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Code No: R21021

II B. Tech I Semester, Supplementary Examinations, May - 2012

FLUID MECHANICS & HYDRAULIC MACHINES(Com. to EEE, ME, MM)

Time: 3 hours Max Marks: 75

Answer any FIVE Questions

All Questions carry Equal Marks

******-*******

1. a) Two large vertical plane parallel surfaces are 5 mm apart and the space between them isfilled with a fluid. A thin plate of 12.5 cm square falls freely between the planes along the

central plane and reaches a steady velocity of 2 m/s. Determine the weight of the plate if the

viscosity of the fluid filling the space is 0.02 Ns/m2.

b) If 5.27 cm3

of a certain oil weighs 4482 kg, calculate the specific weight, mass density

and specific gravity of the oil.

2. a) Define and distinguish between streamline, path line and streak lineb) State and derive Bernoullis theorem, mentioning clearly the assumption underlying it.

3. a) An oil of specific gravity 0.7 is flowing through a pipe of diameter 300 mm at the rate of500 liters/s. Find the head lost due to friction and power required to maintain the flow for a

length of 1000 m. Take = 0.29 stokes.

b) What do you understand by the terms: major energy loss and minor energy losses in

pipes?

4. a) Obtain an expression for the force exerted by a jet of water on a fixed vertical plate in thedirection of the jet.

b) A blade turns the jet of diameter 3 cm at a velocity of 20 m/s by 60. Determine the forceexerted by the blade on the fluid.

5. a) What are the different types of hydropower plant? Describe each one briefly.b) Explain briefly how can be the power available for hydel project be estimated.

6. a) Explain briefly the principles on which a Kaplan turbine works.b) Explain the different types of the efficiency of a turbine

7. a) What is the basis of selection of a turbine at a particular place?b) What are unit quantities? Define the unit quantities for turbine.

8. What do you mean by manometric efficiency, mechanical efficiency and overall efficiencyof centrifugal pump?

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1. a) Two large planes are parallel to each other and are inclined at 30 to the horizontal withthe space between them filled with a fluid of viscosity 20 cp. A small thin plate of 0.125 m

square slides parallel and midway between the planes and reaches a constant velocity of 2

m/s. The weight of the plate is 1 N. Determine the distance between the plates.

b) What is the difference between U-tube differential manometers and inverted U-tube

differential manometers? Where are they used?

2. a) Define and distinguish between i) steady and unsteady flow, ii) uniform and non-uniformflow, iii) rotational and irrotational flow.

b) Define the equation of continuity. Obtain an expression for continuity equation for three

dimensional flows.

3. a) Describe Reynolds experiments to demonstrate the two types of flow.b) Water is flowing through a pipe of 5 cm diameter under a pressure of 29.43 N/cm

2

(gauge) and with mean velocity of 2.0 m/s. Find the total head or total energy per unit

weight of the water at a cross section, which is 5 m above the datum line.

4. A 4 cm diameter water jet with a velocity of 35 m/s impinges on a single vane moving in thesame direction at a velocity of 20 m/s. The jet enters the vane tangentially along the xdirection. The vane deflects the jet by 150. Calculate the force exerted by the water on the

vane.

5. a) Differentiate between storage and pondage. Support your answer with a neat sketchb) Make a neat sketch of a hydropower plant and show clearly the various elements

6. A pelton wheel has a mean bucket speed of 35 m/s with a jet of water flowing at the rate of 1m

3/s under a head of 270 m. the buckets deflect the jet through an angle of 170. Calculate

the power delivered to the runner and the hydraulic efficiency of the turbine. Assume co-

efficient of velocity at 0.98.

7. a) What do you understand by the characteristics curves of turbine? Name the importantcharacteristics of a turbine.

b) What is cavitation? How does it affect the performance of hydraulic machines?

8. Define a centrifugal pump. Explain the working of a single stage centrifugal pump with neatsketches.

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1. a) The specific gravity of a liquid is 3.0, what are its specific weight, specific mass andspecific volume?

b) A body weighing 45 kg with a flat surface area of 930 cm2

slides down lubricated inclined

plane making a 30 angle with the horizontal. For viscosity of 1 poise and body speed of 3

m/sec, determine the lubricant film thickness.

2. a) What is meant by one-dimensional, two-dimensional and three-dimensional flows?b) Explain the terms:

i) Path line ii) Streak line iii) Stream line iv) Stream tube

3. a) Derive the expression for computing discharge through an orifice meterb) Define and explain the terms: i) Hydraulic gradient line and ii) Total energy line

4. a) Derive the expression for the force exerted by a water jet on a plate moving in the samedirection of the jet with a velocity less than that of the jet.

b) A blade turns the jet of diameter 3 cm at a velocity of 20 m/s by 60. Determine the force

exerted by the blade on the fluid.

5. a) What do you understand by a flow duration curve? How is it prepared?b) Explain briefly how can be the power available for hydel project be estimated.

6. a) How will you classify the turbines?b) Differentiate between turbines and pumps.

7. a) List the various efficiencies used to express the performance of hydraulic turbines.b) Explain the function of draft tube in the case of reaction turbines.

8. a) Discuss in general the main operating characteristics of a centrifugal pump. What is theimportance of constant efficiency curves?

b) Define cavitation. What are the effects of cavitation.

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1. a) What is the difference between dynamic viscosity and kinematic viscosity? State theirunits of measurements.

b) A U- tube mercury manometer is used to measure the pressure of oil flowing through a

pipe whose specific gravity is 0.85. The center of the pipe is 15 cm below the level of

mercury. The mercury level difference in the manometer is 25 cm, determine the absolute

pressure of the oil flowing through the pipe. Atmospheric pressure is 750 mm of Hg.

2. a) Differentiate between forced vortex and free vortex flow.b) Given that u = x

2 y

2and v = 2xy, determine the stream function and potential function

for the flow.

3. a) A pitot static tube is used to measure the velocity of water in a pipeline. If the mercurymanometer attached to it shows a reading of 0.17 m, calculate the water velocity in the pipe.

Assume coefficient of velocity as 0.98

b) Derive the expression for computing discharge through a Venturimeter.

4. A water jet with a velocity of 60 m/s enters a series of curved vanes at an angle of 20 to thedirection of blade movement. The peripheral speed of the disc on which the blades are

mounted is 25 m/s. Calculate the vane inlet angle. If at the exit the component of absolutevelocity along the direction of motion is zero, determine the outlet blade angle. Assume

shockless enters and exit.

5. a) What is a mass curve? Explain the procedure for preparing a mass curve and also its usesb) Make a neat sketch of a hydropower plant and show clearly the various elements

6. a) Draw a neat sketch of Pelton turbine and Francis turbine.b) A Pelton turbine delivers 14.25 MW when running at 600 rpm under a head of 900 m.

Assuming an overall efficiency of 89.2%. Determine the jet diameter and the wheel

diameter. Assume Cv = 0.98 and speed ratio as 0.46.

7. a) Differentiate between an inward and an outward flow reaction turbine.b) What is specific speed? State its significance in the study of hydraulic machines.

8. a) Explain condition in which two pumps may be operated in series or in parallel.b) What is multistage pump and what are its advantages.

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Code No: R21041

II B.Tech I Semester, Supplementary Examinations, May - 2012

ELECTRICAL TECHNOLOGY(Com.to ECE, EIE, BME)


Answer any FIVE QuestionsAll Questions carry Equal Marks

*******-******

1. a) Explain the principle of operation of a D.C. generator and mention the parts of a D.Cgenerator.

b) The resistance of the field circuit of shunt wound D.C. generator is 200 ohms when the

output of the D.C generator is 100 KW, the terminal voltage is 500 V and the generated

e.m.fis 525V. Calculate.

i) Armature resistance

ii) The value of the generated e.m.f when the output is 60 KW with a terminal voltage 520V.

2. a) Derive an expression for toque developed in a D.C. motorb) A 6 pole D.C. motor has were connected armature with 87 slots each slot containing 6conductors. The flux/pole is 20m wb. And the armature has a resistance of 0.13 ohm.

Calculate the speed when the motor is connected to 240V. Supply and taking armature

current of 80 A also calculate the toque in Newton meters developed by the armature.

3. a) What is an ideal transformer? Explain the difference between the ideal transformer andreal transformer.

b) A single phase transformer takes 10 Amps on no-load at a power factor of 0.1. The turns

ratio is 4:1 if the load on the secondary is 200 Amp. At a power factor of 0.8 lags. Find the

primary current and power factor neglecting the voltage drop in the windings.

4. a) What is the necessity of open circuit Test on a Transformer? What are the parametersfind out from this test? Explain with a neat diagram.

b) The readings obtained from the open circuit and short circuit Tests on a single phase

transformer of 50KVA, 110V/220V. Calculate the various parameters.

O.C. Test V2 =220V, I0 = 14 A, W0 = 330W.

S.C. Test Vsc =21.5V, I1= 45.45A. Wsc = 490W.

5. a) Explain how the rotating magnetic field is produced in a 3 phase Induction motor withneat diagrams.

b) Explain the term synchronous speed.

6. a) Draw and explain the construction details of an alternator.b) Calculate the distribution factor for a single phase alternator having 6 slots/pole when allthe slots are wound.

7. a) Explain double reechoing field theory of single phase Induction motor.b) Write any two applications of a split phase Induction motor.

8. a) How many types the instruments are classified mention them?b) Explain the working and construction of an indicating instrument.

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Code No: R21041





*******-******

1. a) How do you classify the D.C generator?b) A 4 pole lap wound D.C. shunt generator has a useful flux per pole of 0.07wb. The

armature winding consists of 220-turms each of 0.004 ohms resistance. Calculate the

terminal voltage when running at 900 R.P.M. if the armature current is 50A.

2. Discuss about the operation of 3 point starter for a D.C. Shunt motor with a neat diagram.3. a) Derive the induced e.m.f equation of a single phase transformer

b) The maximum flux density in the core of a 250/3000-V 50 Hz single phase transformer is

1.2 wb/m2. If the e.m.f perturn is 8 volts, Determine

i) Primary and secondary turns.

ii) Area of the core

4. a) Discuss about various losses and efficiency of a transformer.b) In a 25 KVA, 2000/200V, single phase transformer the iron and full load copper losses

are 350 w and 400w, respectively. Calculate the efficiency at unity power factor on

i) Full load ii) half full load.

5. a) Discuss about the principle of operation of a 3 phase induction motor and slip.b) A 4 pole 3 phase induction motor operates from a supply whose frequency is 50 Hz.

Calculate

i) The speed at which the magnetic field of stator in rotating

ii) The speed of the rotor when the slip is 0.04

iii) The frequency of the rotor currents when the slip is 0.03

iv) The frequency of the rotor currents at the stand still.

6. a) Derive the induced e.m.f equation of a 3 phase alternatorb) A 3- phase 16 pole Alternator has a star connected winding with 144 slots and 10

conductors per slot. The flex per pole is 0.03 wb. Sinusoid ally distributed and the speed is

375 R.P.M. Find the frequency and phase and line e.m.f. Assume full pitch coil.

7. Write a short note oni) Shaded pole motorii) Stepper motor.

8. a) Discuss about various torques in meaning instruments.b) A moving coil Ammeter can read up to 1 Amp. Has a resistance of 0.02 ohms. How this

instrument could be adopted to read

i) Voltage up to 300V.

ii) Current up to 100 Amperes.

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Code No: R21041





*******-******

1. a) Write a note on load characteristics of a D.C shunt generatorb) A 1500 K.W. 550V, 16 pole D.C. shunt generator runs at 150 R.P.M. What must be the

useful flex per pole if there are 2500 lap connected conductors in its armature? The full load

copper losses equal to 25 KW. Calculate the area of cross section of the pole shoe if the gap

density has a uniform value of 0.9wb/m2.

2. a) How can you conduct the Swinburnes test on a D.C. machineb) A.D.C. shunt motor takes 2 A on no-load when connected to 250V D.C. mains with an

armature resistance of 1ohm. When the field current is 1 amp, determine the loud currentcorresponding to maximum efficiency.

3. a) Draw and explain the phase diagram of a transformer under no-loud and load conditions.b) Derive an expression for maximum efficiency of a transformer.

4. a) What is the necessity of short circuit test on a transformer, what are the parameters obtainfrom this test. Explain with a neat diagram.

b) A 7.5 KVA 2400V/120V. Transformer was tested by short circuiting the low voltage side

and applying 100V to H.V side. The measured power input was 145W. Determine the

regulation when the load has 0.8 lag power factor.

5. Explain the various starting methods of a 3- phase induction motor.6. a) How can you determine the regulation of an Alternator by wring synchronous Impedance

method?

b) Calculate the distribution factor for a single phase Alternator having six slots/pole, when

only 4 adjacent slots/pole are wound and the removing being not wound.

7. a) Explain the working of a stepper motor with a neat diagram.b) Write a short note on hybrid stepper motor.

8. a) Derive an expression for torque in a PMMC instrument.b) Write the advantages and disadvantages of induction type instrument.

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*******-******

1. a) Derive the induced e.m.fequation of a D.C. Generator.

b) An 8 pole D.C. Shunt generator with 778 were connected armature conductors and

running at 500 R.P.M. Supplies a load of 12.5 ohms resistance and at terminal voltage of

50V. The armature resistance is 0.24 ohms. And the field resistance is 250 ohms. Find the

armature current the induced emf and the flux per pole.

2. a) How van you control the speed of a D.C motori) Flux control method

ii) Armature control method.

b) A 220V D.C. shunt motor is running at a speed of 800 R.P.M and draws 100A calculateat what speed the motor will run when developing half the torque. Total resistance of the

armature and the field is 0.1 ohms. Assume that the magnetic circuit is unsaturated.

3. a) Discuss the constructional features of a transformer in detail.b) The core of a 100 KVA, 11000/550V, 50Hys single phase core type transformer has a

Goss section of 20cm x 20cm Find:

i) The Number of H.V. 4L.V.turns per phase and

ii) The emf per turn if the maximum core density is not to exceed 1.3 Tesla. Assume a

stacking factor of 0.9 what will happen if the primary voltage is increased by 10% on no-

load?

4. How can you conduct open circuit test and short circuit tests on a single phase transformer?Explain with neat circuit diagrams.

5. a) Discuss about torque slip characteristics of a 3 phase induction motor.b) A 3- phase 400/200-V star- star connected wound rotor induction motor has 0.06 ohms

rotor resistance and 0.3 ohm stand still reactance per phase. Find the additional resistance

required in the rotor circuit to make the starting torque equal to the maximum toque of the

motor.

6. a) Discuss about the constructional features of a 3phase alternator.b) Find the no-load phase voltage and line voltage of a star connected 3 phase 6 pole

alternator which runs at 1200 R.PM having flux per pole of 0.1 wb sinusoid ally distributed.Its stator has 54 slots having double layer winding. Each coil has sterns and the coil is

chorded by 1 slot.

7. Discuss about the operation ofi) Split phase induction motor ii) Capacitor start and induction run motor

8. Explain the principle of operation of permanent magnet moving coil instrument with a neatdiagram.

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Code No: R21051


DATA STRUCTURES(Com. to CSE, IT, ECC )



All Questions carry Equal Marks*******-******

1. a) Which of the given options provides the increasing order of asymptotic complexity of thefunctions: 4321 ,, fandfff ? ( )

nnf 21 = ( )

2/3

2 nnf = ( ) nnnf 23 log=

( ) nnnf 2log4 = b) i) Write a recursive C function to compute n Fibonacci numbers of the following:

( )

( ) ( )

+

=

=

=

21

1,1

0,1

nfnf

nif

nif

nf

ii) How many times f is called (including the first call) for an evaluation of ( )7f ? (7M+8M)

2. a) Consider an array: {25, 14, 16, 13, 10, 8, 12} represents a binary max-heap. What is thecontent of the array after two delete operations on a binary max-heap?

b) Write a recursive quick sort algorithm. Trace the algorithm to sort the following elements:

72, 15, 22, 11, 18, 56, 40, 45 (5M+10M)

3. a) What is an equivalent infix form of the following postfix form of arithmetic expression?+ /EDCCBA

b) Let a circular queue is maintained in an array A[0..n-1]. What is the size of the queue interms of F and R, where F, R indicate the FRONT and REAR indices?

c) Write a C program to implement the circular queue operations using arrays.

(3M+3M+9M)

4. a) Write a C program to create a doubly linked list and display all the elements in the list?b) Compare singly and doubly linked lists to perform insertion and operations. (8M+7M)

5. a) A complete n array tree is a tree in which each node has n children or no children. Let I bethe number of internal nodes and L be the number of leaves in a complete n array tree. If

41=L and 10=I , then what is the value ofn ?b) Consider the following in-order and pre-order traversal of a binary tree. What is the post-

order traversal of a binary tree? (7M+8M)

In-order Traversal: D B F E G H A C

Pre-order raversal: A B D E F G H C

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6. a) What is a threaded binary tree? Explain with an example.b) The following numbers are inserted into an empty binary search tree in the given order oneby one: 15, 32, 20, 9, 3, 25, 12, 1.

i) Show the final binary search tree after the insertions.

ii) Draw the binary search tree after deleting 15 from it. (5M+10M)

7. a) Explain the graph traversal methods with suitable examples.b) How many minimum spanning trees does the following graph have? Draw all of them.

(7M+8M)

8. a) Explain the representation of sets using linked lists.b) What is an ADT? What are the ADT operations? Explain ADT implementation of a stack.

(5M+10M)

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Code No-: R21051


DATA STRUCTURES

(Com. to CSE, IT, ECC )Time: 3 hours Max Marks: 75



*******-******

1. a) Find the values of )2,513(f and )10,345(f for the following recursive function definition:

>

+

=

otherwise

nifrr

nfrn

rnf

,0

0,,mod),(

b) Write a recursive binary search algorithm. Trace the algorithm to search the element -5 inthe list of elements: -5, -3, -1, 0, 10, 15, 20, 25 (7M+8M)

2. a) What is a natural merge sort? A natural merge sort is to be used to sort the file of integers:12, 37, 42, 9, 5, 7, 50, 40, 45, and 92. What is the order of the numbers after one pass of the

sort?

b) Write a selection sort algorithm. Trace the algorithm to sort the following elements:72, 15, 22, 11, 18, 56, 40, 45 (5M+10M)

3. a) What is an equivalent infix form of the following postfix form of arithmetic expression?HGFEDCBA ++ // , where represents exponentiation

b) What is the minimum number of stacks of size n required to implement a queue of size

n ? Explain.

c) Write a C program to convert an infix expression to a postfix expression. (3M+3M+9M)

4. a) What are the lists of operations that can be performed on a singly linked list? Explain howto perform insertion and deletion operations in the middle of a singly linked list.

b) What is a circularly linked list? Write a C program to display the number of elements in acircularly linked list. (7M+8M)

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Code No-: R21051

5. a) What is the total number of distinct binary trees with n nodes? Draw all the distinctbinary trees with 5 nodes.b) Consider the following weighted binary tree:

i) What is the weighted external path length of the binary tree?

ii) What is the weighted degree path length of the binary tree? (7M+8M)

6. a) A binary search tree is generated by inserting in order of the integers: 50, 15, 62, 5, 20, 58,91, 3, 8, 37, 60, 24. What is the total number of nodes in the left sub-tree and the rightsub-tree?

b) What is a balanced binary tree? What is the maximum height of any balanced binary tree

with 33 nodes? Assume that the height of a tree with a single node is 0. (7M+8M)

7. a) Consider the graph, G with 12 edges. It has 6 vertices of degree 3 and the rest have degreeless than 3. Determine the minimum number of vertices.

b) Consider a weighted undirected graph with vertex set V = {a, b, c, d, e, f, g, h, i, j} and

edge set E = {(a, b, 6), (a, c, 1), (a, d, 2), (a, e, 8), (b, d, 3), (b, g, 2), (c, d, 2), (d, h, 15), (e, f,11), (e, h, 8), (e, i, 2), (f, h, 4), (f, i, 9), (g, h, 8), (g, i, 14), (g, j, 19), (h, i, 4), (i, j, 5)}. The

third value in the tuple represents the weight of the edge specified in the tuple. What is the

weight of a minimum spanning tree of the weighted undirected graph? (5M+10M)

8. a) What is an ADT? What are the ADT operations? Explain ADT implementation of a queue.b) Explain the information storage using bit strings. (10 +5M)

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Code No-: R21051


DATA STRUCTURES(Com. to CSE, IT, ECC )



All Questions carry Equal Marks*******-******

1. a) Find the value of ( )7,5861f for the following recursive function definition:

+

=

otherwisenff

nifnnf

,11

100,10

c) What is the average successful search time taken by binary search on a sorted array of 10

data items? (5M+5M+5M)

2. a) What is a randomized quick sort? Explain with an example.b) How many swapping are needed to sort the following numbers in ascending order using

bubble sort? : 8, 22, 7, 9, 31, 19, 5, 13c) If one uses straight two-way merge sort algorithm to sort the elements: 20, 47, 15, 8, 9,

4, 40, 30, 12, 17 in ascending order, and then what is the order of these elements after thesecond pass of the algorithm? (5M+5M+5M)

3. a) What is an equivalent infix form of the following postfix form of arithmetic expression?HGFEDCBA ++ // , where represents exponentiation

b) If memory for the run time stack is only 150 cells (words), how big can n be in n!before encountering a stack overflow?

c) Write a C program to implement the round-robin algorithm. Trace the program with an

appropriate input data. (3M+3M+9M)

4. a) What is a circularly linked list? Write a C program to display the number of elementsin a circularly linked list.b) What are the lists of operations that can be performed on a doubly linked list? Explain

how to perform insertion and deletion operations in the middle of a doubly linked list.

(7M+8M)

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5. a) Compare trees and binary trees.b) The set: (A, (B, (E, F)), (C, (G)), (D, (H, I, J))) represents a tree. Find the number of leaf

nodes in the binary tree representation of this tree.

c) Consider a complete k array tree, where every internal node has exactly kchildren.

What is the total number of leaves in such a tree with n internal nodes? (5M+5M+5M)

6. a) How many nodes will become unbalanced when a node is inserted as a child of the node G of the following balanced binary tree?

b) A binary search tree is used to locate the number 43. Which of the following probe

sequences are possible and which are not? Explain.

(5M+10M)

7. a) If the simple graph G has n vertices and e edges, how many edges does the G ,complement of G have? If the simple graph G has 15 edges and G has 13 edges, howmany vertices does G have?

b) A complete, undirected, weighted graph G is given on the vertex set {0, 1, 2, ..., n-1}for

any fixed n. Draw the minimum spanning tree of G if:

i) The weight of the edge (u, v) is vu

ii) The weight of the edge (u, v) is vu + (7M+8M)

8. a) Explain the information storage using bit strings.b) What is an ADT? What are the ADT operations? Explain ADT implementation of aqueue. (5M+10M)

2 of 2

( )i 61 52 14 17 40 43( )ii 2 3 50 40 60 43( )iii 10 65 31 48 37 43( )iv 81 61 52 14 41 43

( )v 17 77 27 66 18 43

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Code No: X0424


ELECTRICAL TECHNOLOGY(Com. to ECE, EIE, BME, ECC)



All Questions carry Equal Marks~~~~~~~~~~~-~~~~~~~~~~~~

1. a) Explain the principle of operation of a D.C. generator and mention the parts of a D.Cgenerator.

b) The resistance of the field circuit of shunt wound D.C. generator is 200 ohms when the

output of the D.C generator is 100 KW, the terminal voltage is 500 V and the generated

e.m.fis 525V. Calculate.

i) Armature resistance

ii) The value of the generated e.m.f when the output is 60 KW with a terminal voltage 520V.

2. a) Derive an expression for toque developed in a D.C. motorb) A 6 pole D.C. motor has were connected armature with 87 slots each slot containing 6conductors. The flux/pole is 20m wb. And the armature has a resistance of 0.13 ohm.

Calculate the speed when the motor is connected to 240V. Supply and taking armature

current of 80 A also calculate the toque in Newton meters developed by the armature.

3. a) What is an ideal transformer? Explain the difference between the ideal transformer andreal transformer.

b) A single phase transformer takes 10 Amps on no-load at a power factor of 0.1. The turns

ratio is 4:1 if the load on the secondary is 200 Amp. At a power factor of 0.8 lags. Find the

primary current and power factor neglecting the voltage drop in the windings.

4. a) What is the necessity of open circuit Test on a Transformer? What are the parametersfind out from this test? Explain with a neat diagram.

b) The readings obtained from the open circuit and short circuit Tests on a single phase

transformer of 50KVA, 110V/220V. Calculate the various parameters.

O.C. Test V2 =220V, I0 = 14 A, W0 = 330W.

S.C. Test Vsc =21.5V, I1= 45.45A. Wsc = 490W.

5. a) Explain how the rotating magnetic field is produced in a 3 phase Induction motor withneat diagrams.

b) Explain the term synchronous speed.

6. a) Draw and explain the construction details of an alternator.b) Calculate the distribution factor for a single phase alternator having 6 slots/pole when allthe slots are wound.

7. a) Explain double reechoing field theory of single phase Induction motor.b) Write any two applications of a split phase Induction motor.

8. a) How many types the instruments are classified mention them?b) Explain the working and construction of an indicating instrument.

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Code No: X0424





All Questions carry Equal Marks~~~~~~~~~~~~-~~~~~~~~~~~

1. a) How do you classify the D.C generator?b) A 4 pole lap wound D.C. shunt generator has a useful flux per pole of 0.07wb. The

armature winding consists of 220-turms each of 0.004 ohms resistance. Calculate the

terminal voltage when running at 900 R.P.M. if the armature current is 50A.

2. Discuss about the operation of 3 point starter for a D.C. Shunt motor with a neat diagram.3. a) Derive the induced e.m.f equation of a single phase transformer

b) The maximum flux density in the core of a 250/3000-V 50 Hz single phase transformer is

1.2 wb/m2. If the e.m.f perturn is 8 volts, Determine

i) Primary and secondary turns.

ii) Area of the core

4. a) Discuss about various losses and efficiency of a transformer.b) In a 25 KVA, 2000/200V, single phase transformer the iron and full load copper losses

are 350 w and 400w, respectively. Calculate the efficiency at unity power factor on

i) Full load ii) half full load.

5. a) Discuss about the principle of operation of a 3 phase induction motor and slip.b) A 4 pole 3 phase induction motor operates from a supply whose frequency is 50 Hz.

Calculate

i) The speed at which the magnetic field of stator in rotating

ii) The speed of the rotor when the slip is 0.04

iii) The frequency of the rotor currents when the slip is 0.03

iv) The frequency of the rotor currents at the stand still.

6. a) Derive the induced e.m.f equation of a 3 phase alternatorb) A 3- phase 16 pole Alternator has a star connected winding with 144 slots and 10

conductors per slot. The flex per pole is 0.03 wb. Sinusoid ally distributed and the speed is

375 R.P.M. Find the frequency and phase and line e.m.f. Assume full pitch coil.

7. Write a short note oni) Shaded pole motorii) Stepper motor.

8. a) Discuss about various torques in meaning instruments.b) A moving coil Ammeter can read up to 1 Amp. Has a resistance of 0.02 ohms. How this

instrument could be adopted to read

i) Voltage up to 300V.

ii) Current up to 100 Amperes.

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Code No: X0424






1. a) Write a note on load characteristics of a D.C shunt generatorb) A 1500 K.W. 550V, 16 pole D.C. shunt generator runs at 150 R.P.M. What must be the

useful flex per pole if there are 2500 lap connected conductors in its armature? The full load

copper losses equal to 25 KW. Calculate the area of cross section of the pole shoe if the gap

density has a uniform value of 0.9wb/m2.

2. a) How can you conduct the Swinburnes test on a D.C. machineb) A.D.C. shunt motor takes 2 A on no-load when connected to 250V D.C. mains with an

armature resistance of 1ohm. When the field current is 1 amp, determine the loud current

corresponding to maximum efficiency.

3. a) Draw and explain the phase diagram of a transformer under no-loud and load conditions.b) Derive an expression for maximum efficiency of a transformer.

4. a) What is the necessity of short circuit test on a transformer, what are the parameters obtainfrom this test. Explain with a neat diagram.

b) A 7.5 KVA 2400V/120V. Transformer was tested by short circuiting the low voltage side

and applying 100V to H.V side. The measured power input was 145W. Determine the

regulation when the load has 0.8 lag power factor.

5. Explain the various starting methods of a 3- phase induction motor.6. a) How can you determine the regulation of an Alternator by wring synchronous Impedance

method?

b) Calculate the distribution factor for a single phase Alternator having six slots/pole, when

only 4 adjacent slots/pole are wound and the removing being not wound.

7. a) Explain the working of a stepper motor with a neat diagram.b) Write a short note on hybrid stepper motor.

8. a) Derive an expression for torque in a PMMC instrument.b) Write the advantages and disadvantages of induction type instrument.

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Code No: X0424






1. a) Derive the induced e.m.fequation of a D.C. Generator.

b) An 8 pole D.C. Shunt generator with 778 were connected armature conductors and

running at 500 R.P.M. Supplies a load of 12.5 ohms resistance and at terminal voltage of

50V. The armature resistance is 0.24 ohms. And the field resistance is 250 ohms. Find the

armature current the induced emf and the flux per pole.

2. a) How van you control the speed of a D.C motori) Flux control method

ii) Armature control method.

b) A 220V D.C. shunt motor is running at a speed of 800 R.P.M and draws 100A calculateat what speed the motor will run when developing half the torque. Total resistance of the

armature and the field is 0.1 ohms. Assume that the magnetic circuit is unsaturated.

3. a) Discuss the constructional features of a transformer in detail.b) The core of a 100 KVA, 11000/550V, 50Hys single phase core type transformer has a

Goss section of 20cm x 20cm Find:

i) The Number of H.V. 4L.V.turns per phase and

ii) The emf per turn if the maximum core density is not to exceed 1.3 Tesla. Assume a

stacking factor of 0.9 what will happen if the primary voltage is increased by 10% on no-

load?

4. How can you conduct open circuit test and short circuit tests on a single phase transformer?Explain with neat circuit diagrams.

5. a) Discuss about torque slip characteristics of a 3 phase induction motor.b) A 3- phase 400/200-V star- star connected wound rotor induction motor has 0.06 ohms

rotor resistance and 0.3 ohm stand still reactance per phase. Find the additional resistance

required in the rotor circuit to make the starting torque equal to the maximum toque of the

motor.

6. a) Discuss about the constructional features of a 3phase alternator.b) Find the no-load phase voltage and line voltage of a star connected 3 phase 6 pole

alternator which runs at 1200 R.PM having flux per pole of 0.1 wb sinusoid ally distributed.Its stator has 54 slots having double layer winding. Each coil has sterns and the coil is

chorded by 1 slot.

7. Discuss about the operation ofi) Split phase induction motor ii) Capacitor start and induction run motor

8. Explain the principle of operation of permanent magnet moving coil instrument with a neatdiagram.

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Code No: X0222


FLUID MECHANICS AND HYDRAULIC MACHINERY(Com. to EEE, MM)




~~~~~~~~~~~~-~~~~~~~~~~~

1. a) Two large vertical plane parallel surfaces are 5 mm apart and the space between them isfilled with a fluid. A thin plate of 12.5 cm square falls freely between the planes along the

central plane and reaches a steady velocity of 2 m/s. Determine the weight of the plate if the

viscosity of the fluid filling the space is 0.02 Ns/m2.

b) If 5.27 cm3

of a certain oil weighs 4482 kg, calculate the specific weight, mass density and

specific gravity of the oil.

2. a) Define and distinguish between streamline, path line and streak lineb) State and derive Bernoullis theorem, mentioning clearly the assumption underlying it.

3. a) An oil of specific gravity 0.7 is flowing through a pipe of diameter 300 mm at the rate of 500liters/s. Find the head lost due to friction and power required to maintain the flow for a length

of 1000 m. Take = 0.29 stokes.

b) What do you understand by the terms: major energy loss and minor energy losses in pipes?

4. a) Obtain an expression for the force exerted by a jet of water on a fixed vertical plate in thedirection of the jet.



5. a) What are the different types of hydropower plant? Describe each one briefly.b) Explain briefly how can be the power available for hydel project be estimated.

6. a) Explain briefly the principles on which a Kaplan turbine works.b) Explain the different types of the efficiency of a turbine

7. a) What is the basis of selection of a turbine at a particular place?b) What are unit quantities? Define the unit quantities for turbine.

8. What do you mean by manometric efficiency, mechanical efficiency and overall efficiency ofcentrifugal pump?

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Code No: X0222






~~~~~~~~~~~~~-~~~~~~~~~~

1. a) Two large planes are parallel to each other and are inclined at 30 to the horizontal with thespace between them filled with a fluid of viscosity 20 cp. A small thin plate of 0.125 m square

slides parallel and midway between the planes and reaches a constant velocity of 2 m/s. The

weight of the plate is 1 N. Determine the distance between the plates.

b) What is the difference between U-tube differential manometers and inverted U-tube

differential manometers? Where are they used?

2. a) Define and distinguish between i) steady and unsteady flow, ii) uniform and non-uniformflow, iii) rotational and irrotational flow.

b) Define the equation of continuity. Obtain an expression for continuity equation for three

dimensional flows.

3. a) Describe Reynolds experiments to demonstrate the two types of flow.b) Water is flowing through a pipe of 5 cm diameter under a pressure of 29.43 N/cm

2(gauge)

and with mean velocity of 2.0 m/s. Find the total head or total energy per unit weight of the

water at a cross section, which is 5 m above the datum line.

4. A 4 cm diameter water jet with a velocity of 35 m/s impinges on a single vane moving in thesame direction at a velocity of 20 m/s. The jet enters the vane tangentially along the x direction.The vane deflects the jet by 150. Calculate the force exerted by the water on the vane.

5. a) Differentiate between storage and pondage. Support your answer with a neat sketchb) Make a neat sketch of a hydropower plant and show clearly the various elements

6. A pelton wheel has a mean bucket speed of 35 m/s with a jet of water flowing at the rate of 1m

3/s under a head of 270 m. the buckets deflect the jet through an angle of 170. Calculate the

power delivered to the runner and the hydraulic efficiency of the turbine. Assume co-efficient

of velocity at 0.98.

7. a) What do you understand by the characteristics curves of turbine? Name the importantcharacteristics of a turbine.b) What is cavitation? How does it affect the performance of hydraulic machines?

8. Define a centrifugal pump. Explain the working of a single stage centrifugal pump with neatsketches.

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Code No: X0222






~~~~~~~~~~~~~~-~~~~~~~~~

1. a) The specific gravity of a liquid is 3.0, what are its specific weight, specific mass and specificvolume?

b) A body weighing 45 kg with a flat surface area of 930 cm2

slides down lubricated inclined

plane making a 30 angle with the horizontal. For viscosity of 1 poise and body speed of 3

m/sec, determine the lubricant film thickness.

2. a) What is meant by one-dimensional, two-dimensional and three-dimensional flows?b) Explain the terms:

i) Path line ii) Streak line iii) Stream line iv) Stream tube

3. a) Derive the expression for computing discharge through an orifice meterb) Define and explain the terms: i) Hydraulic gradient line and ii) Total energy line

4. a) Derive the expression for the force exerted by a water jet on a plate moving in the samedirection of the jet with a velocity less than that of the jet.



5. a) What do you understand by a flow duration curve? How is it prepared?b) Explain briefly how can be the power available for hydel project be estimated.

6. a) How will you classify the turbines?b) Differentiate between turbines and pumps.

7. a) List the various efficiencies used to express the performance of hydraulic turbines.b) Explain the function of draft tube in the case of reaction turbines.

8. a) Discuss in general the main operating characteristics of a centrifugal pump. What is theimportance of constant efficiency curves?

b) Define cavitation. What are the effects of cavitation.

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Code No: X0222






~~~~~~~~~~~~-~~~~~~~~~~~

1. a) What is the difference between dynamic viscosity and kinematic viscosity? State their unitsof measurements.

b) A U- tube mercury manometer is used to measure the pressure of oil flowing through a pipe

whose specific gravity is 0.85. The center of the pipe is 15 cm below the level of mercury. The

mercury level difference in the manometer is 25 cm, determine the absolute pressure of the oil

flowing through the pipe. Atmospheric pressure is 750 mm of Hg.

2. a) Differentiate between forced vortex and free vortex flow.b) Given that u = x

2 y

2and v = 2xy, determine the stream function and potential function

for the flow.

3. a) A pitot static tube is used to measure the velocity of water in a pipeline. If the mercurymanometer attached to it shows a reading of 0.17 m, calculate the water velocity in the pipe.

Assume coefficient of velocity as 0.98

b) Derive the expression for computing discharge through a Venturimeter.

4. A water jet with a velocity of 60 m/s enters a series of curved vanes at an angle of 20 to thedirection of blade movement. The peripheral speed of the disc on which the blades are mounted

is 25 m/s. Calculate the vane inlet angle. If at the exit the component of absolute velocity alongthe direction of motion is zero, determine the outlet blade angle. Assume shockless enters and

exit.

5. a) What is a mass curve? Explain the procedure for preparing a mass curve and also its usesb) Make a neat sketch of a hydropower plant and show clearly the various elements

6. a) Draw a neat sketch of Pelton turbine and Francis turbine.b) A Pelton turbine delivers 14.25 MW when running at 600 rpm under a head of 900 m.

Assuming an overall efficiency of 89.2%. Determine the jet diameter and the wheel

diameter. Assume Cv = 0.98 and speed ratio as 0.46.

7. a) Differentiate between an inward and an outward flow reaction turbine.b) What is specific speed? State its significance in the study of hydraulic machines.

8. a) Explain condition in which two pumps may be operated in series or in parallel.b) What is multistage pump and what are its advantages.

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Code No: X0521


PROBABILITY AND STATISTICS(Com. to CSE, IT)



All Questions carry Equal Marks~~~~~~~~~~~~~-~~~~~~~~~~

1. a) A Single card is drawn from an ordinary deck of 52 cards. Find the probability that the cardis i) a king ii) a face card iii) a red card iv) a red face card.

b) If A and B are two events, than prove that ( ) ( ) ( ) ( ).BAPBPAPBAP +=

c) State and prove Bayes Theorem. (6M+5M+5M)

2. a) Find k in the Probability function ( ) 3,2,1,0,3 =

= x

xkxf and Sketchfand the distribution

function F.b) A random variableXhas density function

( ) .,1

2

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Code No: X0521

6. a) A random sample of 100 recorded deaths in the United States during the past year showed anaverage life span of 71.8 years. Assuming a population standard deviation of 8.9 years, does

this seem to indicate that the mean life span today is greater than 70 years? Use a 0.05 level of

significance.b) In a random sample of 100 tube lights produced by company A, the mean lifetime (mlt) of

tube light is 1190 hours with standard deviation of 90 hours. Also in a random sample of 75

tube lights from company B the mean lifetime is 1230 hours with standard deviation of 120

hours. Is there a difference between the mean lifetimes of the two brands of tube lights at a

significance level of 0.05? (8M+8M)

7. a) From a random sample of 10 pigs fed on diet A, the increases in weight in a certain periodwere 10, 6, 16, 17, 13, 12, 8, 14, 15, 9 lbs. For another random sample of 12 pigs fed on diet B,

the increases in the same period were 7, 13, 22, 15, 12, 14, 18, 8, 21, 23, 10, 17 lbs. Test

whether diets A and B differ significantly as regards their effect on increases in weight? Use a0.05 level of significance.

b) Referring to the data of following table, test the hypothesis that the opinions concerning the

proposed abortion law the same within each political affiliation. Use a 0.05 level of

significance. (8M+8M)

Political Affiliation

Abortion Law Democrat Republican Independent Total

For 82 70 62 214

Against 93 62 67 222

Undecided 25 18 21 64

Total 200 150 150 500

8. a) Derive the average number of customers in the system. In (M/M/1): (/FCFS) model.b) Assume that both arrival rate and service rate following Poisson distribution.

The arrival rate and service rate are 25 and 35 customers/hour respectively, at a single window

in RTC reservation counter. Find .,,,, qsqs WWLL (6M+10M)

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Code No: X0521





All Questions carry Equal Marks~~~~~~~~~~~~~~-~~~~~~~~~

1. a) Suppose three companies X, Y, Z produce T.Vs. X produce twice as many as Y while Yand Z produce the same number. It is known that 2% of X, 2% of Y and 4% of Z are defective.

All the TVs produced are put into one shop and then one TV is chosen at random. Suppose a

TV chosen is defective, what is the probability that this TV is produced by company X?

b) Three balls are drawn successively from the box containing 6 red balls, 4 white balls and 5

blue balls. Find the probability that they are drawn in the order red, white and blue if each ball

is i) replaced, ii) not replaced. (8M+8M)

2. a) Let X be the number of years before a certain kind of pump needs replacement. Let X hasthe Probability functionf(x) = kx

3

x = 0,1,2,3,4. Find k.Sketch f and the distribution function. F.

b) The distribution function for a random variableXis ( )

2),

iii) P(-3

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Code No: X0521

6. a) A manufacturer of sports equipment has developed a new synthetic fishing line that heclaims has mean breaking strength of 8 kilograms with a standard deviation of 0.5 kilogram.

Test the hypothesis that 8=

kilograms against the alternative that 8

kilograms if arandom sample of 50 lines is tested and found to have a mean breaking strength of 7.8

kilograms. Use a 0.01 level of significance.

b) To test the effects a new pesticide on rice production, a farm land was divided into 60 units

of equal areas, all portions having identical qualities as to soil, exposure to sunlight, etc. The

new pesticide is applied to 30 units while old pesticide to the remaining 30. Is there reason to

believe that the new pesticide is better than old pesticide if the mean number of kgs of rice

harvested/unit using new pesticide is 496.31 with s.d.of 17.08kgs while for old pesticide is

485.41 kgs and 14.73kgs.Test at a level of significance 0.05. (8M+8M)

7. a) Two samples of sodium vapor bulbs were tested for length of life and the following resultswere returned:

Size Sample mean Sample S.D

Type I 8 1234 hrs 36 hrs

Type II 7 1036 hrs 40 hrs

Is the difference in the means significant to generalize that type I is superior to type II

regarding length of life? Use a 0.01 Level of significance.

b) A sample poll of 300 voters from district A and 200 voters from district B showed that 56%

and 48%, respectively, were in favor of a given candidate. At a level of significance of 0.05,

test the hypothesis that the candidate is preferred in district A. (8M+8M)

8. a) Explain briefly the main characteristics of Queuing system?b) Explain Traffic intensity?

c) Explain (M/ M/ 1): ( / FCFS) Queuing model. (6M+5M+5M)

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Code No: X0521






1. a) Define Probability of an Event.i) Prove that the impossible event has probability zero.

ii) IfAc

is the complementA of then prove that P (Ac) = 1-P (A

c).

b) What is the Probability of getting a total of7 or 11 when a pair fair dice are tossed?

c) Box I contains 1 white, 2 red, 3 green balls, Box II contains 2 white, 3 red, 1 green ball, Box

III contains 3 white, 1 red, 2 green balls. Two balls are drawn from a box chosen at random.

These are found to be one white and one red. Determine the probability that the balls are drawn

came from box I. (6M+5M+5M)

2. a) Suppose that pair of fair dice are to be tossed, and let the random variable X denote the sumof the points. Obtain the probability distribution for X.b) If the Probability density of a random variable is given by

( )

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Code No: X0521

6. a) Explain briefly the followingi) Null Hypothesis,

ii) Alternative hypothesis

iii) Type I error

iv) Type II error

b) An examination was given to two classes consisting of 40 and 50 students, respectively. In

the first class the mean grade was 74 with a standard deviation of 8, while in the second class

the mean grade was 78 with a standard deviation of 7. Is there a significant difference between

the performances of the two classes at a level of significance of 0.05? (8M+8M)

7. a) A test of the breaking strengths of 6 ropes manufactured by a company showed a meanbreaking strength of 7750 lb and a strength deviation of 145 lb, whereas the manufacturer

claimed a mean breaking strength of 8000 lb. Can we support the manufacturers claim at a

level of significance of 0.05?

b) Fit a Poisson distribution to the following data and test for its goodness of fit at level of

significance 0.05. (6M+10M)

x 0 1 2 3 4 5f 275 138 75 7 4 1

8. a) Derive the average number of customers in the Queue. In (M/M/1): (/FCFS) model.b) The arrival rate of customers at a counter in a bank follows Poisson distribution with a mean

of 45/hour; service rate of the clerk follows Poisson distribution with a mean of 60/hour. Find

the probability of having 0, 5, 10 customers in the system. Find .,,, qsqs WWLL (8M+8M)

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Code No: X0521






1. a) Define Probability of an Event. Write the axioms of Probability.b) What is the Probability of getting a total of8 or 10 when a pair fair dice are tossed?

c) Suppose a student dormitory in a college consists of the following: 30 % are freshmen of

whom 10% own a car, 40 % are Sophomores of whom 20% own a car, 20 % are Juniors of

whom 40% own a car, 10 % are Seniors of whom 60% own a car. A student is randomly

selected from the dormitory,

i) Find the Probability that the student owns a car.

ii) If the student owns a car; find Probability that a student is Junior? (4M+4M+8M)

2. a) Determine the discrete probability distribution of a discrete random variable X whichdenotes the minimum of the two numbers that appear when a pair of fair dice is thrown once.

b) Consider the density function ( )

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Code No: X0521

6. a) Explain briefly the followingi) Level of significance ii) Critical region iii) Left One tailed test iv) Right one tailed test

b) The IQ s (intelligence quotients) of 16 students from one area of a city showed a mean of

107 with a standard deviation of 10, while the IQs of 14 students from another area of the city

showed a mean of 112 with a standard deviation of 8. Is there a significant difference between

the IQs of the two groups at a 0.01 level of significance? (8M+8M)

7. a) Mean life time (mlt) of computers manufactured by a company is 1120 hours with standarddeviation of 125 hours. Test the hypothesis that mean lifetime of computers has not changed if

a sample of 8 computers has a mlt of 1070 hours? Use 0.05 level of significance.

b) Fit a Binomial distribution to the following data and test for its goodness of fit at level of

significance 0.05. (6M+10M)

No. of Heads 0 1 2 3 4 5

No.of Tosses(Frequency) 38 144 342 287 164 25

8. The containers from railway goods wagons are unloaded at a single platform of a railwaygoods yard. The arrival rate of wagons is 8 wagons per day and service rate is 14 wagons perday. Assuming the arrival rate and service rate to follow Poisson distribution, determine the

following:

a) Utilization of railway goods yard

b) Average number of waiting wagons in the queue

c) Average number of waiting wagons in the system

d) Average waiting time per wagon in the queue

e) Expected waiting time per wagon in the system (16M)

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Code No: X0321


PRODUCTION TECHNOLOGY(Com. to ME, AME)

Time: 3 hours Max Marks: 80Answer any FIVE Questions


~~~~~~~~~~~~-~~~~~~~~~~~~

1. a) What are composite moulds? Why are they used? Where are they used?

b) What are the different types of gates in sand moulding process?

2. a) What are the necessary steps involved in sand moulding? Explain.

b) What are the functions of core bonding agents and what are some of the important features

of the bonds that allow them to serve their purpose?

3. a) List and explain the destructive tests applied in welding.

b) What are the essential steps in brazing operation?

4. a) Write the applications, advantages and limitations of gas welding.

b) Write about various types of spot welding electrodes with neat sketches.

5. a) Distinguish between friction in hot rolling and cold rolling.

b) Explain briefly re-crystalization and grain growth in hot rolling?

6.

a) Explain the design considerations in spinning process.b) How do you estimate the force and power requirements in Drawing process?

7. Write the expression for determining the force required to produce an extrusion and discuss the

effect of various parameters on the extruding force?

8. a) Differentiate between blow moulding and injection moulding.

b) Discuss any two processing methods for plastics.

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Code No: X0321





~~~~~~~~~~~~-~~~~~~~~~~~~

1. a) How do you design a gating system?

b) What is the significance of shrinkage in the production of castings?

2. a) Describe the solidification of a pure metal with a neat sketch in moulding process.

b) Large castings are not made by investment casting. Explain.

3.

a) What is HAZ? How do you reduce it?

b) Explain the pre and post heat treatments of weldments?

4. a) What do you mean by Weld bead geometry? Explain the bead geometrical parameters.

b) Discuss the typical applications of

i) Spot welding and

ii) Thermit welding.

5. a) What is the effect of strain hardening on mechanical properties of metals?

b) How do you estimate the rolling load?

6. a) What are the various ways in which presses can be classified?

b) Explain shearing action in press working.

7. a) Why hydrostatic extrusion is better than the conventional extrusion process?

b) Why does forging impart greater strength to such parts as crankshafts and gears that

could be obtained by casting or welding of alloys of the same com-position?

8. a) Discuss engineering applications of plastics.

b) Explain the processing methods for thermo setting plastics.

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Code No: X0321





~~~~~~~~~~~~-~~~~~~~~~~~~

1. a) Write notes on nucleation and grain growth related to casting?

b) What must be the preferred shape of a riser? Explain.

2. a) Describe the solidification of a pure metal with a neat sketch in moulding process.

b) Large castings are not made by investment casting. Explain, why?

3.

a) Why is it possible for fusion zone to have a chemistry that is different from that of the filler

metal? Explain.

b) Sketch and explain various welding positions. Give their applications.

4. a) What are the low temperature joining processes? Explain briefly.

b) Why is brazing an appropriate method for joining dissimilar metals with widely different

melting points?

5. a) Distinguish between plastic formations in single crystals and polycrystalline aggregates in

rolling.

b) How do you eliminate spring back effect in rolling?

6. a) Explain the working of hydraulic press with neat sketch.

b) Describe i) Wire drawing and ii) Tube drawing

7. a) Discuss the principle of rotary forging.

b) How do you eliminate defects in forgings?

8. a) What is the main advantage of Injection moulding for thermoplastics parts as compare to hot

compression moulding?

b) Explain the method used for processing of Bottle, floatable objects of thermo- Plastics. Stateits advantages?

.

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Code No: X0321





~~~~~~~~~~~~-~~~~~~~~~~~~

1. a) Describe with the help of a neat sketch, the working of a sweep pattern and also state its

advantages?

b) What is gating ratio? Explain.

2. a) What are the advantages of casting process over other production processes?

b) Give advantages of different pattern materials?

3. a) How do the weld bead geometrical parameters affect the mechanical properties of

weldments?

b) Discuss typical defects in fusion welding and their remedial measures.

4. a) What design features can be altered to permit the joining of different thickness or different

conductivity metals?

b) What types of weld joints commonly employ filler welds? Explain.

5. a) Distinguish between friction in hot rolling and cold rolling.

b) Explain briefly re-crystallization and grain growth in hot rolling?

6. A cylindrical lead alloy billet of 70mm dia and 100mm length is extruded to a final diameter of

35mm by using backward extrusion process. The average tensile yield stress for the alloy is 12

N/mm2. Determine the maximum force required. Make suitable assumptions to first derive the

extrusion for the force?

7. a) What are the various ways in which presses can be classified?

b) Explain shearing action in press working.

8.

a) What are the important considerations to be taken while designing plastic parts? Discuss?b) Explain briefly testing of plastics.

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Code No: X0201/R05 Set No. 1

II B.Tech I Semester Supplementary Examinations, Apr/May 2012MATHEMATICS-III

( Common to Electrical & Electronic Engineering, Electronics &Communication Engineering, Electronics & Instrumentation Engineering,

Electronics & Control Engineering, Electronics & Telematics, Electronics &Computer Engineering and Instrumentation & Control Engineering)


All Questions carry equal marks

1. (a) Show that (n) =

10

(log1/y)n1

dy.

(b) Prove that10

dx1xn =

n

( 1n)

( 1n+ 1

2).

(c) Prove that10

x2dx1x4 =

(3/4)(1/4)

[5+5+6]

2. (a) When n is a positive integer prove that Pn(x) =1

0

(x x2 1 cos )nd.

(b) Prove that

1

0 xJ

n(x)Jn(x)dx = 0 if = =12

J()

n+12

if = where and are the roots of Jn (x) = 0. [8+8]

3. (a) Determine the analytic function f(z) =u+iv given that3u + 2v = y2 x 2 + 16x.

(b) If sin ( + i) = x + iy then prove that x2

cosh2 + y

2

sinh2 = 1 and x

2

sin2 y2

cos2 = 1.

[8+8]

4. (a) Evaluate2+3i1i

(z2 + z)dz along x=t and y=t2 using Cauchys integral formula.

(b) EvaluateC

sin6 z dz(z

2)3

where C is |z| = 1 using Cauchys integral formula.

(c) EvaluateC

cosz2 dz(z1)(z2) where C is |z| = 3 using Cauchys integral formula.

[5+5+6]

5. (a) Show that when | z + 1 | < 1, z2 = 1 +

n=1

(n + 1)(z+ 1)n .

(b) Expand f(z) = 1z2z6 about (i) z = -1 (ii) z = 1. [8+8]

6. (a) Find the poles for the function f(z) = eiz

(z2

+1)and corresponding residues.

(b) EvaluateC

z(z1)(z2)2 dz Where C is the circle | z 2 | = 12 using residue

theorm. [8+8]

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7. (a) Evaluate2

0

d(53sin )2 using residue theorem.

(b) Evaluate0

x sin mxdxx4+16

using residue theorem. [8+8]

8. (a) Prove that the transformation w=1/z transforms circles and straight lines inthe z-plane into circles or straight lines in the w-plane.

(b) Find the bilinear transformation which maps the points( l, i, l) into thepoints (i, o, i). [8+8]

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1. (a) Evaluate

10

x2

dx1x5 interms of function.

(b) Prove that10

(1 xn)1/ndx = 1n

[( 1n)]2

2(2/n).

(c) Prove that 1n

2n

3n

.........

n1n

= (2

)n12

n1/2. [5+5+6]

2. (a) Show that Jn1 (x) + Jn+1(x) =2nx

Jn(x).

(b) Prove that J1/2(x) =

2x

cos x.

(c) Show that (n+1) Pn+1

(x) - (2n+1) x Pn

(x) + n Pn1

(x) = 0. [5+5+6]

3. (a) State necessary condition for f ( z ) to be analytic and derive C-R equationsin Cartesian coordinates.

(b) If u and v are functions of x and y satisfying Laplaces equations show that(s+it) is analytic where s = u

y v

xand t = u

x+ v

y. [8+8]

4. (a) EvaluateC

(y2 + 2xy)dx + (x2 2xy)dy where c is the boundary of the regionby y=x2 and x=y2.

(b) Evaluate using Cauchys theoremc

z3 ez dz(z1)3

where c is

|z

1

|= 1/2 using

Cauchys integral formula.

(c) Evaluate(1,1)(0,0)

(3x2 + 5y + i(x2 y2))dz along y2=x. [6+5+5]

5. (a) Expand logz by Taylors series about z=1.

(b) Expand 1(z2+1)(z2+2)

in positive and negative powers of z if 1 < |z| < 2. [8+8]

6. (a) Find the poles and the residues at each pole of f(z)= zz2+1

.

(b) Evaluate C

zezdz(z2+9)

where c is

|z

|= 5 by residue theorem. [8+8]

7. (a) Evaluate20

d(53cos)2 using residue theorem.

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(b) Evaluate0

sin mxx

dx using residue theorem. [8+8]

8. (a) Find the image of the domain in the z-plane to the left of the line x=3 underthe transformation w=z2.

(b) Find the bilinear transformation which transforms the points z=2,1,0 intow=1,0,i respectively. [8+8]

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1. (a) Prove that (2n) =

22n1

(n)(n +

1

2).

(b) Prove that (m, n) =10

xm1+xn1

(1+x)m+ndx [8+8]

2. (a) Prove that J20 +2 (J21 + J

22+ ....) = 1.

(b) Prove that x4 = 835

P4(x) +47

P2(x) +15

P0(x). [8+8]

3. (a) Find the analytic function whose imaginary part isf(x,y) = x3y xy3 + xy +x +y where z = x+iy.

(b) Prove that

2

x2+

2

y2

|Real f(z)|2 = 2|f(z)|2 where w =f(z) is analytic.

[8+8]

4. (a) Using Cauchys Integral Formula evaluateC

z2 dz(z+1)(zi)2 where C is ellipse

9x2+ 4y2=36.

(b) Integrate z2 along the straight line OM and along the path OLM consisting oftwo straight line segments OL and LM. Where O is the origin L is the pointz=3 and M is z=3+i.

(c) Evaluatec

(z3+z2+2z1) dz(z1)3 where C is | z| = 3 using Cauchys integral formula.

[6+5+5]

5. (a) Represent the function z+1(z1) as Laurent series in powers of |z| > 1.

(b) Expand f(z)= (z+3)z(z2z2) in powers of z if |z| < 1. [8+8]

6. (a) Find the poles for the function f(z) = eiz

(z2+1)and corresponding residues.

(b) EvaluateC

z(z1)(z2)2 dz Where C is the circle | z 2 | =

12

using residue

theorm. [8+8]

7. (a) Evaluate

2

0

d

(53cos)2 using residue theorem.

(b) Evaluate0

sin mxx

dx using residue theorem. [8+8]

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8. (a) Find the image of the infinite strip 0

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1. (a) Evaluate

10

x2

dx1x5 interms of function.

(b) Prove that10

(1 xn)1/ndx = 1n

[( 1n)]2

2(2/n).

(c) Prove that 1n

2n

3n

.........

n1n

= (2

)n12

n1/2. [5+5+6]

2. (a) Show that Jn1 (x) + Jn+1(x) =2nx

Jn(x).

(b) Prove that J1/2(x) =

2x

cos x.

(c) Show that (n+1) Pn+1

(x) - (2n+1) x Pn

(x) + n Pn1

(x) = 0. [5+5+6]

3. (a) Show that the real and imaginary parts of an analytic functionf(z) = u(r,) + i v(r,) satisfy the Laplace equation in polar form2ur2

+ 1rur

+ 1r2

2u2

= 0 and 2v

r2+ 1

rvr

+ 1r2

2v2

= 0 respectively.

(b) If u is a harmonic function, show that w = u2 is not a harmonic functionunless u is a constant. [8+8]

4. (a) EvaluateC

(sinz2+cosz2) dz(z1)(z2) where C is the circle |z| = 3 using Cauchys integral

formula.

(b) Evaluatez=1+iz=0

(x2 + 2xy + i(y2 x))dz along y=x2. [8+8]

5. (a) Expand coshz abouts z = i.

(b) Find the Laurent series expansion of the function z21

(z+2)(z+3)if 2 < |z| < 3.

[8+8]

6. (a) Find the poles and residue at each pole of the function z2

(z41) .

(b) EvaluateC

(1+ez)dz(z cos z+sinz)

where C is |z| = 1 by residue theorem. [8+8]

7. (a) Evaluate20

Cos25+4Cos

d using residue theorem.

(b) Evaluate

x2dx(x2+1)(x2+4)

using residue theorem. [8+8]

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8. (a) Prove that the transformation w=1/z transforms circles and straight lines inthe z-plane into circles or straight lines in the w-plane.

(b) Find the bilinear transformation which maps the points( l, i, l) into thepoints (i, o, i). [8+8]

a5_21915

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