4th Semester Mechanincal Engineering (2012-June) Question Papers

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Fourth Semester B.E. Degree Examination, June 2O12

Engineering Mathematics - IV

Time: 3 hrs.

carry out two modiiications at each step.

comector formula twice.

2 a. Employing the Picard's method, obtain the second order approximatefollowing problem at x = 0.2.

dv O1=, *r*: v(0)= l. z(ot=-1.-=x+yz: a*

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Max. Marks:100

(07 Marks)

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PART - A1 a. Using the Taylor's method, find the third order approximate solution at x = 0.4 of the

/twproblem * = *'y + I , with y(0) = 0. Consider terms upto fourth degree. (06 Marks)

ox

b. Solve the differential equation 9 = -ry' under the initial condition y(O) = 2,by using the'dxmodified Euler's method, at the points x = 0.1 and x = 0.2. Take the step size h = 0.1 and

c. Given9=rr+y';y(0)=1,y(0.1)=1.1169,y(0.2)= 1.2'773,y(0.3)=l.5049,findy(0.4)dx

corlect to three decimal places, using the Milne's predictor-corrector method. Apply the

. at x = 0. I under the

Take step length h = 0.1 .

Using the Milne's method, obtain an approximatelt i

problem l{ rf *9I-Oy =0. y(0) = l. y'(0)ox oxY(0. l) = 1.0399s,

y'(0. 1) = 0.69ss, y(0.2) = 1.138036, y'(0.2) = 1.2s8, y(0.3) = 1.29865, y'(0.3) = 1.373.(07 Marks)

Derive Cauchy-Riemann equations in polar form. (06 Marks)3a.

b.

c.

Iff(z) isaregularfunctionofz.prove,n^,({-!]ptrll' =+lflfal'. (07Marks)\dx' cy' )

If w = 0 + iy represents the complex potential for an electric field and y = x2 -y2 + ,i-x'+y'determine the function Q. Also find the complex potential as a function of z. (07 Marks)

4a.b.

C.

Discuss the transfbrmation of w =z+{.Z

Find the bilinear transformation that transforms the

points wy = l, wz = 0, w3 = co respectively.

Evaluate ['T -,,1.t*11' dz where c is the circle lzl = 3, using Cauchy's integral fbrmula.! tz-ll'tz-2t

(07 Marks)

PART _ BObtain the solution of x2y'+ xy'+ (x2 - n')y = 0 in terms of Jn(x)andJ,(x).Express f(x) = xa + 3x3 - x2 + 5x - 2 in terms of Legendre polynomials.

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(06 Marks)

points z1 = i, zz = l, zz - -l on to the(07 Marks)

(06 Marks)

(07 Marks)

(07 Marks)

5a.b.

c,

6a.

b.

From five positive and seven negative numbers, five numbers are chosen at random andmultiplied. What is the probability that the product is a (i) negative number and (ii) positivenumber?' (06 Marks)

If A and B are two events with P(A) = +, P(B) =+, P(A n B) =f , ma P(A/B), P(B/A),

P(A / B) , P(B / A) and P(A / B) . (07 Marks)

q. In a certain college, 4a/o of boy students and l9o of gilil students are taller than 1.8 m.Furthermore, 60"/o of the students are girls. If a student is selected at random and is foundtaller than L8 m, what is the probability that the student is a girl? (07 Marks)

a. A random variable x has rhe density function p(^l ={K*'' 0(x<3. Evaluate K, and

[ 0. e]sewhere

find: i) P(x< l), (iDP(l <x<2), (iii)P(x<2), iv)P(x> l), (v) P(x > 2). (06 Marks)b. Obtain the mean and standard deviation of binomial distribution. (07 Marks)c. In an examination 77o of students score less than 35o/o marks and 897o of students score less

that 60Vo marks. Find the mean and standard deviation if the marks are normally distributed.It is given that P(0 < z< 1.2263) =0.39 andP(0<z<1.4757)=0.43. (07 Marks)

8 a. A random sample of400 items chosen from an infinite population is found to have a meanof 82 and a standard deviation of 18. Find the 95o/o confidence limits for the mean of thepopulation from which the sample is drawn. (06 Marks)

b. In the past, a machine has produced washers having a thickness of 0.50 mm. To determinewhether the machine is in proper working order, a sample of l0 washers is chosen for whichthe mean thickness is found as 0.53 mm with standard deviation 0.03 mm. Test thehypothesis that the machine is in proper working order, using a level of significance of(i) 0.05 and (ii) 0.01. (07 Marks)

c. Genetic theory states that children having one parent ofblood type M and the other ofbloodtype N will always be one of the three tlpes M, MN, N and that the proportions of thesetypes will on an average be I : 2 : I . A report states that out of 300 children having one Mparent and one N parent, 307o were found to be of type M, 457o of type MN and the

remainder of type N. Test the theory by 1' lChi square) test.

2. of 7.

(07 Marks)

Impotu Noc : l. On coDpleting you answeu. compubonly draw diaeoml *ms lines on the tmaidn8 blant Pages.2. Any Everling ofidenlificntion, appeal to evrlumr and /orequations {t'inen e9,12+8 = 50, uillbe treaed !s mllPnc ce.

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Max. Marks: 100

Fourth Semester B.E. Degree Examination, Jlu:ne 2012

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Applied Thermodynamics

Time: 3 hrs.Notez Answer FIVE full questions, selecting

at least TWO questions from each part.

PART - AI a. Explain the following with reference to a combustion process:

i) Percent excess air ii) Enthalpy of formationiii) Adiabatic flame temperature iv) Enthalpy of combustion. (08 Marks)

b. The products of combustion of an unknown hydrocarbon C* H, have the followingcomposition as measured by an Orsat apparatus:CO2 = 9.67o, gg =0.9Va,Oz= 8.87o, N2 = 82.3%. Determine:i) The composition of the fuelii) The air-fuel ratioiii) The fercent excess air used andiv) Dew point temperature of the product if the total pressure of the product is I .01325 bar.

(12 Marks)

2 a. Derive an expression for efficiency of diesel cycle in terms of compression ratio, cut-offratio and specific heats ratio. (08 Marks)

b. An air-standard limited pressure cycle has a compression ratio of l5 and compression beginsat 0.1 MPa,40 'C. The maximum pressure is limited to 6 MPa and the heat added is 1675kJ/kg. Compute:i) The heat supplied at constant volume per kg airii) The heat supplied at constant pressureiii) The cycle efficiencyiv) The cut-off ratio andv) m.e.p of the cycle.

3 a. Explain the 'William's line method for calculating the

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b. A test on a two-stroke engine gave the following results at full load:Speed = 350 rpm, Net brake load = 65 kgl, m.e.p = 3 bar, Fuel consumption = 4 kg/h,Jacket cooling water flow rate = 500 kg./h, Jacket cooling water temperaturc rise = 20 "C,

Air used per kg offuel = 32 kg, Cylinder diameter = 22 cm, Stroke = 28 cm,Effective brake drum diameter = I m, CV of fuel = 43 MJ/kC, Cp* = I kJ/kg,Exhaustgas temp = 400 'C, Room temperature = 20 C.

Find the mechanical efficiency and also draw a heat balance sheet on minute andpercentage basis. (10 Marks)

6. A 4-cylinder petrol engine has a rated output of52 kW at 2000 rym. A Morse test is camiedout and the brake torque readings are 177,l7O, 168 and 174 N-m respectively. For normalrunning at this speed, the BSFC is 0.25 kg/kW-h and C.V of fuel used is 42500 kJ/kg.Calculate the mechanical and brake thermal efficiency. (06 Marks)

4 a. Draw a schematic diagram and show the actual regenerative vapour power cycle. Alsoderive an expression for its efficiency. (08 Marks)

I of 2

lOME/AU43

b. An ideal Rankine cycle with reheat is designed to operate according to the followingspecification:Pressure at the inlet of HP turbine = 20 MPa.

Temperature of steam at the inlet of t{P turbine = 550 "C.

Temperature of steam at the end of reheat = 550 "C.

Pressure of steam at the turbine exit = l5 kPa

Quality of steam at the turbine exit = 90Ea. Determine:i) Reheat pressure ii) Temperature in the condenseriii) Ratio of pump work to turbine and iv) Cycle themal efficiency.

PART - BWhat are the advantages of multi-stage compression?

(12 Marks)

(04 Marks)5 a.

b.

c.

Derive an expression for volumetric efficiency of a single stage reciprocating air compressorin terms ofclearance factor (K), pressure ratio ("/r,) *O index ofcompression (n). (04 Marks)

A single acting, two-stage air-compressor delivers air at 17 bar when the pressure and

temperature of air at the end of suction are I bar and 303 k. The interstage pressure is 4 barand there is perfect intercooling. If LP cylinder diameter is 23 cm and common stroke is

l-5 cm and speed of the compressor is 350 rpm. Detemine:i) Volumetric efficiency of LP stage compressor.ii) Heat transfer in the inert cooler in kJ/min and

iii) Capacity of the motor required to drive the compressor if the mechanical efficiency is85Vo.

Assume the clearance volume of LP compressor = 5Vo of stroke volume. The compressionand expansion in both cylinders follow the law PVl 25

= constant. (12 Marks)

a. What are the advantages of closed cycle gas turbine over the open cycle gas turbine plant?(04 Marks.)

b. Write a short note on jet-propulsion. (04 Marks.l

c. In an open cycle gas turbine plant, air enters the compressor at I bar and 27'C. The pressure

after compression is 4 bar. The isentropic efficiencies ofthe turbine and compressor are 85clc

and 807o respectively. Air fuel ratio is 80: I . Calorific value of the fuel used is 42000 kJ/kg.Mass flow rate of air is 2.5 kg/s. Detemine the power output from the plant and the cycle. efficiency. Assume Cp and y to be same for both air and products of combustion. (12 Marks,

7 a. Sketch and explain the Ammonia-Water absorption refrigeration system. (08 Marks)b. What are the desirable thermodynamics and thermo-physical properties of a good

refriserant? (04 Marks)c. In an air-refrigeration plant working on a reversed Brayton cycle, air enters into the

compressor at I bar and- 15 'C, where it is compressed to a pressure of 5.5 bar. Air enters the

expander at 15"C. Determine:i) COP of the cycle and

ii) Mass flow rate of air into the compressor per minute for I ton of refrigeration.Assume both compression and expansion process are isentropic. (08 Marks)

8 a. Derive an expression for specific humidity of air-water vapour mixture. (06 Marks)b. Sketch and explain the winter air-conditining showing the processes on a psychrometric

chart. (07 Marks)c. The dry and wet temperatures of atmospheric air at 101.325 KPa pressure are measured with

a sling psychrometer and determined to be 25 'C and l5 "C respectively. Determine:i) Dew point temperatureiii) Relative humidity and

ii) Specific humidityiv) Enthalpy of moist air.

Use properties of table only, without using psychrometric chart.

2of2

(07 Marks.t

USN lOME/AU/PM/TL45

(07 Marks)(04 Marks)

Fourth Semester B.E. Degree Examination, Jane 2Ol2

Time: 3 hrs. Max. Marks:100

PART-AI a. With neat sketches, explain clearly the different types of chips by enumerating the

conditions under which each variety ofchip will be formed. (09 Marks)

b. Mild steel bars of 50 mm diameter are to be turned over a length of 160 mm with a depth ofcut of I .5 mm, feed of 0.2 mm/rev at 230 rpm by HSS tool. If the tool life equation is given

by, VTo'f "do '' = 50, determine how many components may be tumed before regrinding of

Manufacturing Process - llNote: Answer FIVE full questions, selecting

at least TWO questions from each part.

the tool.c. Write an explanatory note on flank wear.

2a.b.c.

3a.b.c.

7 a. Distinguish clearly between push broach and pull broach. )..a 1f,

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List and explain the essential properties ofcutting tool materials. (08 Marks)List the Various functions of a cutting fluid in metal cutting. (o4 Marks)State the various methods of measuring the tool tip temperature and hence explain any oneof them with neat sketch. (08 Marks)

Distinguish clearly between shaping and planing. (04 Marks)Explain clearly the tail stock offset method oftaper turning in a lathe. (07 Marks)With a neat sketch, explain clearly the construction and working of a shaper. (09 Marks)

4 a. With a neat diagram, explain briefly the construction and working principle of uprightdrilling machine. State its relative merits and demerits. (10 Marks)

b. Explain briefly with suitable sketches the various operations to be performed on a drillingmachine. (10 Marks)

PART-B5 a. With the aid of suitable sketches, explain clearly the concepts of up milling and down

(08 Marks)m illing.b. With a neat sketch, explain briefly the working of a universal dividing head. (08 Marks)c. Differentiate between simple indexing and compound indexing. (04 Marks)

6 a. With neat sketch, explain clearly the construction and wo_rffidfpfuqiple of a surfacegrindingmachine ,($X?,)i (loMarks)

b. Explain the following: /9i) Types of abrasives used in grinding wheels. , .)f g6*rlrn"- 1S .

iit Dressing and truing of grinding wheels. \ .{ 1la;.-ilT f ; .' ( t0 Mar*,s)

n:-r:--..:^l- ^l^--1.. L^r.,,^^- ^..-L L-^-^L ^-l -..11 L-^^^L :\ /t (04 Marks)b. What is honing? With a neat sketch, explain clearly the verticriltid'l{figrha--chine. (09 Marks)c. Explain with a neat sketch, the process of lapping. (07 Marks)

8 a. With a neat sketch, explain clearly the principle of working and construction of a AbrasiveWater Jet Machining (AWJM). State the process parameters. (10 Marks)

b. Explain briefly the principle of EDM, with a neat sketch. List the various factors affectingthe MRR in EDM process and explain any one of them. (10 Marks)

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Fourth Semester B.E. Degree Examination, Jane 2012Kinematics of Machines

Time: 3 hrs- Max. Marks:100

Note: 1. Azswer any FIVE full questinns, selecting atleast TWOquestions from each part.

2. Graphical solutions may be obtained on graphsheets or onanswer book itse$

PART - A

1 a. Define the following: i) Kinematic chain ii) Mechanism iii) Structureiv) Inversions v) Degrees offreedom. (10 Marks)

b. Sketch and explain the working of an elliptical trammel. Prove that it traces an ellipse.(10 Marks)

2 a. Explain with a neat sketch, crank and slotted lever quick retum motion mechanism.(08 Marks)(06 Marks)(06 Marks)

3 In the toggle mechanism shown in fig.Q3, the slider D is constrained to move on a horizontalpath. The crank OA is rotating in the counter clockwise direction at a speed of 180 rpm. Thedimensions of the various links are as follows : OA = l80mm , CB = 240mm, AB = 360mmand BD = 540mm. For the given configuration find ,

a. Velocity ol the slider.b. Angular velocity of the links AB, CB and BD.c. Velocity of rubbing on the pins of diameter of 30mm at A and D.

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b. Explain with a neat sketch, pantograph mechanism. State its applications.c. Explain with a neat sketch, Geneva wheel mechanism.

d. Torque applied to the crank OA for a force of 2kN at D.A

(20 Marks)

Fig.Q3

4 a. Explain the procedure for velocity and acceleration of the piston in a reciprocating enginemechanism- (10 Marks)

b. Explain how by means of Klein's construction the acceleration of a reciprocating engine is

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1of 2

(10 Marks)

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PART . B

The crank of a reciprocating engine is 90mm long, the connecting rod is 360mm long and the

crank rotates at l5brpm clockwise. Find the velocity and acceleration of the piston and the

angular velocity and ingular acceleration ofthe connecting rod when the angle which the crank

maies with inner dead Centre is 300. Solve the problem through complex algebra. (20 Marks)

a. Derive the expression for length of path of contact, length of arc of a contact and contact

ratio for a pair of involute gears in contact. (10 Marks)

b. The following data relate to a pair of involute spur geal in mesh : Module = 6mm i

Number ofteeth on wheel =49 ; Numberof teeth on pinion = 17 ; Addendum of pinion

and gear wheel interms of module = I , find the number ofpairs of teeth in contact?, _,(10 Marks)

a. Sketch and explain different types of gear trains. (06 Marks)

b. Figure Q7(b), shows an Epicyclic gear train where the arm A the driver and annular gear D

is -the

follower. The wheel D has I l2 teeth and B has 48 teeth. B runs freely on pin P and D

is separately driven. The an]1 A runs at 100 rym and wheel D at 50 rpm in same direction.

Find the speed ofwheel B and C. (14 Marks)

D

Fig.Q7(b)

The following data relate to a cam profile in which the roller follower moves wittr uniform

acceleration and retardation motion during ascent and descent'

Minimum radius of cam = 25mm ; Roller radius = 8mm ; Lift = 32 mm ; Offset of

follower axis = l2mm towards righi ; Angle of ascent = 600 ; Angle of descent = 900 ;

Angle of dwell between ascent and descent = 450 ; Speed of cam = 200 rpm clockwise.

Driw the profile of the cam. (20 Marks)

2of2

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USN lOME/AU46B

Fourth Semester B.E. Degree Examination, Jturae 2012Fluid Mechanics

Time: 3 hrs. Max. Marks:100

Note: 1. Azsrver any FIVE full questions, selecting atleast TWOquestions from each part.

2. Missing data may be assumed suitably with proper reasoning.

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PART - AI a. Distinguish between the following :

i) Mass density and weight densityii) Dynamic viscosity and kinematic viscosity.iii) Ideal fluid and real fluid.

b. Prove that an ideal gas undergoing an adiabatic process, the bulk modulus of elasticity (K)(06 Marks)

(04 Marks)(04 Marks)

(0,6 Ma rks)

(06 Marks)

(08 Marks)ii) Rotational flow and

(04 Marks)

C.

d.

is y time the pressure (P) where y = ColC".Derive an expression for surface tension on a liquid jet.

0.2mls. Find the dynamic viscosity of the oil.

State and prove hydrostatic law.

An oil film of thickness l.5mm is used for lubrication between a square plate of size0.9m x 0.9m and an inclined plane having an angle of inclination 200 with horizontal. Themass of the square plate is 40 kg and it slides down the plane with a uniform velocity of

2a.b. Find the pressure difference between A and B in kPa in meters of water for the fig.Q2(b).

(06 Marks)

it6"oA'

Fig.Q2(b)

c. A circular plate of 4.5m diameter is submerged in water withbelow the water surface being 3m and l.5m respectively. Find i) the total pressure on thefront face of the plate and ii) the position of centre of pressure. (08 Marks)

3 a. A hollow wooden cylinder (s = 0.6) has an outer diameter of 0.6m and an inner diameter of0.3m. It is required to float in an oil of sp.gr.0.9. Calculate i) the maximum length (height)ofthe cylinder so that it shall be stable when floating with its axis vertical ii) the depth towhich it will sink.

b. Distinguish between : i) Steady flow and uniform flowirrotational flow.

c. In a two - dimensional flow field for an incompressible fluid, the velocity components are :

u=v'/+2x-xzy and Y=xy2-2y- *Zi) Check for the continuity ii) Find an expression for the stream function. (08 Marks)

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5a.b.

6a.b.

IOME/AU46B

Derive Euler's equation of motion along a stream line. Also derive Bemoulli's equationfrom Euler's equation of motion and list the assumptions made for deriving Bemoulli'sequation. (10 Marks)

b. A conical tube is fixed vertically with its smaller end upwards and it forms a part of pipeline. The velocity at the smaller end is 4.5m/s and at the large end is l.5m/s. Length of theconical tube is I .5m. The pressure at the upper end is equivalent to a head of l0m of water.i) Neglecting the frictional loss. determine the pressure at the lower end of the tube.ii) If head loss in the tube is 0.3 tvr - vt)'/29, where v1 and v2 are the velocities at smaller

and larger end respectively, determine the pressure at the larger end assuming flowdownward. (10 Marks)

PART -BDerive an expression for discharge through V - notch. (06 Mart<s)A horizontal venturimeter with inlet diameter 20cm and throat diameter l0cm is used tomeasure the flow of water. The pressure at inlet is 147 kPa and vacuum pressure at thethroat is 40cm of mercury. Find the discharge of water through venturimeter. TakeCa = 0.98. (06 Marks)

c. The shear stress (r) in a pipe flow depends upon the diameter ofthe pipe (D), velocity (v) ofthe fluid, mass density (p) and dynamic visocity (p) ofthe fluid and height ofroughness ofprojection (k). Using dimensional analysis, obtain the relation for shear stress in a non -dimensional form. (08 Marks)

Derive Chezy's equation for loss of head due to friction in pipes. (06 Marks)Water is to be supplied to the inhabitants of a college campus through a supply main. Thefollowing data is given :

Distance of the reservoir from the campus = 3km, Number of inhabitants = 4000,Consumption of water per day of each inhabitant = 180 litres, Loss of head due tofriction = l8m, Coefficient of friction for the pipe, f= 0.007. If half of the daily supply ispumped in 8 hours, determine the size of the supply main. (06 Marks)

c. Three pipes of diameters 300mm, 200mm and 400mm, and length 450m, 255m and 3l5m.respectively are connected in series. The difference in water surface levels in two tanks is

l8m. Determine the rate of flow of water if co-efficient of frictions are 0.0075, 0.0078 and0.0072 respectively. Neglect the minor losses. Also find the equivalent diameters ofthe pipeif the equivalent coefficient of friction is 0.0075. (08 Marks.l

Show that the average velocity is equal to the half of the maximum velocity in a laminarflow through pipe. (10 Marks)Determine i) the pressure gradient ii) the shear stress at the two horizontal platesiii) discharge per meter width for laminar flow of oil with a maximum velocity of 2mlsbetween two plates which are l50mm apan. Given p:2.5 Pa-s. (10 Marks)

Differentiate between : i) Pressure drag and friction drag ii) Stream line body andbluffbody iii) Lift and drag. (06 Marks)

b.

b. Find the displacement thickness and momentum thickness for the velocity distribution in theboundary layer given by :

Y- =2(t1\-lt1\'. ,oE Mar*.s,u \/o) \/o.)c. Find the velocity of the bullet fired in standard air if the Mach angle is 300, Assume

temperature of air as I 50C. (04 Marks)

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