1. e
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r i,"1'{
I
L'
1OMAT41
USN
Fourth Semester B.E. Degree Examination, Dec.2013 /Jan.20l4
Engineering Mathematics - lV
Max. Marks:100
Time: 3 hrs.
Note: Answer FIVEfull questions, selecting
at least TWO questions from each port.
a)
o
o
...
L
I a.
d
()
b.
-.o
oo
l1
troo
.= ol
c.
ts
Emplo,y Taylor's series method to obtain the value of y at
2 a.
x:
0.1 and 0.2 for the differential
* =rr+ 3e* . y(0) : 0 considering upto fourth d.gr.. t*rrn.
dx
(06 Marks)
y":i
+y2using modified
Determinethe value of ywhenx:0.1, giventhaty(0):1and
Euler's lormula. Take h : 0.05.
.
Apply Adams-Bashforth method to solve the equatron
y(1.
i50
oi
do
o>
PART_A
equation
OJ
ox
...
I):
Solve
t
1.233,
=t*
y(.2):
dv )---!-;;'1t+y).
:
v(O) =
Q,z(0):1atx:0.3
grven
dx
1.979. Evaluate y(1.4).
t.548,:y11.3)
r*. 9- -xy.
(07 Marks)
oO
bQi
,€
b.
c.
1,
by taking h
:
0.3. Applying
(06 Marks)
Applying Picard's method to compute y(1.1) from the second approximation to the solution
(07 Marks)
of the differential equation y" * fy': x'. Given that y(1) : 1, y'(1) : 1.
Using the Mitni's method obtain an approximate solution at the point x
*= t-ZV!.
" dx
dx'
5ir
:
(07 Marks)
Runge-Kutta method of fourth order.
a=
y(1)
y(0.41
:
give rhat y(0)
:0. y'(0) 0. y(0.2) :
0.0795. y'(0.4) :0.3937.y(0.6) :0.1762.y'(0.6)
:
:
0.8 of the problem
0.02. y'(0.2):
0.1996.
(07 Marks)
0.5689.
p- 6.
o"
oj
!o
5.:
}'(ts
boe
i al)
o=
3 a.
b.
(06 Marks)
Derive Cauchy-Riemann equations in Cartesian form.
Give tr.-- v (x
-
yXx2
+
4xy +
f(z):
y2; find the analytic function
c. tf f(z): u * iv is an analyic tunction then prove thrt (*
|
f(r)
u + iv.
l) .
[*
(07 Marks)
|f
(r)
I) =1f '1ztl)
(07 Marks)
o-B
tr>
Xo
()-
(r<
-
o
o
C.l
4 a.
b.
Z
o
c.
Find the image of the straight lines parallel to coordinate axes in z-plane under the
(06 Marks)
transformationw: z2
Find the bilinear transformation which maps the points z : l, i, -1 on to the points
w:0,
(07 Marks)
1, oo.
where c is the circle
Evaluate r,f---gj-.
(z + ll(z + 2)
I
zl :
I of2
3.
(07 Marks)

2. 1OMAT4l
PART _ B
5 a.
Find the solution of the Laplace equation in cylindrical system leading to Besseis differential
(06 Marks)
equation.
If
c.
6 a.
b.
c.
7 a.
.lm
cx
and B are two distinct roots of J,(x)
:
I
0, then prove that
fx J, (ux)
o
+ n.
Eipq*ur (x)
:
*o
- 2*' + l* -
4x + 5 in terms of legendre polynomial.
J,,
(BX)di = O,
r;...
,,
'
"""
(07 Marks)
(07 Marks)
A coiilfufttee consists of 9 students, 2 from first year, 3 from second year and 4 from third
year. 3 st'"udepts are to be removed at random. What is the probability that (i) 3 students
belongs to different class (ii) 2 belongs to the same class and third belongs to different
(06 Marks)
class. (iii) All the 3 belongs to the same class.
State and prove Ba$Cs
:::'::"'
'1""''r
theorem.
:':::
"t
(07 Marks)
The chance that adodtirw^ill diagnose a disease correctly is 600/o. The chance that a patient
will die after correct diagncise is 40Yo and the chanCe bf death after wrong diagnose is 70o/o.
(07 Marks)
If a patient dies, what is the bhhrpE that diseasdWas conectly diagnosed.
The probability distribut ion of finite random variable x is siven by the following table:
x
0
o(x)
0
:
')
1
Ir
J
4
5
6
7
2k 2k 3k k
2k
7k'+k
Find k, p(x < 6), p(x > 6), p(3 < x < 6)
(06 Marks)
b.
Obtain the mean and variance of Poisson distribution.
(07 Marks)
c.
The life of an electric bulb is normally distributed wiXh average life of 2000 hours and
standard deviation of 60 hours. Out of 2500 bulbs, find the number of bulbs that are likely
(07 Marks)
to last between 1900 And 2100 hours. Given that p(0 < z < 1.57) : 0.4525.
8 a.
b.
,
l'
'.,'-
Explain the foilbwing
i)
Null
hy
sis
',,;
terms:
(ii) Type I and Tlpe II
error
.
,- ,
,,':"-"
(iiil Confidgnce limits.
(06 Marks)
The weight of workers in a large factory are normally distributediWith mean 68 kgs, and
starydard deviation 3 kgs. If 80 samples consisting of 35 workers each are chosen, how many
of,80 samples will have the mean between 67 and 68.25 kgs. Given p(0 < z < 2) : 0.4772
and p(0 3 z < 0.5): 0.1915.
.,,,", ,{07 Marks)
Eleven students were given a test in statistics. They were provided additional coaching and
then a second test of equal difficulty- was held at the end of coaching. Marks scored by then
in the two tests are given belo
ven
I
II
t9
24 19 22 t8 20
20 20 23 20 t7
Do the marks give evidence that the student have benefited by extra coaching? Given
t005(10) :2.228. Test the hypothesis at 5Yo level of significance.
(07 Marks)
Test
Test
23
20
19
21
*8ri<**
2
of2
18
20
22
18
t7
23
t6

3. MATDTP4Ol
USN
Fourth Semester B.E. Degree Examination, Dec.2013/Jan.2$t4
Advanced Mathematics
- ll
Max. Marks:100
Time: 3 hrs.
Note: Answer any
()
o
o
*
g
.=
o
o
!
Eg
cEe
76
-o0
coo
an
2 a.
Find the equation of the plane through the points
c.
b0i
ccd
-o
>!
e
3o
aLE
LO
)E
>- (!
-^o
eoo
o=
so
tr>
^-o
5e
Z
!
o
-2) and perpendicular to
(07 Marks)
x-2:,u-l _r-3 end x+i_>-3_z-1
(07 Marks)
0
(07 Marks)
ii) (2a+ 36) x (a +,::,45)
(07 Marks)
b.
c.
rr
a'
b.
c.
a'.1
O
o
(l; -2,2) (-3, l,
are coplanar.
Prove the following: ,
i) (34 - 26) x 1-la + 2b-; = l4(A + 6)
U<
-
(06 Marks)
c.
a.
-_I
{*i=,
Find the sine of the angle between d = 2il2 j_+ k jrLb =
2i
1- 12ka
Find the value of ), if the vectors a = 4r+ 6j+ 2k, b=3i +10j +5k and c
^X
'ii
+
a'
b.
a6
tro.
o."
o
theplane2x-y-z+6:0"
t22*1
'od
3A
OE
I
Find the angle between the following lines:
oE
-o
UO
Prove that the equation of the plane in the intercept form is
b.
tso
;:r
questions.
I a. Prove that sin' cr + sin' B + sin' y = 2.
(06 Marks)
b. If 11; ml, n1 and 1.2, mz, fl2 are direction cosines of two lines then pxove that the angle
(07 Marks)
between,,them is cos 0: l-J-zt m1m2 * nrflz.
: ,,ir
c. Find the equation of the plane through the interaction of the pl4nes'2x + 3y - z : 5 and
(07Marks)
x-2y -32= - 8, also perpendicularto the plane x +y -z:2.
I
.:
FIVEfull
a.
b.
c.
E
d.
(06lVlarks)
=-41+5J+i[-
'
= 5(a + 6)
along the curve i = (t' -4O1+(t2 +at)j+(8t2-.3t3;[. nina the velocity
(06 Marks)
and acceleration at t : 1 and also find their magnitude.
.,
:4 at the point (- 1 , -1 , 2).
nind,ihe unit normal vector to the surface xy3 z2
:_ (07 Marks)
(07Marks)
Findthedirectionalderivative ofx2yz3 at(1, 1, 1)inthedirectionof i+j+2k
A particle
rr,lclVes
{,;
(06 Marks)
Find div F and curl F, where F = xti + ytj + zt[ .
,,"'l
Prove that curl grad Q : 0.
(oiiMarks)
Find the constants a,b, c such that the vectorF =(x* y +az)i+(x+ cy +22)k+(bx+ 2y -r)j
(07 Marks)
is irrotational.
Find the Laplace transform of the following:
sin 4t cos3t
cos hat
t e-t sin t
1 - cost
GENTH'al
LlElgi&RY
20 Marks)

4. MATDIP4Ol
7
Find the inverse Laplace transform
of
a' - /s+1
'"1r r.,J
s+l
- __-:_
b.
(06 Marks)
(07 Marks)
s'+2s+2
t'
(o7ilIarks;
G+1)G{2X,L:5
.,
",{}1*
,
8 a. tr;'@g
,,.,.
Laplce transforms, solve the differential equation
subjectEffi-the conditions y(0)
b.
:
:0.
y'(0)
gy-*x
**r=sint, dt
dt
Given that x : 1, yffiwhen t : 0.
Solve the siffilppeous equations
Lfl./
{furgl.
dt'-
6y
dt
,
=5e"
(10 Marks)
=9oF$, using Laplace transforms.
,.ftrI*
(lo Marks)
4 d,.
**{<i<{<
,"
,
"
...
q
t:: ti'
'
; "'*
,,*;t
i:
:::
::
-
I
::
'!i;-,::'
i"
{;lli};,..,
::::.
::"
' .{ }.
_r*!#U
''
',,,"""""",,,,':1
,
.
,,,-,
=.=
,
.::::
q
tl, '{+,t
t-
,,1'
:
ta..""':':""""' '"'
-.::::-
'::::,
'
2 of2
u-

5. 10cY42
USN
Fourth Semester B.E. Degree Examination, Dec. 20l3lJan.2Ol4
Goncrete Technology
Max. Marks:100
Time: 3 hrs.
Note: Answer FIVEfull questions, selecting
atlesst TWO questions from each part.
PART _ A
()
o
o
1 a.
a
b.
What are Boughe's compounds in cement? Explain the role of each compound in strength
(10 Marks)
gaining and hardening process.
of flow,lt"Jlr.u,
Exp14,,1$he process of "Dry Process" of manufacturing cement with a help
()
o
3e
=h
3
ool
=ca
.=
2a.
b.
3 a.
a-.1
nbo
Yo
otr
b.
-O
o>
o2
Define water cement ratio, and how this w/c ratio will have influence on workability of fresh
concrete.
::: ,. ,,
4 a.
b.
,,
(10 Marks)
What are admixtures? Why ihey..ale used in ttle,,manufacture of concrete? Explain any three
(10 Marks)
admixtures used in concrete manufacture. ',,,,, '''i
ni'";
o=
oO
(10 Marks)
What are the physical requirements of good fine and coarse aggre$ates?
Define "Grading of aggregates", what is the importance of.grading of aggregates in the
(10 Marks)
manufacture of quality concrete.
''.
tt"''
Write notes on
i) Segregation
-
..
"
"t"'
ii) Bleeding.
(10 Marks)
What are the filed tests condtrCted on quality of cement at site of
construction.
(10 Marks)
boe
",,,,
PART
a6
-e)
5-E
s5.
=:!
o''
5 a.
b.
A,i
related with compressive strength of
.,,i ,,
r
(10 Marks)
tr. ttt
Define: . ,',ll'
i)
i)
iD
tr<
z
it
concrete?
Write shoft notes on
=o
EL
o
'''"'
':::::"""
""'
i,.,.*-
6 a., Fxplain the relation between the modulus of elasticity and compressiv
tr>
-61
,,'
Define "Tensile "strength of concrete". How is
Flex$ml'strength
ii) Cofuressive strength
iii) : Sptit tensile strength.
o=
!o
v,
boo
co!
o=
o. ;i
,,'
-B
7a.
b.
8 a.
b.
r1r1'..
,
(10 Marks)
th of concrete.
:
Factors affecting the shrinkage
Factors affecting creep.
What are the factors contributing to cracks in concrete?
Explain the significance of durability of concrete in its
affecting the durability of concrete.
a
i
!l (lo Marks)
the factors
(10 Marks)
Define nominal mix, and its types, explain the importance of design mix in the RCC design
(10 Marks)
of structural members.
Write step by step procedure for I.S method of mix design (preferably flow chart) (10 Marks)

6. l0cv43
USN
Fourth Semester B.E. Degree Examination, Dec.2013 lJan.20l4
Structural Analysr's -
I
Time: 3 hrs.
Max. Marks:100
Note: 7, Answer FIVEfull questions, selecting
ot least TWO questions from each part.
2. Assume any missing data suitably.
o
o
o
L
a
I
PART _ A
b.
between determinate a.rd indeterminate structures with examples. (06 Marks)
Determine the static and kinematic indeterminacy for the structures shown in Fig.Q1(b).
c.
; Fig.Ql(b)
Write strain energy expressions fbr 4xrql, shear bending and twisting.
a.: Distinguish
C)
=
()
3e
bo69
=n
-bo
troo
.= c
I
hoo
yo
ol
-O
o>
o :]
a=
oc)
2 a.
(10 Marks)
(04 Marks)
Determine slope and deflection at the free end for the cantilever beam shown in Fig.Q2(a),
(10 Marks)
using moment area method.
botr
26
6L=
5u
aX
66x$"r*
oi
b.
o=
dtE
@
Fig.Q2(a)
Fig"Q2(b)
,
Deterftine the slopes of support and deflection under the load ror the
,bea*
Fig.Q2(b), using conjugate beam method.
i,?"#Lil
!o
5."
^:
3a.
ia0
.-c
6=
go
=(€
tr>
=o
5L
J<
f, .i
,,,
'o
(06 Marks)
State and prove Maxwell's reciprocal theorem.
point C of the
Using the method of virtual work determine the horizontal displacement of a
(14 Marks)
frame shown in Fig.Q3(b). Take E :2x10s N/mm2 and I :4x106 mma.
I
o
o
'7
(n
o
,kN
Fie.Q3(b)
a*r^
Fig.Q4
-n

7. 10cv43
Determine the vertical and horizontal deflections at point C of the truss as shown in Fig.Q4,
using unit load method. Area of cross section of all the members is 6x10-a m'.
Take E:200 GPa.
(20 Marks)
PART _ B
3a.
A three hinged parabolic arch is loaded as shown in Fig.Q5(a). Determine the B.M- at
loaded points.
lookN
h6"
b.
6a.
b.
(10 Marks)
lSoLrJ
-'l
t+u
-aw
Fie.Q5(at =l
Fie.e6(a)
A flexible suspenSioa cable of weight 0.0075 kN/m hangs between two vertical walls 60 m
apart, the left end being attached to the wall at a point 10 m below the right end.
A concentrated load of I kN is attached to the cable in such a manner that the point of
attachment of the load is 20 mhorizontal from the left and wall and 5 m below the left hand
support. Show that maximum tension occurs at the right hand support and find its value.
A cantilever beam of constant flexural rigidity is propped at its free end to the level of fixed
end. Determine the reaction of the prop when the beam carries udl over the entire span.
Hence draw BMD and SFD. Fig.Q6(a).
(10 Marks)
Determine the fixed end moments or support moments for the beam loaded as shown in
Fie.Q6(b).
,
(to Marks)
Fie.Q6(b)
Fig.e7(b)
a. Derive the generalized Clapeyron's theorem of three moments.
(06 Marks)
,
b. Analyze the continuous beam ABC shown in Fig.Q7(b), using Clapeyron's thoorem of three
rnbments. Hence draw BMD and SFD. Also sketch elastic curve.
(14 Marks)
Find the horizontal thrust for the two hinged parabolic arch as shown in Fig.Q8. The moment of
inertia at any section is I. secO, wheie 0 is the slope at section and I. is M.I. at the crown.
Neglect the effect of rib shortening. Draw BMD.
(20 Marks)
Fig.Q8
*ri<*ri<*
2of?-

8. r0cY44
USN
Fourth Semester B.E. Degree Examination, Dec.2013 /Jan.20l4
Sunreying - ll
Max. Marks:100
Time: 3 hrs.
Note: Answer FIVE
full
questions, selecting
"' l"
at least TWO questions from each part.
.,..""".',
' .'ll"
PART - A
..
I a. List out the miscellaneous operations that can be performed with a transit tlreodolite
::,,,,
::.
6)
o
o
L
a
b.
C)
ts
0)
Eg
Q;-y, N,9
=rn
oJl
2 a.
I
explain the procedure for setting the horizontal angle which is less than the least count of the
(10 Marks)
instrument
Explain the procedures for extending a straight line using a transit'when it is in adjustment
''.
(10 Marks)
and not in adjustment.
What are the fundamental lines of a transit theodolite and state the desired relationships
apart. The readings on the,'st4Jf when held at the stations 'A" and 'B' were 2.250 and2.025
respectively. The instrumeilt,has then moved and set up at 'D' on the line 'BA' produced
which is at a distance of 20 m from'A'. The respective staff readings on'A'and'B'were
1.875 and 1.670. Calculate the coirect staff readings on'A' and'B'to give a horizontal line
of sight and state whether the line oicollimation is inclined upwards or downwards.
i-- 50
gc)
oa
FO
o>
?a
(tr0 Marks)
a=
,:,....,,,,,,
o()
3 a.
b0i
(!(€
-v
d!(!
b.
c.
,(J
5E
^X
oj
6:
3o
qtE
!o
5.!
>, q:
boco0
,,,,,
(J=
go
tr>
4,.,
L,<
z
o
q
6i
An instrument was set up at 'P{ alld the angle.,o"f elevation to a vane 4 m above the foot of
the staff held at 'Q' was 9o30,', The horizontal distance between 'P' and 'Q' was measured to
be 2 km. Determine the RL of the staff station'Q'. given that the back sight reading taken on
a bench mark of RL 50.217 m was 0.880 m. Apply the necessary corrections. (06 Marks)
(02 Marks)
Write a note on total station and mention its advantages. To find the elevatio,ir of the top 'Q' of a hill, a flag staff of 2 m height was erected and
observations were made from two stations 'P' and 'R' 60 rti';-a The horizontal angle
measured at 'R' between the top of the flag staffand 'P' was 68o18'and that measured at 'P'
between'R' and the top of the flag staff was 60o30'. The angle of eleVation to the top of the
flag ;iaff 'Q' was measured to be 10o12' at'P' and that at 'R' was 10o4$r. Staff readings on
the bench mark when the instrument was at P : 1.965 and that when the inStrument was at
R: Z.OSS. Calculate the elevation of the top of the hill if that of bench mark was 250.075 m.
" '1"{12 }Iarks)
'"'l
a.
=o
o-
o
o
and
(10 Marks)
between them. ,,,,,,
b. A dumpy level was set up at 'C' exactly midway between 'A' and 'B' which are 100 m
,: ol
-.,;
.'
;
b.
c.
Write a note on tacheometric surveying. Derive the standard expression for he ho TI
',Fc
distance with usual notations.
,{A Mffir
Briefly explain the stadia method and subtense method of tacheometry.
;.
Ihe following observations were made using a tacheometer fitted with an a rafl# fo"k*q &fh$- 1 (
i{.tl
havins the constant to be 100 and the staff held vertical.
t , lr!
r*.fr $affiY
Instrument Height of Staff
WCB
Vertical
Hair Readings
Station
Instrument
Angle
Station
1 550
A
1.155, r.755,2.355 RL oF0.--s.l
0
30030'
4"30',
B
r.250,2.000,2.750 150.000 m
75030',
10015',
Calculate: (i) The horizontal distance AB (ii) RL of AB (iii) Gradient from A to B
1
r
(08 Marks)

9. t0cY44
PART _ B
5a.
Define degree of a curve. Establish the relationship between degree of curve and its radius.
(04 Marks)
b.
Explain the method of setting out a simple curve by the offsets from chord produced.
(06 Marks)
c.
,,
6a.
b.
7a.
b.
c.
a.
Tabulate the necessary data to set out a right handed simple circular curve in the field having
a radius of 250 m, connecting two straiglrts which intersect at chainage 1250 m at an angle
150'by Rankine's method. Take peg interval of 20 m and least count of the instrument
,"(10 Marks)
as 20"
What do you understand by a reverse curve and mention its significance. Derive the
relationships between various elements of a reverse curve between the parallel straights.
(10 Marks)
Two tangents AB and BC intersect at B. Another line DE intersects AB and BC at D and E
such that Z/ff,E: 150o and IDEC: 140o. The radius of the first eurve is 200m and that of
the second is 3Q0 rn. Calculate all the data necessary for setting out a compound curve if the
Write a note on traniition curve and list out its advantages. What are the pre-requisites for
(08 Marks)
the design of a transition curve?
Calculate the length of the iransition culve, when the rate of radial acceleration is 30 cm/s3,
allowable speed on curve is 60 kmph and radius of the circular curve is 200 m. (04 Marks)
When would you prefer a vertical curve and how are these classified? Explain the role of
(08 Marks)
change of gradient in the design of a vortical curve.
A page of the field book of a cross-staff Survey is given in Fig.Q8(a). Plot the required figure
and compute the area.
(10 Marks)
b
A
F- - *-6D
qo
5s ---E
-
D -z-o
4o
20
A
A
Fig.Q8(a)
An embankment of width 10 m and side slopes l%:1 is required to be made on a ground
which is level in a direction transverse to the center line. The central heights at 40 m
intervals are as follows:
0.90, 1.25, 2.15, 2.50, 1.85, 1.35 and
0.85
Calculate the amount of earthwork according to :
(ii) Prismoidal formula
(i) Trapezoidal formula
*
,i< {< {<
2
of2
,,<
(10 Marks)

10. 10cv4s
USN
Fourth Semester B.E. Degree Examination, Dec.2013 lJan.20l{
Hydraulics & Hydraulic Machines
Max. Marks:100
Time: 3 hrs.
Note: Answer FIVEfull questions, selecting
at lesst TWO questions from each port,
d
o
o
(!
PART _ A
o
E
a.
State the Buckingham theorem and mention the advantages of dimensional uralysisloo
Marks)
0)
Capillary rise h depends on density p, acceleration due to gr,avity g, surface tension o
and radius of the tube r. Show by using the Buckingham n-theorem that
=
a,)
L
ox
1-, '( o)
r =01 --.
Pgr')
-o!l
(08 Marks)
I
d9
I
a6
.= (
c.
i b{,
gc)
scale is
ol:
FO
o>
In the model of a spillway, the discharge and velocity of the flow over the model were
2rilsec and 1.5 m/sec, respictively. Calculate V and Q over the prototype spillway if the
2a.
'
1/36.
(06 Marks)
Derive an expression for the discharge through an open channel using Chezy's formula.
*,a
a=
(06 Marks)
b.
oO
botr
,?(]
6il
c.
3 a.
d_g
o(e
o:
b.
a--
6,i,
A flow of water flows at
150 litres per second in a rectangular channel of width 70 cm and
depth of flow 40 cm. Uniform flow occurs at a certain bed slope with Chezy's C equal to 60.
(06 Marks)
Find the bed slope of the channel.
A canal is to have a trapezoidal section with one side vertical and the other sloping at 45'. It
has to carry 30 m'/sec of water with a mean velocity of 1 m/sec. Compute the dimensions of
(08 Marks)
the section which will require the minimum lining.
What is specific energy curve? Draw specific energy curve and then derive expressions for
(06 Marks)
critical depth and critical velocity.
Show that the relation between alternate depth )1 and yz in a rectangular channel can be
expressed by
,,,
J
> (F
-^o
co0
o=
o. ;j
tr>
o(., <
:o
o
Z
'
_
2yly)
(y,
,
*yr)
(06 Marks)
c.
Explain the term hydraulic jump. Derive an expression for the depth of hydraulic jump in
(08 Nlarks)
terms of the upstream Froude number.
4 a.
Find an expression lor the efficiency of a series of moving curved vanes when a jet of water
strikes the vanes at one of its tips. Prove that maximum efficiency is when u : v and the
(10 Marks)
value of maximum efficiency is 50%,
jet of water coming out of a nozzle of 10 cm diameter with a velocity of 10 m/sec strikes
A
the flat plate. Find out the force exerted on the plate, work done, power developed and
efficiency when (i) plate is stationary (ii) plate is moving with a velocity of 10 m/sec
(10 Marks)
towards the jet (iii) plate is moving with a velocity of 10 misec the jet
b.
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11. 10cv45
PART _ B
5a.
Prove that the work done per second on a series of moving curved radial vane is
pav, [v*,u, * v*, u,
]
(10 Marks)
b.
A jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a
velocity of 20 m/sec. The jet makes an angle of 30' to the direction of motion of vahes when
entering and leaves at an angle of 120o. Draw the triangles of velocities at inlet and outlet
and find:
(i) The angles of vanes tips so that water enters and leaves without shock.
(ii) The work done per unit weight of water entering the vanes.
(10 Marks)
(iii) The efficiency.
a.
Obtain an expr€ssion for the work done per second by water onthe runner of a Pelton wheel.
(10 Marks)
Design a Pelton wheelwith the lollowing data:
b.
Shaft power
Cv:
,
:735.75 kW
:0.45.
;
b.
8a.
b.
:
200 m
;
N.= 800 rym
;
116
:
0.86
,
? =,0,
r'
0.98
$
Determine D, d and number
la.
H
ofjets
(10 Marks)
What are the uses of a draft tube? Describe with neat sketches different types of draft tubes.
,:
(08 Marks)
A Kaplan turbine working under a head of 20. m develops 11772 kW shaft power. The outlet
diameter of the runner is 3.5 m and hub diameter 1.75 m. The guide blade angle at the
extreme edge of the runner is 35o. The hydraulic,and overall efficiencies of the turbines are
88% and 84olo respective$irlf the velocity of whirl is zgro at outlet, determine:
(D Runner vane angles-at inlet and outlet at the extrerhe edge of the runner and
(ii) Speed or,n.,,,,u.O*".
(12 Marks)
Define a centfifugal pump. Explain the working of a singld-sthge centrifugal pump with
(08 Marks)
sketches. :
A centrifual pump delivers water against a net head of 14.5 meties and a design speed of
1000 qpm. The vanes are curved back to an angle of 30o with the periphery. The impeller
diameter is 300 mm and outlet width 50 mm. Determine the discharge of the pump, if
(12 Marks)
manometric efficiency is 95oh.
2
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