1. 10M862
USN
Sixth Semester B.E. Degree Examination, Dec.20L3 lJan.2014
Design of Machine Elements
- ll
Time: 3 hrs.
Max. Marks:100
Note: 7. Answer FIVEfutt
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PART _ A
A'eurved link mechanism made from a round steel bar is shown in Fig.Ql.(a). The material
for1ffi.is plain carbon steel 30C8 with an allowable yield strength of400 MPa. Determine
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(10 Marks)
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A high pressure cylinder consists ofa steel tube with inner and outer diameter of 20 mm and
40 mm respectively. It is jackeled by an outer steel tube with an outer diameter of 60 mm.
The tubes are assembled by shrl[king process in such a way that maximum principal stress
induced in any tube is limited to 100 MPa. Calculate the shrinkage pressure and original
(10 Marks)
dimensions of the tubes, Take the Young's modulus as 207 GPa.
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a note on construciion
of flat and 'V'
belt.
(05 Marks)
'V" belt drive to connect a 7.5 kW, 1440 rlmin induction motor to a
fan. running at approximately 480 r/min lor a service of 24 hr/day. Space is available for a
centre distance of about 1 m. Determine the pitch lengtn or rna,.,U-lt and number of belts
(15 Marks)
required. ,'
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4a.
b.
is required to design a
Enumerate the applications of springs. Also derive an expression for the deflection of a close
(06 Marks)
coiled helical spring.
A Spring is subjected to a load varying from 500 N and 1200 N. It is to be made of oil
tempered cold drawn wire. Design factor based on Wahl's line is 1.25. The spring index is to
be 6. The compression in the spring for the maximum load is 30 mm. Determine the wire
diameter, mean coil diameter and free length of the spring. Take the yield stress in shear as
700 MPa and endurance stress in shear as 350 MPa for the material of the wire. (14 Marks)
(06 Marks)
Write a note on design of gears based on dynamic loading and wear.
teeth spur pinion operating at 1150 rlmin transmits 3 kW to a cast steel
56 teeth spur gear. The gears have the following specifications:
Module : 3 mm
Allowable stress : 100 MPa
Face width : 35 mm
Tooth form : 14%' full depth profile
Factor of dynamic loading, C: 350N/mm Wear load factor, K: 0.28 MPa.
Determine the induced stress in the weaker gear. Also determine the dynamic load and wear
(14 Marks)
load. Comment on the results.
A cast steel24
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2. 10M862
PART _ B
a.
b.
Write a note on formative number of teeth in bevel gear.
(04 Marks)
Hardened steel worm rotates at 1250 r/min and transmits power to a phosphor bronze gear
with a transmission ratio of 15: I . The centre distance is to be 225 mm. Design the gear drive
and give estimated power input ratings from the stand point of strength, endurance and heat
dissipation. The teeth are of l4%' full depth involute.
(16 Marks)
a.
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,
A cone clutch has a semi cone angle of 12.It is to transmit 10 kW power at 750 r/rain,iiilhs
width of the face is one fourth of the mean diameter of fiiction lining. If the normql'intensity
b.
A band,break arrangement is shown in Fig.Q6(b). It is used to generate a maximum braking
torque of 200 N-m. Determine the actuating force 'P' , if the coefficiept''of friction is 0.25.
The angld'of wrap of the band is 270".Determine the maximum,,iritehsity of pressure, if the
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band width is30 mm.
(10 Marks)
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of pressure between contacting surfaces is not to exceed 0.085 N/m# and the psbfficient
friction is 0.2, assuming uniform wear conditions, calculate the dimensions of thb clutch.
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(10 Marks)
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a.
Fie.Q6(b)
Explain the following types of lubrieation:
(i) Hydrodynamic lubrication (ii) Hydrostatic lubrication
(iii) Boundary lubrication
(iv) Elasto hydro dynamic lubrication. (0s Marks)
b. The following data are given for a 360o hydro-dynamig bearing:
Bearing diameter : 50.02 mm
Joumal diameter : 49.93 mm
Bearing length : 50 mm
Journal speed : 1440 rlmin
Radialload-:8 kN
Viscosiiyoi1.utii;ca"t : 12 cp.
The bearing iS,,machined on a lathe from bronze casting, while'tlie steel journal is hardened
and ground; The surface roughness values for turning and grinding are 0.8 and 0.4 microns
respectiifely. For thick film lubrication the minimum film thickness stiould be five times the
sum.of silrface roughness values for the journal and the bearing. Calculate:
(i),,' fhe permissible minimum film thickness
(ii) The actual film thickness under the operating conditions
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, (iii) Power loss in friction.
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(iv) Flow requirement.
{"I2 Marks)
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8a.
b.
lri'
Explain the considerations given in the design of pistons for IC engines.
(05 Marks):
Design a trunk piston for an IC engine. The piston is made of cast iron with an allowable
stress of 38.5 MPa. The bore of the cylinder is 200 mm and the maximum explosion
pressure is 0.4 MPa. The permissible bending stress of the material of the gudgeon pin is
100 MPa. The bearing pressure in the gudgeon pin bearing of the connecting rod is to be
taken as 200 MPa.
(15 Marks)
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2 of2

3. 10ME63
USN
Sixth Semester B.E. Degree Examination, Dec.2013 lJan.201^4
Heat and Mass Transfer
Time: 3 hrs.
Max. Marks:100
'
Note: 1. Answer FIVEfull questions, selecting
at lesst TWO questions from each part.
(Jse of heat transfer data book is permitted.
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(08 Marks)
A plate of thickness 'L' whose one side is insulated and the other side is maintained at a
An electric cable of l0mm diameter is to be laid in atmosphere at 20'C. The estimated
surface temperature of the cable due to heat generation is 65"C. Find the maximum
percentage increase in heat dissipation,,,*hen the wire is insulated with rubber having
K: 0.155 WmK. Take h: 8.5 WrnlK,,. ,
(06 Marks)
Diflerentiate between the effectivenoss;,and efficiency of fins.
(04 Marks)
In order to reduce the thermal qesistance at the surface of a veftical plane wall (50 x 50cm),
100 pin fins (1 cm diameter, 10sm long) are attached. If the pin fins are made of copper
having a thermal conductivity of 300 WmK and the value of the surface heat transfer
coefficient is 15 Wm2K,;,Calculate the decreur. in the thermal resistance. Also calculate the
consequent increase in heat transfer rate from the wall if it is ma@@ined.qt a temperature of
200"c and the surroundings are ar 30oc.
(r0 Marks)
.Zr(j-{)}
givenov"ffi=+=*r[#) W-*%7i
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cooling is
(06Marks)
pCV
ThesGel ball bearings
50 WmK, o 1.3 x 10-5 m2lsec),_ _--::::::/,,
er are heated
to'atemperature of 650"C. It is then quenched in a oil bath at 50oC, where the heat transfer
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coordinates.
Show that fhel.'temperature distribution in a body during ]1id
(.) j
9E
to
4 tr=
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'-' (06 Marks)
representation of three commonly used
temperature Tr i5 dtphanging heat by convection to the surrounding area at a temperature T2,
with atmospheric air being the outside medium. Write mathemitical formulation for one
dimensional, steady Stste heat transfer, without heat generation.
(06 Marks)
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iiketches, write down the mathematical
different types of boundary conditions for one dimensional heat. e(uation in rectangular
0)
bo-
:
Explain briefly the mechanism of conduction, convection and radiation heat transfu:;.
b. Witli
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coefficient is estimated to be 300 Wm2K. Calculate:
The time required for bearings to reach 200"C.
The total amount of heat removed from a bearing during this time and
The instantaneous heat transfer rate from the bearings, when they are flrst immersed in
oil bath and when thev reach 200'C.
(14 Marks)
' i)
ii)
iii)
4 a.
b.
::
With reference to fluid flow over a flat plate, discuss the concept of velocity boundary and
thermal boundary layer, with necessary sketches.
(05 Marks)
The exact expression for local Nusselt number for the laminar flow along a surface is given
,xz
bv Nu' = hx - 0.332 nll' pJ". Show that the average heat transfer coefficient from
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r
x
k
0 to x : L over the length
transfer coefficient at x: L.
x
:
'L'
of the surface is given by 2hr where hl is the local heat
(05 Marks)
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4. 10ME63
A vertical plate
15cm high and 10cm wide is maintained at 140"C. Calculate the maximum
heat dissipation rate from both the sides of the plates to air at 20oC. The radiation
heat
transfercoefficient is 9.0 wm2K. Forairat 80.c, take r:2L09 x 10-6 ni/sec,pr:0.692,
kr: o.o3 wmK.
(lo Marks)
5a.
b.
c.
PART - B
Explain the physical signiflcance of i) Nusselt number; ii) Groshoffnumber. (04 Marks)
Air at 2 atm and 200oC is heated as it flows at a velocity of 12 m/sec through a tube with a
diameter of 3cm. A constant heat flux condition is maintained at the wJl and the wall
t-emperature is 20oC above the air temperature all along the length of the tube. Calculate:
.,
i) The heat transfer per unit length of tube.
,
ii) , The increase in bulk temperature of air over a 4m length of the tube., ' .
Tale,ths following properties for air pr : 0.6g1, trt:2.57 x 10-5 kg/mi; K : 0.03g6 wmK
and Co = 1.025 kJ/kg K.
(ro Marks)
Obtain a ielationship between drag coefficient, c. and heat transf,er'coefficient, hn,,
for the
llow over a flat plate.
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(06 Marks)
a'
Derive an expression for LMTD of a counter flow heat exchanger. State the assumptions
b.
c'
What is meant by the term fouling factor? How do you determine it?
(04 Marks)
Engine oil is to be coded from 80'C to 50'C by using a single pass counter
flow, concentric
tube heat exchanger with cooling water available ul20"C. Water flows inside
a tube with
inner diameter of 2.5cm and at a rate of 0.08 kg/sec and oil flows through the
annulus at the
rate of 0.16 kg/sec. The heat transfer coeficient for the water side and oil
side are
F,:
the tube length
7a.
b.
c.
:
1000 Wm2oC and h.l : 80 Wm2oC. The fouling factors is
0.00018m2oC/W on both the sides ard the tube wall resistance is negligible.
Calculate
respectively h,"
required.
(08 Marks)
Sketch a pool boiling curvq for water and explain'briefly the various regimes
in boiling heat
transfer.
,,,
,-'''.
'
coerficient.
transfer
?..1".
A l2cm outside diameter and 2m long tube is used in a big condenser to condense [8iXff[]
the steam
n 0.1 bar,-Estr3{e the unit surface conductance i) in iertical position; iil i, horizontal
mass
position. Also find the amount of condensate formed per hour
The satutation temperature of the steam :74.5"C.
Aver,age wall temperature : 50.C.
infin
the cases.
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75'4j50
=62.7oC are given below
lp:982.2kglm3, hr_ =2480kJ/kg,K:0.65WmK, p:0.47 x 10-3kg/ms. ''
liolvrarks)
The'properties of water film at average temperature
8a.
b.
c.
of
State and prove Wiens displacement law of radiation.
The temperature of a black surface 0.2rfi in area is 540.c. calculate:
The total rate of energy emission.
i)
ii) The intensity of normal radiation.
Iti) The wavelength of maximum monochromatic
Derive an
only.
(06 Marks)
emissive power.
(06 Marks)
expression for a radiation shape factor and show that it is a function of geometry
(08 Marks)
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2
of2

5. 10ME64
USN
Sixth Semester B.E. Degree Examination, Dec.2013 /Jan.20l4
Finite Element Methods
Time: 3 hrs.
Max. Marks:100
Note: Answer FIVEfull questions, selecting
ut least TWO questions from each part.
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1
PART _ A
a,, r Differentiate between plane stress and plain strain problems with examples. Write the stressstrain relations for both.
(08 Marks)
b. Explain the node numbering scheme and its effect on the half band-width. (06 Marks)
c. List down the basic steps involved in FEM for stress analysis of elastic solid bodies.
(06 Marks)
2 a.
State the piineiple of minimum potential energy. Determine tl.le displacements at nodes for
the spring system qhown in the Fig.a.,2J3).
(08 Marks)
lsoN/nn
a
Jh
-.^t
Fig.Q.2(a)
Eoo
ts.)
oEl
-o
b.
Determine the deflection
of a cantilevel beam of length 'L'
-!
distributed load (UDL) of Po/unit iength, using the trail function y
o2
subjected
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a sin [
the results with analyical solution and comment on accuracy.
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. Comnare
(12 Marks)
Derive an expression for Jacobian matrix for a four-noded quadrilateral element. (10 Marks)
For the triangular element shown in the Fig.Q.3(b). Obtain the strain-displacement matrix
'B' and determine the strains €r. €y and y*y.
Nodal displacements {q} : {2 | 1 -4 -3 7} x 10-2mm.
(10 Marks)
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Note; All dimensions in mm.
4 a.
an' axial load P : 300 x
103
,, , temperature is then raised to
D
ii)
Fig.Q.3(b)
N is applied at 20'C to the rod
as shown in the Fig.Q.41a.y. The
60oC.
Assemble the global stiffness matrix (K) and global load vector (F).
Determine the nodal displacenrents and element stresses.
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Fig.Q.a(a)
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r:70 x 10e N/m2,82:
200
Ar :900mm2, Az: l200mm2
a1
:23 x 10-6/oC, az:
71.7
x
x
10eN/m2
(12 Marks)
10'61'C.
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6. b.
10M864
Solve the following system of equations by Gaussian-Elimination method:
xr -2xz * 6x: : 0
2x1-t 2x2 + 3x3 : 3
-xy
5a.
* 3x2:2.
PART _ B
Using Lagrangian method, derive the shape function of a three-noded one-dimension (1D)
element [quadratic
-ll
b
c.
6a.
(08 Marks)
element].
(06 Marks)
rl
Lvuruulv '--lL"
Evaluate I: ll 3e^+xt+
rA *G*2)-l''"
l.d*
using one-point and two-point Gauss quadrature.
Wtite short notes on higher order elements used in FEM.
(06 Marks)
(08 Marks)
For the two-bar truss shown in the Fig.Q.6(a). Determine the nodal displacements and
element stross.es- A force of P: 1000 kN is applied at node 1, Take p,: ZtO GPa and
A
:
600mm2'for each element.
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t ''
,
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(12 Marks)
Fie.Q.6(a)
b.
Derive an expression for stiffness matrix for a2-D truss element.
a.
Derive the Hermite shape functions of a beam eleiirent.
(08 Marks)
A simply supported beam'of span 6m and uniform flekural rigidity EI : 40000 kN-m2 is
subjected to clockwise couple of 300 kN-m at a distanCe of 4m from the left end as shown in
the Fig.Q.7(b). Find the deflection at the point of application of the couple and internal
loads.
,
,,"
(08 Marks)
(12 Marks)
?wW'n't
Fig.Q.7(b)
F
8 a.
Find the temperature distribution and heat transfer through an iron fin of thickness 5mm'-rr.j---- :-;nrn and uidth 1000mm. The heat transfer coefficient around
the fin is 10 Wim2.
K and ambient temperature is 28oC. The base of fin is at 108'C. Take K : 50 Wm.K. Use
two elements.
(10 Marks)
I
Fig.Q.8(a)
b.
t,
I flil
{r^rn
jr,.n
* rEry
Derive element matrices for heat conduction in one-dimensional element using Galerkin's
approach.
(10 Marks)
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