Upload
others
View
5
Download
0
Embed Size (px)
Citation preview
Enroll. No. _____________
SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY
ADITYA SILVER OAK INSTITUTE OF TECHNOLOGY
BE - SEMESTER–III • MID SEMESTER-I EXAMINATION – WINTER 2018
SUBJECT: ADVANCED ENGINEERING MATHEMATICS (2130002) (ALL BRANCHES)
DATE: 09-08-2018 TIME: 10:00 am to 11:45 am TOTAL MARKS: 40
Instructions: 1. All the questions are compulsory. 2. Figures to the right indicate full marks. 3. Assume suitable data if required.
Q.1*
(a) Find the Laplace Transform of the function 𝑓(𝑡) = {0, 0 < 𝑡 < 𝜋𝑠𝑖𝑛𝑡, 𝑡 > 𝜋
. [03]
(b) Find 𝐿−1(𝑡𝑎𝑛−1 2𝑠⁄ ). [03]
(c) Find a Fourier Series for 𝑓(𝑥) = 𝑥2, where −𝜋 ≤ 𝑥 ≤ 𝜋. [04]
Q.2
(a) Find 𝐿−1 [1
(𝑠2+4)2] using Convolution theorem. [06]
(b) State the convolution theorem and verified it for 𝑓(𝑡) = 𝑡 and 𝑔(𝑡) = 𝑒2𝑡. [05]
(c) Find the Fourier integral representation of the function 𝑓(𝑥) = {2 , |𝑥| < 20 , |𝑥| > 2
. [04]
OR
Q.2 (a) Solve using Laplace transform: 𝑦" − 3𝑦′ + 2𝑦 = 4𝑡 + 𝑒3𝑡, 𝑦(0) = 1, 𝑦′(0) = −1. [06]
(b) Find (i) 𝐿−1 {1
(𝑠2+4)(𝑠2+9)} (ii) 𝐿−1 {
1
𝑠 (𝑠2+4)}. [05]
(c) Find the Fourier cosine series of 𝑓(𝑥) = 𝑒−𝑥, where 0 ≤ 𝑥 ≤ 𝜋 . [04]
Q.3
(a) Expand 𝑓(𝑥) in Fourier series in the interval (0,2𝜋) if (𝑥) = {−𝜋 ; 0 < 𝑥 < 𝜋
𝑥 − 𝜋 ; 𝜋 < 𝑥 < 2𝜋 .
Hence show that ∑1
(2𝑟+1)2 =𝜋2
8∞𝑟=0 .
[06]
(b) Find the Fourier Series for 𝑓(𝑥) = 𝑒𝑎𝑥 in (0,2π); a>0. [05]
(c) Find the Laplace Transform of (𝑖) 𝑓(𝑡) = tt 3sin 2
(𝑖𝑖) 𝑓(𝑡) =𝑠𝑖𝑛𝑤𝑡
𝑡. [04]
OR
Q.3
(a) Express the function 𝑓(𝑥) = {1 𝑓𝑜𝑟 |𝑥| ≤ 1
0 𝑓𝑜𝑟 |𝑥| ≥ 1 as a Fourier integral.
Hence, evaluate (a) ∫sin 𝜔 cos(𝜔𝑥)
𝜔𝑑𝜔
∞
0 (b) ∫
sin 𝜔
𝜔
∞
0𝑑𝜔
[06]
(b) Find Fourier series of 𝑓(𝑥) = 𝑥 + 𝑥2, − 𝜋 < 𝑥 < 𝜋. Hence deduce that 𝜋2
6=
1
12+
1
22+
1
32+ ⋯ .
[05]
(c) Find (𝑖)𝐿(𝑡3 + 𝑒−3𝑡 + 𝑡3/2) (𝑖𝑖)
t t
dtt
teL
0
sin
[04]
Enroll. No. _____________
SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY
BE - SEMESTER–III • MID SEMESTER-I EXAMINATION– WINTER 2018
SUBJECT: MECHANICS OF SOLIDS (2130003) (CL/ME/AERO)
DATE: 10-08-2018 TIME: 10:00 am to 11:30 am TOTAL MARKS: 40
Instructions: 1. All the questions are compulsory. 2. Figures to the right indicate full marks. 3. Assume suitable data if required.
Q.1 (a) State the fundamental principles of mechanics and explain any one. [03]
(b) Explain parallelogram law of forces in brief with a neat figure. [03]
(c) What does notations E, G, K & μ mean? Explain the significance with
relationship between any three.
[04]
Q.2 (a) An electric lamp in street as shown in Fig 1 is having 50 N weight suspended by
two wires of 4 m and 3 m length. The horizontal distance between two fixed
points is 5 m from which two wires were suspended. Find out tension in both
wires.
[06]
(b) Determine the support reactions at A & B for the beam loaded as shown in Fig 2 [05]
(c) State ‘Hooks Law’. Derive formula to determine change in length (δL) for the
uniform, homogeneous axially loaded member of length (L), c/s area (A) and
modulus of elasticity (E), subjected to axial tensile force (P).
[04]
OR
Q.2 (a) A system of four forces shown in Fig 3 has resultant 50 kN along + X - axis.
Determine magnitude and inclination of unknown force P.
[06]
(b) Discuss types of loads & supports based on the reactions that occur in beams
with neat sketch for each.
[05]
(c) A stepped circular bar ABC is axially loaded as shown in Fig 4 is in equilibrium.
The diameter of part AB is 50 mm throughout its length, whereas diameter part
BC is uniform decreasing from 40 mm at B to 30 mm at C. Determine (i)
magnitude of unknown force ‘P’ (ii) stress in part AB and (iii) change in length
of part BC. Take modulus of elasticity = 2 x 105 N/mm2.
[04]
Q.3 (a) Determine deformation in each part of the bar ABCD shown in Fig 5
Take E = 2 x 105 N/mm2.
[06]
(b) State Lami’s theorem and derive the equation with neat diagram. [05]
(c) A cylindrical roller weighing 1000 N is resting between two smooth surfaces
inclined at 60º and 30º with horizontal as shown in Fig 6. Draw free body diagram
and determine reactions at contact points A and B.
[04]
OR
Page 1 of 2
Q.3 (a) Derive formula for the elongation (δL) of a uniformly tapering circular bar of
length (L) subjected to axial tensile force (P), c/s area (A) and modulus of
elasticity (E).
[06]
(b) State and prove Varignon’s theorem with a neat diagram. [05]
(c) Explain drawing a neat graph the salient features of a stress-strain curve for mild
steel in tension test.
[04]
Page 2 of 2
Figure 1 Figure 2
Figure 3 Figure 4
Figure 5 Figure 6
Enroll. No. _____________SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY
ADITYA SILVER OAK INSTITUTE OF TECHNOLOGY
BE - SEMESTER–III • MID SEMESTER-I EXAMINATION – WINTER 2018
SUBJECT: Manufacturing Process-I (2131903) (ME)
DATE: 08-08-2018 TIME: 10:00 am to 11:30 am TOTAL MARKS: 40Instructions: 1. All the questions are compulsory.
2. Figures to the right indicate full marks.3. Assume suitable data if required.
Q.1 (a) Define machining process. Give detail classification of machiningprocess.
[03]
(b) Explain with neat sketch different types of chips.[Any three] [03](c) Draw a front view, top view and side view of single point cutting
tool with labeling. [04]
Q.2 (a) Draw a neat sketch of lathe machine. Explain a working of variouslathe machine parts.
[06]
(b) Different between capstan and turret lathe machine. [05](c) Enlist various accessories of lathe machine. Explain any one with
neat sketch.[04]
ORQ.2 (a) Enlist a different method of taper turning. Explain taper turning
method by the using of taper attachment with neat sketch. [06]
(b) Classify a various operations of lathe machine. Explain any fouroperations with neat sketch.
[05]
(c) What is mandrel? Classify different types of mandrel. [04]
Q.3 (a) Explain with neat sketch of Jig boring machine. Write anadvantage, disadvantage and application of Jig boring machine.
[06]
(b) Draw and explain working of horizontal boring machine. [05](c) Figure out a various operation i) Reaming ii) Boring iii) Counter
boring iv) Counter sinking. [04]
ORQ.3 (a) Classify a various sawing machine. Explain with neat sketch of
vertical band saw machine.[06]
(b) Explain geometry of broaching tool. [05](c) Define the term “broaching”. Write an advantage, disadvantage
and application of broaching. [04]
Enroll. No. _____________
SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY
ADITYA SILVER OAK INSTITUTE OF TECHNOLOGY
BE - SEMESTER–III • MID SEMESTER-I EXAMINATION – WINTER 2018
SUBJECT: MATERIAL SCIENCE & METALLURGY (2131904) (ME)
DATE: 07-08-2018 TIME:10:00 am to 11:30 am TOTAL MARKS:40
Instructions: 1. All the questions are compulsory. 2. Figures to the right indicate full marks. 3. Assume suitable data if required.
Q.1 (a) Explain the requirement of engineering materials. [03]
(b) What is Powder Metallurgy? Explain the process of Powder Metallurgy. [03]
(c) Explain Criteria for Selection of Engineering Material. [04]
Q.2 (a) Explain with neat sketches the arrangement of atoms, in S.C, B.C.C, F.C.C. and
H.C.P. lattice. And Also write Effective Number of atom, Atomic Packing Factor,
Co-ordination Number for all Lattices. Define unit cell.
[06]
(b) Explain edge dislocation and screw dislocation. [05]
(c) Draw a unit cell and show the following planes (a) (113) (b) (102) (c) (111) and (d)
(001).
[04]
OR
Q.2 (a) Explain the strain hardening process. Also mention the effect of strain hardening
on properties of metals.
[06]
(b) Draw sketch of Recovery, Recrystallization and Grain growth graph. [05]
(c) Explain the difference between slip and twinning mechanisms [04]
Q.3 (a) Differentiate between Homogeneous and Heterogeneous nucleation processes. Also
discuss the conditions under which growth may be of planar and dendritic type.
[06]
(b) Define Powder Metallurgy. State advantages, limitations and applications of
Powder Metallurgy.
[05]
(c) With neat sketches, explain Solidification of Metal. [04]
OR
Q.3 (a) Explain the “Hune-Rothery Rules” for solid solution, with suitable case study. [06]
(b) What is phase diagram? Explain Lever rule. [05]
(c) What is Gibb’s phase rule? Calculate the degree of freedom, for eutectic
composition in binary phase diagram.
[04]
Enroll. No. _____________
SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY
BE - SEMESTER–III • MID SEMESTER-I EXAMINATION – WINTER 2018
SUBJECT: ENGINEERING THERMODYNAMICS (2131905) (ME)
DATE: 11-08-2018TIME: 10:00 am to 11:30 am TOTAL MARKS: 40
Instructions: 1. All the questions are compulsory. 2. Figures to the right indicate full marks. 3. Assume suitable data if required.
Q.1 (a) Derive steady flow energy equation for a given control volume. Apply SFEE to following
engineering applications: a) Nozzle b) Boiler [05]
(b) Explain the effect of regeneration on Brayton cycle. [05]
Q.2 (a) Gases produced during the combustion of a fuel-air mixture, enter a nozzle at 300 kPa,
1500C and 20 m/s and leave the nozzle at 100 kPa and 1000C. The exit area of the nozzle
is 0.03 m2. Assume that these gases behave like an ideal gas with Cp = 1.15 kJ/kg-K and
γ = 1.3, and that the flow of gases through the nozzle is steady and adiabatic. Determine
(i) the exit velocity and (ii) the mass flow rate of the gases.
[06]
(b) Derive the air standard efficiency of constant volume cycle. [05]
(c) Define a thermodynamic system. Differentiate between open system, closed system and
an isolated system. [04]
OR
Q.2 (a) The air compressor takes in air steadily at the rate of 0.6 kg/sec from the surroundings
with pressure of 100.0kPa and density of 1.05 kg/m3. The air entry velocity is 7 m/sec.
The pressure ratio of air compressor is 7. The leaving air has density of 5.26 kg/m3 and
leaves with velocity of 5.0 m/sec. The internal energy of the leaving air is 100kJ/kg more
than that at entering. Cooling water in the compressor jackets absorbs heat from air at the
rate of 65 KW.
i) Compute the rate of shaft work to air ii) Find the ratio of inlet pipe diameter to outlet pipe diameter.
[06]
(b) Explain Joule Experiment in details. [05]
(c) Justify that heat & work transfer is a path function and not a point function. [04]
Q.3 (a) A closed cycle ideal gas turbine plant operates between temperature limits of 800°C and
30°C and produces a power of 100 kW. The plant is designed such that there is no need
for a regenerator. A fuel of calorific 45000kJ/kg is used. Calculate the mass flow rate of
air through the plant and rate of fuel consumption.
Assume Cp = 1 kJ/kg-K and γ = 1.4.
[06]
(b) Compare Otto, Diesel and Dual cycle for
i) Same compression ratio and heat supplied
ii) Same Max. Pressure and temperature
[05]
(c) Prove that “Energy is a property of a system”. [04]
OR
Q.3 (a) In an air standard Diesel cycle the compression ratio is 14 and the beginning of Isentropic
compression is at 110kPa and 30˚C. If the fuel cut off takes place at 5% of stroke, find the
air standard efficiency and mean effective pressure.
[06]
(b) Draw schematic and T-S diagram of intercooling and reheating on Brayton cycle. [05]
(c) Differentiate between microscopic and macroscopic point of view. [04]
Enroll. No. _____________
SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY
ADITYA SILVER OAK INSTITUTE OF TECHNOLOGY
BE - SEMESTER–III • MID SEMESTER-I EXAMINATION – WINTER 2018
SUBJECT: KINEMATICS OF MACHINES (2131906) (ME)
DATE: 06-08-2018 TIME: 10:00 am to 11:30 am TOTAL MARKS:40
Instructions: 1. All the questions are compulsory. 2. Figures to the right indicate full marks. 3. Assume suitable data if required.
Q.1 (a) Explain the terms in relation to gears:
(1) Module
(2) Circular Pitch
(3) Pressure Angle
[03]
(b) What is inversion of mechanism? Explain all inversion of four bar chain
mechanism.
[03]
(c) Explain degree of freedom with neat sketch. Also explain Grubler’s criterion and
State Grashof’s law.
[04]
Q.2 (a) PQRS is a four bar chain with link PS fixed. The lengths of the links are
PQ= 62.5 mm; QR = 175 mm; RS = 112.5 mm; and PS = 200 mm.
The crank PQ rotates at 10 rad/s clockwise.
Draw the velocity diagram when angle QPS = 60° and Q and R lie on the same side
of PS. Find the angular velocity of links QR and RS.
[06]
(b) Explain whitworth quick return motion mechanism with neat sketch. [05]
(c) Classify and explain different types of kinematic pair. [04]
OR
Q.2 (a) The crank of a slider crank mechanism rotates clockwise at a constant speed of
300 r.p.m. The crank is 150 mm and crank angle of 45° from inner dead centre
position. The length of connecting rod is 600 mm long.
Determine :
1. linear velocity of the midpoint of the connecting rod, and
2. Angular velocity of the connecting rod,
[06]
(b) Sketch and explain any two inversions of a double slider crank chain. [05]
(c) Explain different types of constrained motions with neat sketch. [04]
Q.3 (a) 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 10 mm addendum. Find the
length of path of contact, arc of contact and the contact ratio.
[06]
(b) State and prove the law of gearing. [05]
(c) What do you understand by the term ‘interference’ as applied to gears? What are the
various ways to avoid interference? [04]
OR
Q.3 (a) Two 20° involute spur gears have a module of 15mm. The addendum is one module.
The larger gear has 50 teeth and the pinion has 13 teeth will be interference occur? If
it occurs,
(i.) To what value the pressure angle be changed to eliminate interference.
(ii.) If the pressure angle is to be kept 20° only, by what value the addendum of
gear tooth be decreased to avoid interference.
(iii.) Calculate the length of path of contact and contact ratio for the case (i) above.
[06]
(b) Derive an expression for the length of the path of contact in a pair of meshed spur
gears.
[05]
(c) Derive an expression for the minimum number of teeth required on the pinion in
order to avoid interference in involute gear teeth when it meshes with wheel.
[04]