6*
otr
-c g)
StructuralAnalysis-l 4
rime: 3 hrs. M*. r"rffFirdo
Note: Answer any FIWfull questions, selecting il $.
atleast I"WO questionsfrom each part. d*
xvJ
PART - A t,
a)r
I a. Define : (i) Degree of static indeterminacy and ii) Degree of qqffi (05 Marks)
b. Derive an expression for strain energy due to bending. ^t _, u (06 Marks)
c. Determine the degree of static and kinematic indeterm&@s for the structures shown in
Fig.Ql(c) (0e Marks)
BT
E A 2 a. For the beam loaded ,, ,fuffiffi Fig.Q2(a), determine the slope and deflection at the free
S E end. Take E :204x10o*ffi&r' Use moment area method. (10 Marks)(Bcl
€ i ,.Lxt
EE -e h lalsr
;t 4* , =*, ,,F;t'* I a-*'ouu'; E /-*,v'
E; * B t
Fig.Q2(b)
Fig.Ql(c)
Fig.Q3(c)
I of2

7. 10Cv43
.l
4 a. Using strain energy method determine reaction at B for the beam shown in Fig.Qa(a). Draw
BMD and SFD. (10 Mcrks)
cV-l"r'
A
Fig.Qa(a) Fig.Qa@) dlrb. Analyse the fixed beam shown in Fig.Qa@) using strain energy method and dgv/BMD.
(10 Marks)
PART - B
5 a. A three hinged symmetrical parabolic arch has a span of 36m
b. A cable is suspended between two points A and B,A cable is suspended between two points A and B, ffigr aliart
of 6 m. It supports a UDL of intensity 20lcTrtim. Coffie:
i) The length of the cables. f1....
ir) Maximum and minimum tension in the
W
(08 Marks)
For the beam shown in Fig.Q6(a), cpanptrte the reaction at B by consistent deformation
method. Draw BMD and SFD.
^L.$
(10 Marks)
I 6ok+. r
gokv
n I i'"- n [l --'*rt'n
f- o* {--tra -f ?-- * - 'rf 6ro C zt
FieffiMi Fie.e6(b)
b. Analyse the fixeffim shown in Fig.Q6(b) using consistent deformation method.
,N
**."*o -l,W
(10 Marks)
-#7 Analyse the*ffifruous beam shown in Fig.Q7 by Clapeyron's theorem. Draw SFD & BMD.
(20 Marks)
d*f t-,^.
65P -3"$lo
A two hinged parabolic arch has a span of 32m and a rise of 8m. A uniformly distributed load of
1 kN/m coverc 8 m horimntal length of the left side of the arch. If I : Io sec0, where 0 is the
inclination of the arch section to the horizontal, and Io is the moment of inertia at the crown.
Find the horizontal thrust at hinged and bending moment at 8 m from the left hinge. Also find
the normal thrust and radial shear at this'section.
**{.1r{(
2 of2
rise of 6m. The
arch carries a UDL of intensity 30 lcIt{/m over left half a concentrated load of
60 kN at 9 m from right support. Compute the bending normal thrust and radial
shear at 9 m from left support. *'
&-"/ (12 Marks)
afrart horizontally and a central dipdip
6a.
qs-^
(10 Marks)
Fig.Q6(b)
Fig.Q7
(20 Marks)

8. USN
Time: 3 hrs.
theodolite not in adjustment.
c. List the errors eliminated by repetition method.
(rf i'- {
a note on:
d*yry rurarrilurlu lsrts. rr,, JuDlcn!
tii'-" Explain the method of determining the
ffi" aounactic lens. ii) Subtense diaphragm.
The instrument is fitted with anallactic lens and the constant is
PQ and reduced level of Q, that of P being 321.500 M.
100. Compute the length of
(10 Marks)
t0cY44
(08 Marks)
(04 Marks)
(10 Marks)
' r ri c4q,ii*fg, ltl*ifl*, ,r tlri
(04 Marks)
(06 Marks)
following
"sti+
Fourth Semester B.E. Degree Examination, Dec.20l5 I Jan.20l6
Surweying - ll
,f
,r^r3fl1
Max. Marks:ffi"
()
o
9
L
o
a
d
c)
.i tttGl- '- n)
,.JJ
1B ,r
l1E
=_1 *1=
::.J :It I
=h-oo ll
coo
.=N
(d+
ETotr
-c c)
oB
$q
d:I
bd
-!do
o13
o0c
Ex
>xF3
Ed
,-a. ts
5 .lJ
Ad
XE
tro.Ed
:_ *,:{
:5
Note: Answer FIVE fall questions, selecting
at least TWO questionsfro* each part.
P.{RT _ A
I a. Distinguish between:
D Plunging and swinging of the telescope.
ii) Clamp screw and tangent screw.
. ii| Transitting and line oicollimation.
"',;jj'-* b;l
'.With neat sketches, explain measurement of a straight line by a theodolite in adjustment and
it-,,;*;
..:.*i
i,iffi
@r.
2 a. What are the permanent adjustments of a theodolite? Explain the spire test. (08 Marks)
b. Explain the procedure to lay off an angle with a greater precision than the least count of the
instrument. (08 Marks)
What is an'index error'? WJry it isis ne.ffiary to be adjusted?
"lri.
(04 Marks)
c. In order to ascertain t
3 a. Derive the expression for the -|rorizintal distance, vertical distance and the elevation of an
elevated object by double pla4qmethod, when the base is inaccessible. (07 Marks)
b. List the advantages of total$, ion over the conventional surveying instruments. (03 Marks)
In order to ascertain the'..devation of the top (Q) of the signal on a hill, observations were
made from two instnriYrrjnt stations P and R at a horizontal distance 100 M apart, the stations
,.P and R being leqi,i,ith Q. The angles of elevation of Q at P and R were 28'42' and 18o6'
respective
staff readings upon the bench mark of elevation 287.280 M were
M and 3.750 M when the instrument was at P and R, the telescope being
ine the elevation of the foot of the signal if the height of the signal aboveho
its
r
3M.
x!oov
-E' E
C)
'o
z
(!
!
&
&**&i'+, ,i $+hr.i{{, r:
:XE:
tir r.. r
i!! - t,
;ftr' .
E E d*
E H,#'
.E .i' ^ ,,^qb.'" Explam the method of determining the constant of a tachometer, in the field.
E E v* p. A tachometer is setup at an intermediate point on a traverse course PQ ariate point on a traverse course PQ and the
observatiatrons were made on a vertrcally held statt
Staff station Vertical ansle Staff intercept (M) Axial Hair Reading (M)
P +9o36, 2.3s0 2.r0s
o +606' 2.055 r.895
L of2

9. ttF Ii rW E'
r(rcv44
ti ;i
PART _ B "I
5 a. Define degree of a curve. Establish the relationship between degree of curve and its radius.
b. Calculate the ordinates at 10 M fof a circulat'"cunq'ffih
80 M and the versed sine is 4 M. ,r
c. The chainage at the point of irt..r..tibn of the tangents to a raiiway to*.1sl:
angle between them is 150'. Calculate allthe data necessary for curve setting out agffibf
radius 250 M by the deflection angle method. The peg intervals may be taken as ffiffi.Also
apply the arithmetic check.
*e*W
Marks)
Distinguish between compound curve and reverse curve. {*--*
* (0+ Marks)
Derive the relationships between various elements of a reverse curv6"&$vdeen two parallel
| ;-: jgl . ..tJ;rr .; I
6a.
b.
c.
7a.
b.
c.
straights. u%m
* (08 Marks)
Two parallel railway lines are to be connected by a reverse culqei &ch section having tfie
same radius. If the lines are lzll.4 apart and the maximur" d@{re betrry9gg,!g"ngdg!J_".S.f*;
measured parallel to the straights is 48 M, find the maxirpqln aiowable'ihAifs:Tf65ffi'
radii are to be different, calculate the radius of the secondrffich if that of the frst branch is
60 M. Also calculate the length of both the branches. "., & (08 Mark'i) i
{::ry
What is a transition curve? Explain the requirenffiqof a transition curve. (06 Marks)
Why are vertical curves provided on highwaysrl,Di$t ttre different types of vertical curves. '':
# (04 Marks)
A transition curve is required for a (gular curve of 200 M radius, the gauge being 1.5 M
and maximum super elevation is to 0.15 M. The transition is designed for a
velocity such that no lateral imposed on the rails and the rate of gain of radial
acceleration is 30 cmlsec3. Calq ihe required length of curve and the design speed.
(10 Marks)
8 a. What ts "Zero circle" of a planimeter? Explain any one method of finding its area.(06 Marks)
b. Calculate the area of a figure from the following using a planimeter with the point inside the
figure.
Initial reading : 9.918
Final reading= 4.254
Constant M and C respectively are 100 cm2 and23.52L The zero mark of the disc crossed
the inde*..once in anticlockwise direction. (04 Marks)
Tfre #h'ir enclosed by the contours in a lake are as follows:enclosed b the contours in a lake are as fo
Contour (M) 270 275 280 285 290
Area (M") 2050 8400 16300 24600 31s00
Calculate the volume of water between the contour 270}l4 and290 M by the trapezoidal and
prismoidal rule. (10 Marks)
:f*Xr<*
c.
H*j
$ 1i{Tffii*+rji,l;1,t,,
,'
2 of2

10. USN IOCV45
Max" Marks: l0O
(06 frAarles)
(09 Marks)
({}4 Marks)
{02 Ntarks}
Fourth Semester B.E. Degree Examinatiod 015/Jan.2016
Tirne: 3 hrs.
4a.
b.
Hydraulics and Hydraulic Machines
Note: 7. Answer FIVE fuU questions, selecting
at least TWO questions from each XsarL
2. Missing data may suitably be sssuvned"
1a.
Ltr.
c.
o
o
.J
d
c.
(d
a
a3
(-)
d
o
oX
ida
"
eO
F-
o>
8*
a=
o()
-k(60
e!-C
>t,N
6t
u=
o-F
t; .9,
@tE
6c
!O
o.i
>1 +
^.o
tr>
-Pa-
!J<
..al
C)
o
Z
f
a,
F
A 2.5ro ship model was tested in fresh water p : 1000kg/rm3 and measureffrents indicated
that there was resistance of 45N when the rrodel was moved at Zrnls. Workout the veiocity
of 40m prototype. Also calculate the force required to drive the prototype at this speed
throngh sea water ( p : 1025k g
^. {{}5 Marks)
2 a. With neat sketches differentiate between flow through pipes and flow through open channels
with examples. {SS N[arks)
b. Derive an expression for the discharge through an open channel using Manning's forrrulia"
(06 Mark-s)
c. An earthen channel ,,rrith a base width 2m and side slope lF{ to 2V carries waier rvith a
depth of ira. The bed slope is I in625. Calcuiate the discharge if n:0.03. Also calculate
average shear stress at the channel boundary. (06 Marks)
3 a. Define specific eneigy. Draw specific energy curve, and then derive expressions f'or critical
depth, critical velocity and rninimum specific energy. (tr0 klarks)
b. Derive the expression for sequent depth of hydraulic jump interrns of Froude number befcre
a hydraulic jump in a rectangular channel flow. {CI6 &tarks}
c. A horizontal rectangular channel 4rn wide carries a discharge of i6rni3/s. Deterrnine whether
a jump may occur at an initial depth of 0.5m or not. If'a jurnp occurs, deterraine the sequent
PART _ A
Deflrne the dimensional homogeneity. Give an example.
Briefly explain geornetric, kinematic and dynamic similarities.
detpth to this initiai depth. Also determine the energy loss in the Jump.
State impulse rnomentum equation.
c.
Shou, that in case of jet striking the flat plates mounted on wheels. tkre eff,rciency will be
rnaximum when the tangential velocity of wheel is half that of jet and maximum efficiency
is only 50%. (10 i[arks)
.A T5mm diameter jet having a velocity of 30m/s strikes a flat pla.te, the norrnai of which is
inclined at 45o to the axis of the jet. Find the normal force exeded on the plate.
i) When the plate is stationary ii) when plate is moving with velocity of i5m/s in the
direction ofjet away ftom the jet.
Also determine the power and efficiency of the system when the plate is moving. ($E ivlarks]
PART _ B
5 a. Show that when the jet of water sffiking symmetrical moving curved vane at tire centre, the
8
rnaximum efficiency for semicircular vane is _ (1+ cos0).
27'
1 of2
(1t) k[arks)

11. r trCIcv4s
b. A jet ofl water, 50mm in diameter, strikes a curved vane at its centre with a veiocity of
18na/s. The curved vane is rnoving with a velocity of 6mls in the direction of the jet. The 1et
is deflected through an angle of 165o. Assurning the plate to be srnooth, Find :
i) Thrust on the plate in the direction ofjet
ii) Fcwer: of the jet, and
iii) Efficieney of ttrre jet (trO l{arks)
With the help of velocity triangles derive an expression for work done and rnaximum
hydraulic efficiency of a pelton wheel. {10 Marks)
A Pelton wheel is receiving water from a penstock with a gross head of 510rn. One third of
gross head is los1" in friction in the penstock. The rate of flow through the nazzle fitted at the
end oflthe penstock is 2.2ri ls. the angle of deflection of the jet is 165o. Detennine :
6a.
i^
t_r.
7a.
b.
o^oa,
b.
C.
0 Fower given by water to the ruflner,
ii) Hydraulic efficiency of the pelton wheel.
Take Cv: 1'0 and sPeed ratio : 0'45'
Draw the neat sketch of Kaplan turbine and mention the parts.
Explain with the help of neat sketches the different types of draft tubes.
7Sa/o. Deterrnine the vane angle at the outer periphery of the impeller.
A Kaplan turbine develops 22000kW at an average head of 35m. Assriming a speed ratio of
2, flow ratio of 0.6, diameter of the boss equal to 0.35 times the diameter of the runner and
an overall effici.enicy of 88%, calculatethe diarneter, speed and specific speed of the turbine.
({}6 Marks)
Explain brriefly the various types of efficiencies of a centrifugal pump. (08 Marks)
(10 Marks)
(08 Marks)
(S6 Marks)
(05 Marks)
Distinguish bertween pumps in series and pumps in parallel. (07 Marks)
A centrifligal pump is to discharge 0.118m3/s at a speed of i450rpm against a head of 25m.
The impelier diarneter is 250mrn, its width at outlet is 50mm and manometric efficiency is
*****
2 af2