Subject: Mathematics - IV

Time: 3 Hours Max. Marks: 70

Note: Answer all questions. All questions carry equal marks.

1.~ Derive Cartesian form of Cauchy - Reimann equations of an analyticalV' ~unction f(z) = u + i v.v(ii) Show that the function u = 1/2 log (x2 + i) is harmonic and also find f(z) = u + iv.

OR~If f(z) u + i v is an analytic function. Show that the family of curves

, ~, y) = C1 and v(x,Y) = C2 are orthogonal.~ Show that f(z) = sin z is analytic function.

~ Discuss the transformation w = cos z.

. OR¥DiSCUSS the transformation w = eZ

•

:uaM If f(z) = u + iv is analytic in the region D bounded by a closed curve 'c' and Zo

. . t i D Sh th t f() 1 J-f(Z)dZISany POIn In. ow a Zo = -. .. 2m c z - zo

(i~valuate f3~ -1 where c is [z] = 2.v' - z -z 2c

~~aluate

~valuate

OR2zdJ e Z where c is [z] = 3 using Cauchy's integral formula.

c(z-1)(z-2)

e2zdzJ where c is I z-1\ = 2c (Z+1)4

4.(~\~xpand the f(z) = 2 1 in the regions~ t; z -4z+3

(i) I zl < 1 (ii) 1 < 1 z 1 < 3 (iii) 1 z 1 > 3

OR~tate and prove Taylor's theorem.

~"" x2dx

. ) Evaluate f (a > 0), b > 0) using residues.--oo(x2 +a2)(x2 +b2

)

OR(a > 0, b> 0) using residues.

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.'

Subject: Engineering ThermodynamicsTime: 3 Hours Max. Marks : 70

(7)(3)

, ,., /.. Note: Answer all questions. All questions carry equal marks.1.(a{Wvyrite short note on internal energy.

«6£xplain the term 'Thermodynamic equilibrium'.(in) 6ne kg mole of an ideal gas with Cv= (5/2) Rand cp+ (772)R expandsJ from 8 bar and 350°C to 1 bar by the following paths:

(A) Constant volume (8) Adiabatic.Calculate W, Q, ~H for the above process.

OR(b) (i) State the mathematical expression of the first law of the thermodynamics

which is applicable to a control volume and explain the meaning of eachterm appearing in it. (5)

(ii) The Vander waals equations of state is given by a (p + ;) (v - b) = RT,

where 'a' and 'b' are constants of Vander waals equation. Develop relationto determine the constants 'a' and 'b' in terms of critical temperature andpressure.

2.(a~stinguish between "Heat Engines" and "Heat Pumps".(ii) rove the equivalence of Kelvin-Planck and Clausius statements

of t \I law of thermodynamics.(iii ISCUSS Carrrot cycle for an ideal gas.

OR(b) (i) Define 'Entropy'. Is it a path function? (4)

(ii) A metal casting weighing 4.5 kg at a temperature of 1000°C is quenchedby dropping it into a well insulated tank containing 50 kg of water at 20°C.Calculate entropy changes of metallic casting, water and total entropychange of the process. Take Cp for metal casting as 2930 J/Kg-k andfor water as 4186.8 J/Kg-k.

(Hi) What is third law of thermodynamics?

(4)(4)

(6)

(9)

(3)

(6)(5)

3~~;ive Maxwells relations.(ii sing fundamental property relations and Maxwell equations, show that

( (dT) (av)dS = Cp T - aT p dP .

(8)

(6)

OR

(b)(i) Show that Joules-Thompson coefficient 'fl' is given by _1_[( av) - v] andCp aT p

obtain the values of fl for ideal gas and Vander waals gas. (7)(ii) Discuss thermodynamic diagrams to estimate thermodynamic properties

of gases. .

~ )tVfite about Rankine cycle.~ Derive an expression for thermal efficiency of an Otto engine.

. OR(b)(i) Discuss absorption refrigeration process with a neat schematic diagram. (7)

(ii) Distinguish between linde process and c1ande process for gas liquefaction. (7)

5.(a) ~Iain in detail the calculation of ideal work and lost work for flow~ processes. (14)

OR(b) Write a short notes on the following:

(i) Convergent nozzle and convergent divergent nozzle(ii) Turbines (iii) Compressors and pumps

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(7)

(7)(7)

(4)(5+5)

•••............... -- .............•.. ......, .••.•...•...•.. ....,~.B.Tech. 2/4 (Chem. Engg.) II-Semester (Main) Examination, May 2011

Subject: Organic Chemical Technology

Time: 3 Hours Max. Marks: 70

Note: Answer all questions; All questions ~~rry equal marks.

1.(a) Crude petroleum is made up of hundreds of different individual chemicals.Explain. (7)

(b) Discuss the procedure for the manufacture of phenol formaldehyde. (7)

OR6scribe with the help of a flow sheet, the refinery operations.19Y Explain the manufacturing process of acrylonitrile.

(7)(7)

(7)(7)

2.(a) Explain the concept and mechanism of polymerization.(b) Discuss the procedure for manufacture and uses of HPDE.

OR~SXPtain the procedure for the manufacture of formal dehyde.~hat is SBR? Describe its manufacturing process.

3.(a) Discuss the following:(i) Classification of synthetic fibres(ii) Additives of paper(iii) Pulping methods

(7)(7)

(5)(4)(5)

OR(b)(i) Explain the manufacture of Nylon-66.

(ii) Write a note on the recovery of chemicals from black liquor.(7)(7)

4.~xplain the unit operation and chemical conversions in the manufacture_2f--cane sugar. (7)

J.UJDescribe the industrial alcohol manufacture process form molasses. (7)

OR(b) Describe the manufacture of the antibiotic pencil in by an aerobic batch

fermentation process, with the aid of a neat flow sheet. (14)

~ Discuss with flow charts, the manufacture of vegetable oils by solventextractions. (6)

{9)/ Write short notes on the following: - - - - >

(i) ingredients and composition of paints and varnishes. .. (4)(ii) Hyderogenation of oils (4)

OR(c) Explain the classification of surfactants. (7)(d) Describe the manufacture of detergents. (7)

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B.Tech. 2/4 (Chern. Engg.) II-Semester (Main) Examination, May 2011

Subject: Fluid Mechanics

Time: 3 Hours Max. Marks: 70

Note: Answer all questions. All questions carry equal marks ..

1.(a) /clerive the hydrostatic equilibrium equation and give its applicationV for two situations. (7)

(b) escribe the Rheological behaviour of Non-Newtonian fluids in detail. (7)

OR(c) Give a detailed classification of pressure measuring devices. (7)(d) The pressure and temperature of the atmosphere at ground level are

14.7 psi and 650F. Find the pressure and density of the air at a heightof 15,000 ft.

(i) assuming an isothermal atmosphere(ii) Find the pressure, temperature and density of air assuming an

(1b Iff)ft3adiabatic atmosphere (Take y = 1.4 and R = 1545.3 -'----"c---'-_. 1bmo/eoR

(7)

~/ and enumerate the importance of different types of fluids.

~erive the kinetic energy correction factor.

OR

(10)

(4)

(c) With a neat diagram explain the Reynolds experiment and give itssignificance. (7)

(d) Derive equation of continuity. A 20cm pipe conveying water branchesinto two pipes of diameter 15cm andtOcm respectively. If the averagevelocity in the 20 cm and 15 cm pipe are 3 m/s and 1.8 m/s determinethe velocity in 10cm pipe.

3.(a) 2.16m3/h of water at 3200K is pumped through a 40 mm ID pipe througha length of 150m in a horizontal direction and up through a vertical heightof 12 mts. In the pipe there are fittings equivalient to 260 pipe diameterswhat power must be supplied to the pumps if it is .60% efficient. Takef = 0.008, viscosity = 0.65 cp and density = 1 gm/cc. (8)

(7)

(b) Define a pipe fitting and mention atleast five pipe flttinqs along with theirloss coefficients. (6)

OR\,~fine friction factor and derive the equation for laminar flow through pipe. (7)

(d) efine dimensional analysis and mention in detail the procedure ofBuckinghem pi method. (7)

..2

Code No. 4477

..2 ..

4.(a) Calculate the minimum fluidization velocity for the given data,porosity = 0.40, particle diameter = 1.25 mm. Density difference = 0.25 gm/cc,Fluid viscosity = 1cpo (7)

(b) Mentioning the merits and demerits of a packed bed column, derive theKozeny carman equation. . (7)

OR(gY"'Derive the equation for generalized Reynold's number and give the

J si . .cance of viscosity coefficient. (7)

Mention the significance of different types of settings? A gas flows in aconduit vertically at a velocity of 20 cm/s. What is the maximum particlesize (density = 1.2 gm/cm) that may be carried by it? Take gas 1.2 gm/ccdensity = 1.15 gm/cc, and viscosity = 2.25 x 10-5 pas. '

5.(a)/'Oistinguish between orifice and orificemeter, and derive the equationV for fin ing out the discharge in case of an orificemeter. (7)

(b) A centrifugal pump of 1.5 mts diameter runs at 210 rpm and pumps1800 lits/sec of water. The angle which the Vanes make at exist with thetangent to the impellar is 25°. Assuming radial entry and velocity of flowthrough out as 2.5 mts/sec. Determine the power required to drive thepump. If efficiency is 65%, find the average liftof the pump. (7)

OR(c) Distinguish between weirs and notches. Derive equation for finding

coefficient of discharge of a 'V-Notch'. (7)

(d) Describe in detail the operational difficulties in case of a centrifugal. (7)

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Subject: Electrical and Electronics Engineering

Time: 3 Hours Max. Marks: 70

Note: Answer all questions. All questions carry equal marks.

1.(a)(nStat and explain Kirchoff's laws. Show that KCL and KVL follow fromV-' tt principles of conservation of charge and energy respectively. (6)

(ii n the circuit shown below find the value of Resistance 'R' acrossterminals A & B so that it may draw maximum power: (8)

Figure-_ OR

(b)(i) What is Norton's equivalent circuit? In what respect if it different fromThevenin's equivalent circuit? Explain with circuit diagrams. (6)

(ii) In the circuit shown below find the voltage across 10 ohm resistance byapplying superposition theorem.

.~_2_t~V ~2__5L ,

ioJL

(~)

Figure2.(a)(!)Exp1ain the rule to find the direction of magnetic field due to a current,

carded by a conductor. Draw relevant figures for the same. (6)(ii) Two coils 'A' and 'B' are situated close by. Their number of turns are

500 and 300 respectively. It is found that a 3A current causes a fluxof 0.06 mWb. In coil 'A' while same current in coil'B' causes a fluxof 0.09 mWb. If 45% of flux created in coil 'A' links coil'B',find L1, L2, M and K. (8)

I~\//. OR~) ~.ow the generators are classified? Explain the types of generators with

proper circuit diagrams. Mention their applications? (6)(ii) A 6 pole D.C. generator has 250 armature conductors. The generator

runs at a speed of 20 revolutions per second. If flux per pole is 0.04 Wb.Find e.m.f induced in the generator if the machine has. (8)(A) Wave winding (B) Cap winding

Code No. 4478..2 ..

3~~i) at are the various losses in a D.C. machine? Discuss. (4)(ii hat are the methods adopted for speed control of D.C. shunt motor?

~

lain one of the methods with circuit diagram and relevantharacteristics. (6)

",) A voltage V = 141 sin (314 t + 1t/3) is applied to a resistance of 20 ohm.Find instantaneous value and R.M.S. value of current and also averagepower consumed. (4)

OR(b)(i) How can a sine wave be represented bya phasor? What is the importance

of this representation? Explain with proper diagrams. (4)(ii) Draw the circu.it diagrams for D.C. shunt and series motors. Explain their

torque-speed characteristics (6)(iii) A 6 pole Lap wound shunt motor is fed from a 400 v D.C. supply. The

armature 'current drawn is 50 A and armature resistance is 0.2 ohm. If theflux per pole is 0.05 Wb, and the motor has 540 conductors, find the speed. (4)

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4.(a)(i~raw and explain the exact and approximate equivalent circuits of a two~\~nding transformer. (6)./ (ii)/ffle power input to a 3-phase, 50Hz, 400v, 4 pole induction motor isV 60 kw. The stator losses are 1 k.w. Friction and windage losses are 1.2 k.w.

Find Rotor copper loss, total mechanical power developed, power suppliedto load and load torque if the motor is running at 4% slip. (8)

OR(b)(i) Derive the equation for Torque developed in a 3-phase induction motor.

_ Eind the \Lall,e of slip.for .maxlrnum.torque, - - -- (6)(ii) A 220 / 110 V, single phase two winding transformer is fed from 220V

supply. The input at no load is 400 VA and 150 watts.Find(A) No load current and power factor(8) Magnetizing current and working component of no load current and(C) Iron losses (8)

5.(a)(i) What is filter circuit? What are the types of filter circuits? Discuss them withproper circuit diagrams. (7)

(ii) Draw the symbols of different types of Transistors and explain them. (3)(iii) Explain the characteristics of a transistor with common base configuration.(4)

OR.(P}(i) Explain the action of P-N-P junction transistor. (5)/(Ti) Discuss the function of a Diode as rectifier. (4)Jill) Draw neat circuit diagram for full wave rectifier and explain its operation

with output waveforms. (5)

Subject: Environmental Studies

Time: 3 Hours Max. Marks : 70

Note: Answer all questions. All questions carry equal marks.

1.~ Explain in the detail the role of an individual in conservation of naturalresources. (7)

~Vvhat are the major causes of deforestation? Discuss its consequences. (7)

OR(c) Write a note on non-renewable energy sources. (7)(d) Mention the effects of soil erosion and desertification on environment. (7)

/"-,,,2.B> <Discuss the types, characteristic features structure and function of grass:_, ~ and forest ecosystems. (7)

~vhat is an ecosystem? List the components of an ecosystem. / (7)

OR(c) Discuss the concept of food chain, food web and ecological pyramid. (7)(d) Explain how the ecosystems are destroyed by human activities. (7)

3.(a) Explain the evolution of diverse species in an ecosystem.(b) What are hotspots of biodiversity? Explain.

(7)(7)

ORY) India is a mega diverse nation. Explain.Y) Discuss on the ethical and aesthetic values of biodiversity.

(7)(7)

JY(a) Explain the role of an individual in prevention of pollution. (8)~ What are the causes and control measures to water pollution? (6)

OR(c) Discuss the causes, effects and control measures of urban and industrial

solid wastes. (14)

5. D~l:Iss briefly on the following :'-{a})Nater conservation

v(t5) Urban problems related to energy-(t) !3ain water harvesting~Acid rains

(3.5x4)

OR(e) Explain the role of information technology in environment and human

health. (8)(f) Bring out the issues involved in enforcement of environmentallegislation.(6)

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