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Code No: W0122/R07 Set No. 1

II B.Tech I Semester Supplementary Examinations, April/May 2011BUILDING MATERIALS AND CONSTRUCTION

(Civil Engineering)Time: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

? ? ? ? ?

1. How is soluble glass prepared? What are glass blocks and explain the importanceof glass as an engineering material. [16]

2. (a) What are the factors affecting the strength of bricks.

(b) Write briefly about the different tests for bricks.

[8+8]

3. (a) Enumerate the laboratory tests for cement and describe any two of them.

(b) What is consolidation of concrete? Describe the methods of compacting con-crete.

[2+3+3+3+5]

4. What is seasoning of timber? Explain various methods? [16]

5. (a) What do you understand by raft foundation? When do you prefer this typeof foundation?

(b) Explain with the help of sketches common types of raft foundation.

[6+10]

6. (a) State the advantages of cavity walls.

(b) Explain with the help of sketches, the details of cavity walls at the Foundationlevel and the Parapet level.

[6+10]

7. (a) Define a lintel and mention the materials which are commonly used to con-struct it.

(b) Describe briefly the construction of R.CC lintel.

[8+8]

8. (a) What are the Qualities expected of a good paint?

(b) Describe briefly the meaning of the following terms:-

i. Paints.

ii. Varnishes.

iii. Distemper.Discuss their uses, merits and demerits.

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[6+10]

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1. (a) What are the qualities of good building stones? Discuss them.

(b) What is the texture of rock. Enumerate its various types.

[8+8]

2. (a) Describe the process of burning bricks in intermittent kilns.

(b) Give the detailed and neat sketch of the Hoffman’s kiln.

[8+8]

3. (a) Describe the field tests for cement.

(b) Can seawater be used for making concrete? Explain.

[8+8]

4. (a) What is meant by decay of timber? What are its causes?

(b) Explain how aluminum is alternate material for wood.

[3+5+8]

5. Explain in detail the procedure for proportioning a trapezoidal combined footingfor two columns carrying unequal loads when the distance between the columns isgiven. [16]

6. (a) Explain the following terms with neat sketches

i. Corbel.

ii. Cornice.

iii. Coping.

iv. through stones.

(b) Explain any four tools used in stone masonry.

[8+8]

7. (a) Differentiate between Mosaic and Terrazzo floors? For what type of works yourecommend the above floorings?

(b) “For large spans shell roofs are provided”. Discuss the factual situation of theabove statement.

[8+8]

8. Describe the procedure of carrying out plastering in cement mortar on new and oldwall separately? [16]

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1. (a) What are the precautions to be taken in the process of blasting.

(b) Write a brief note on preservation of stones.

[8+8]

2. (a) Describe the process of burning bricks in intermittent kilns.

(b) Give the detailed and neat sketch of the Hoffman’s kiln.

[8+8]

3. (a) Describe the chemical composition of cement.

(b) What are the good characteristics of aggregate used in cement concrete?

[8+8]

4. (a) Describe the process of conversion of timber.

(b) What are the factors that affect physical properties of steel.

[8+8]

5. (a) What is a raft foundation ? When and where is it preferred to other shallowfoundations. Explain with a neat sketch.

(b) What are floating foundations? Where are they useful? How does they differfrom other foundations.

[10+6]

6. (a) Explain the following terms with neat sketches

i. Corbel.

ii. Cornice.

iii. Coping.

iv. through stones.

(b) Explain any four tools used in stone masonry.

[8+8]

7. What are single roofs? Explain with the help of neat sketches the various types ofsingle roofs. [16]

8. (a) What are the Qualities expected of a good paint?

(b) Describe briefly the meaning of the following terms:-

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i. Paints.

ii. Varnishes.

iii. Distemper.Discuss their uses, merits and demerits.

[6+10]

? ? ? ? ?

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? ? ? ? ?

1. What are the various tests for stones and explain them in detail. [16]

2. (a) What are the factors affecting the strength of bricks.

(b) Write briefly about the different tests for bricks.

[8+8]

3. (a) What are the various ingredients of cement concrete. Explain their impor-tance.

(b) What is setting of cement. How initial and final setting of cement is determinedin the laboratory?

[8+8]

4. (a) Describe the process of conversion of timber.

(b) What are the factors that affect physical properties of steel.

[8+8]

5. Describe two methods of foundations on black cotton soils in detail. [16]

6. (a) What are the requirements of partition walls.

(b) Write short notes on the Concrete partitions and Glass partition.

[6+10]

7. Differentiate between the following:- [5+7+4]

(a) Stone lintels & brick lintels.

(b) Steel lintels & RCC lintels.

(c) Lintel and Arch.

8. Differentiate between the following:- [4+4+4+4]

(a) Lime mortar and cement mortar.

(b) Beaded pointing & flush pointing.

(c) Flaking and peeling.

(d) Gugal and hump.

? ? ? ? ?

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Code No: X0225/R07

II B.Tech I Semester Supplementary Examinations, May- 2011

ELECTRO MAGNETIC FIELDS

(Electrical and Electronics Engineering)

Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks

1. a) Derive the expression for D due to infinite sheet of charge placed in Z = 0 plane, using

Gauss’s law

b) Point charges are located at each corner of an equilateral triangle. If the charges are

3Q, -2Q and 1Q, find E at midpoint of 3Q and 1Q side

2. a) Obtain the torque expression of an electric dipole in an electric field

b) In spherical co-ordinates V=0 at r = 0.1m and V=100volts at r =2m. Assuming free space

between these concentric spherical shells, find E and D

3. a) Explain and derive the boundary conditions for a conductor free space interface

b) A parallel plate capacitor with air as dielectric has a plate area of 236 cmπ and a

separation between the plates of 1mm. It is charged to 100 volts by connecting it across a

battery. If the battery is disconnected and plate separation is increased to 2mm, calculate the

change in

i) p.d across the plates and

ii) Energy stored.

4. a) Explain the oesterd’s experiment with neat diagram

b) A uniform solenoid 100mm in diameter and 400mm long has 100 turns of wire and a

current of I= 3A. Find the magnetic field on the axis of the solenoid

i) at the centre and

ii) at one end

5. a) Derive the Maxwell’s third equation

b) Obtain the expression for H in all the regions of a cylindrical conductor carries a direct

current ‘I’ and its radius is ‘R’ meter. Plot the variation of H against the distance ‘r’ from

the center of the conductor

6. a) Define magnetic dipole. What is magnetic moment? Describe how a differential current

loop behaves like a magnetic dipole

b) A wire 1 metre long carries a current of 10 A and makes an angle of 300 with uniform

magnetic field with B = 1.5 wb/m2. Calculate the magnitude of the force on the wire.

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Code No: X0225/R07

7. a) Derive the expression for mutual inductance using Neuman’s formulae.

b) Using the concept of vector magnetic potential, find the magnetic field density at a point

due to along straight filamentary conductor carrying a current ‘I’ in za direction

8. a) State and explain the poynting theorem

b) Does the fields ym atxEE sinsin= and z

m atxE

H coscos0µ

= satisfy Maxwell’s

equations

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Code No: X0225/R07







1. a) Explain the Gauss’s law applied to the case of infinite line charge and derive the

expression for D due to the infinite line charge

b) It is required to hold four equal point charges each in equilibrium at the corners of a

square. Find the point charge which will do this, if placed at the centroid of the square

2. a) Derive poisons and Laplace equations

b) Calculate the potential due to a dipole of dipole moment 45x10-10

C/m at a distance 1m

from it

i) on its axis and

ii) on its perpendicular bisector

3. a) State and explain continuity equation of currant in integral form and point from

b) An air capacitor consists of parallel square plates of 50cm side and is charged to a

potential difference of 250V, when plates are 1mm apart. Find the work done in separating

the plates from 1 to 3mm. Assume perfect insulation

4. a) Using Biot Savart’s law, find H due to a circular loop

b) Two narrow circular coils A and B have common axis and are placed 10 cm apart. The

coil A has 10 turns of radius 5 cm with a current of 1 Amps passing through it. The coil B

has a single turn of radius 7.5cm. If the magnetic field at the centre of coil A is to be zero,

what current should be passed through coil B.?

5. a) Describe any two applications of Ampere’s circuital law

b) A uniformly wound solenoid of 5000 turns is 1m long. If the current I=2A, what is

i) the flux density and

ii) Magnetic field H at the centre of the solenoid

6. a) Derive the expression for Lorentz force equation

b) A solenoid 25 cm long and 1cm mean diameter of the coil-turns has a uniform distributed

winding of 2000 turns. If the solenoid is placed in a uniform field of 2 wb/m2 flux density

and current of 5A is passed through the solenoid winding. What is the maximum

i) force on the solenoid and

ii) torque on the solenoid

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Code No: X0225/R07

7. a) Derive the expression for vector magnetic potential ‘A’ which satisfies the vector

poison’s equation

b) A toroidal coil of 500 turns is wound on a steel ring of 0.5m mean dia and 2x10-2

m2

cross sectional area. An excitation of 4000 A/m produces a flux density of 1 Tesla. Find the

inductance of the coil. If a 10 mm long gap is cut in the ring, find the current require to

maintain the flux density at 1 Tesla. Also find the inductance under these new conditions.

Neglect all leakage and fringing.

8. a) Explain the faraday’s law’s of electromagnetic induction and derive the expression for

induced EMF

b) Show that for a capacitor the conduction current in the wire equals the displacement

current in the dielectric if subjected to a time changing field

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Code No: X0225/R07







1. a) State coulomb’s law of force between any two point charges and state the units of

force

b) Find the electric field at any point between the two concentric spherical shells, inner

spherical shell has charge 1φ and outer spherical shell has charge 2φ

2. a) Explain the behavior of conductors in an electric fields

b) Find V at P(2, 1, 3) for the field of two axial conducting cones, with V=50 volts at 030=θ and V = 20 volts at 050=θ

3. a) Derive the expression for the energy stored in the parallel plate capacitor

b) At the boundary between glass )4( =rε and air, the lines of electric field make an

angle of 400 with normal to the boundary. If electric flux density in the air is 0.25

,/ 2mCµ determine the orientation and magnitude of electric flux density in the glass

4. a) State and explain Biot- savart’s law

b) A circular loop of wire of radius ‘a’ laying in xy plane with its centre at the origin

carries a current I in the φ+ direction using Biot-savarts law, find ),0,0( zH and

).0,0,0(H

5. a) Using Ampere’s circuital law, find H due to an infinite sheet of current

b) Consider the volume current density distribution in cylindrical coordinates as

arzrJ <<= 0,0),,( φ

braaa

rJ <<��

�

��

�= ,

2

2

0

∞<<= rb,0

6. a) Derive the expression for the force between two current carrying conductor in the same

direction

b) Show that BmT ×= also holds for the torque on a solenoid situate in a uniform

magnetic field.

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Code No: X0225/R07

7. a) Explain the concept scalar and vector magnetic potentials

b) A solenoid of 500 turns has a length of 50 cm and the radius of 10cm.A steel rod of

circular cross section is fitted in the solenoid coaxially. Relative permeability of steel is

3000. A dc current of 10 A is passed through solenoid. Compute the inductance of the

system and energy stored in the system

8. a) State Maxwell’s equations for static fields. Explain how they are modified for time

varying electric and magnetic fields

b) Find the frequency at which conduction current density and displacement current

density are equal in a medium with 81,/102 4 =×= −

rmmho εσ

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Code No: X0225/R07







1. a) Obtain an expression for total force experienced by a point charge due to infinite number

to point charges around it

b) The flux density rar

D3

= nC/m2 in the free space

i) Find E at r = 0.2 m

ii) Find the total electric flux leaving the sphere of r = 0.2 m

iii) Find the total charge within the sphere of r = 0.3m

2. a) Derive the expressions for potential and electric field intensity due to an electric dipole

b) Verify whether the potential fields given below satisfy Laplace equation.

i) V=4x2 -6y

2+2z

2

ii) zV 4cos += φρ

3. a) Derive the ohms law in point form

b) FA µ2 Capacitor is charged by connecting it across a 100 V dc supply. It is now

disconnected and then it is connected across another Fµ2 capacitor. Assuming no

leakage, determine the p.d between the plates of each capacitor and energy stored

4. a) Using Biot Savart’s law, find H due to infinite long straight conductor

b) A steady current I amps flows in a conductor bent in the form of hexagon. Find the

intensity at the centre of the loop. The distance between the centre and each side is ‘a’ meter

5. a) State and explain Ampere’s circuital law

b) A ‘Z’ directed current distribution is given by

J = arforrur ≤+ ),( 2

Find B at any point ar ≥ using Ampere’s circuital law

6. a) Derive an expression for the torque on a current loop placed in a magnetic field

b) The force between two long parallel conductors is 15 kg/m. The conductors spacing of

10cm. If one conductor carries twice the current of the other, calculate the current in each

conductor

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Code No: X0225/R07

7. a) Derive the expression for energy stored and energy density in a magnetic field

b) Given the magnetic vector potential, mwbaA z /4

�2−

= , calculate the total magnetic

flux crossing the surface mzm 50,21,2

≥≤≤≤= ρπ

φ

8. a) Write and explain differential and integral form of Maxwell’s equations for fields varying

harmonically with time

b) A faraday’s copper disc 0.3m diameter is rotated at 60 r.p.s on a horizontal axis

perpendicular to and through the centre of the disc, the axis lying in a horizontal field of 20

micro Tesla. Determine the emf measured between the brushes.

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Code No: X0323/R07


MECHANICS OF SOLIDS

(Com. to ME, MM, AME)




1. a) Sketch and explain salient points of the stress-strain curve of mild steel specimen in

tensile test.

b) A round copper rod, 560 mm long, has a diameter of 30 mm over a length of 200mm, a

diameter of 20 mm over a length of 200 mm and diameter of 10mm over its remaining

length. Determine the stress in each section and elongation of the rod when it is subjected to

a pull 30kN. Take E=100 kN/mm2.

2. A simply supported beam of 10m long carries a uniformly distributed load 2kN/m over

entire length and point loads 1kN and 2kN at distances 2m and 5m from the left support.

Draw the shear force and bending moment diagrams.

3. a) Prove that the maximum bending moment occurs at a section where the shear force shows

a discontinuity on a loaded beam.

b) A beam of length L carries a udl and rests on two supports. How far from the ends must

the supports be placed if the greatest bending moment is to be as small as possible?

4. A beam of I section 400mm × 200mm has a web and flange thickness 20mm. Calculate the

maximum intensity of shear stress across the section and sketch the shear stress distribution

across the section of the beam, if it carries a shearing force of 300 kN at a section.

5. A beam AB of length L is loaded with a couple applied at an intermediate point as shown in

Figure. Calculate the slopes at the ends and the deflection under the point of application of

the couple.

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Code No: X0323/R07

6. a) State and explain moment area theorems.

b) Calculate the slope and deflection at the free end of the cantilever shown below, by

moment area method. The beam is having uniform flexural rigidity.

7. a) A thin cylindrical air vessel contains air at a pressure of 10 N/mm2. If the thickness is

10mm, length is 2 m and internal diameter is 500mm, calculate changes in length and

diameter if the young’s modulus of elasticity of the material of cylinder is 2x105 N/mm

2 and

Poisson’s ratio is 0.3.

b) A thin seamless spherical shell of 1.5m diameter is 10mm thick. It is filled with a liquid

so that the internal pressure is 2 N/mm2. Determine the increase in diameter and capacity of

the shell. Take poisson’s ratio =0.3 and E=2x105 N/mm

2.

8. Compare the values of maximum and minimum hoop stresses for a cast steel cylindrical

shell of 600 mm external dia. And 400mm internal dia. Subjected to a pressure of 30

N/mm2 applied

i) Internally and

ii) Externally.

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Code No: X0323/R07


MECHANICS OF SOLIDS





1. a)Define

i) Proof resilience

ii)Bulk modulus of elasticity

iii) Yield point

iv) Poisson’s ratio

b) A compound tube consists of a steel tube 140mm internal diameter and 10mm thickness

and outer brass tube 160mm internal diameter and 10mm thickness. The two tubes are of the

same length. The compound tube carries an axial tensile load of 900kN.

Find the stresses and the load carried by each tube. Also determine the change in length if

the length of each tube is 120mm. Take young’s moduli of elasticity for steel and brass as

2x105N/mm2 and 1x105N/mm

2 respectively.

2. A horizontal beam of 10m long is carrying a uniformly distributed load of 1 kN/m over the

entire length. The beam is simply supported on two supports 6m apart. Find the position of

the supports, so that the BM on the beam is as small as possible. Also draw the SF and BM

diagrams.

3. a) State the assumptions made in the theory of simple bending.

b) A rectangular beam 300mm deep is simply supported over a span of 4 meters.

What uniformly distributed load per meter the beam may carry, if the bending stress is not

to exceed 120 mm2? Take I = 8 × 10

6 mm

4.

4. a) Obtain from first principles the expression for maximum shear stress in a triangular

section of a beam. Sketch the variation of shear stress.

b) A beam of I-section is having overall depth as 600mm and overall width as 200mm. The

thickness of flanges is 25mm where as the thickness of the web is 20mm. If the section

carries a shear force of 55kN, calculate shear stress at salient points and sketch the shear

stress distribution across the section.

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Code No: X0323/R07

5. Determine the maximum deflection for a cantilever beam subjected to a uniform distributed

load of w per unit length. (Fig)

6. a) Derive the equation of the elastic curve of a member subjected to bending.

b) The cross section of a beam is square. In one case its orientation is such that the sides

are vertical. In the second case one diagonal is horizontal. The bending takes place about

the horizontal axis in both cases. For the same allowable stress, determine the ratio of

maximum allowable bending moments.

7. a) A hollow cylindrical drum 500 mm in diameter has a thickness of 10 mm. If the drum is

subjected to an internal pressure of 3 N/mm2, determine the increase in the volume of the

drum. Take young’s modulus of elasticity, E=2x105N/mm

2 and Poisson’s ratio = 0.3.

b) A 2m diameter spherical shell is subjected to an internal pressure of 1.5MN/m2.

Determine the force transmitted across 200mm length of the joint uniting the two halves of

the sphere.

8. State assumptions and derive the Lame’s equations and also sketch the pressure &

hoop stress distribution across the thickness of the shell.

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Code No: X0323/R07


MECHANICS OF SOLIDS





1. Three vertical wires in the same place are suspended from a horizontal support. They are all

of the same length and carry a load by means of a rigid cross bar at their lower ends. One of

the wires is of copper and the two other are of steel. The load is increased and temperature

changed so that the stress in each wire is increased by 10 N/mm2. Find the change of

temperature.

Es =205,000 N/mm2, Ec = 102,000 N/mm

2, �s = 11 x 10

-6/oC, �c = 18 x 10

-6/oC.

2. Draw shear force and bending moment diagrams for the beam shown in Fig. Also indicate

the various ordinates.

3. A steel beam of hollow squares section of 60mm outer side and 50mm inner side is simply

supported over a span of 4 meters. Find the maximum concentrated load the beam can carry

at the middle of the span if the bending stress is not to exceed 150 N/mm2

4. a) Obtain from first principles the expression for shear stress at any point in a circular

section of a beam where it is bujected to a shear force F. Shetch the stress variation.

b) An I-section has the following dimensions.

Top and bottom flanges = 165 mm x 20 mm

Web = 15 mm thick and 200 mm deep

The maximum shear stress developed in the beam is 17 MPa.

Find the shear force to which the beam is subjected.

5. An overhanging beam ABC 8 m long is supported at A and B such that AB = 6 m and the

overhang BC=2m. It has a point load of 3 kN at the end C and a uniformly distributed load

of 2 kN/m run for a length of 2.5 m at a distance of 1 m from the end A. If E=200 x 106

kN/m2 and I = 4.5 x 10

-6m

4.

Determine

Deflection at the free end and Maximum deflection between A and B.

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Code No: X0323/R07

6. A beam simply supported at ends A and B is loaded with two point loads of 60 KN and 40

KN at distance 1m and 4m respectively from end A determine the position and magnitude of

maximum deflection. Take young’s modulus of elasticity as 2x105N/mm

2 and moment of

inertia as 8500 cm4.(Fig)

7. A cylindrical shell is 3 meters long, 1 meter in diameter and is subjected to an internal

pressure of 1.2 N/mm2. If the thickness of the shell is 15mm, find the hoop and longitudinal

stresses. Find also the maximum shear stress and the changes in the dimensions of the shell.

Take E = 2x105 N/mm

2 and poissions ratio, v = 0.3.

8. A cylindrical drum 600mm diameter has to withstand an internal pressure of 1.8N/mm2.

Calculate the necessary wall thickness for a factor of safety of 3 if the criterion for failure is

the maximum strain energy and the elastic limit in pure tension is 237N/mm2. Take poisons

ratio is 0.3.

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Code No: X0323/R07

II B.Tech I Semester

Time: 3 hours


1. a) Differentite between:

i) Primary strain and lateral strain

ii) Direct stress and thermal stress

b) A railway line is so laid that the rails are fre

Calculate.

i) the stress in the rails at 400

ii) if an expansion allowance of 5mm per rail of le

iii) Minimum clearance required to avoid any stress61011 −

×=z

a 200kNEz

=

2. Sketch the shear force and bending moment diagrams

loaded beam shown in the below

3. aA horizontal beam of the section shown in

supported at the ends. Find the maximum uniformly

compressive and tensile stresses must not exceed 50


MECHANICS OF SOLIDS


Max Marks: 80



i) Primary strain and lateral strain

ii) Direct stress and thermal stress

b) A railway line is so laid that the rails are free of stresses at temperature of 20

0C if all expansion is prevented.

ii) if an expansion allowance of 5mm per rail of length 30m.

iii) Minimum clearance required to avoid any stresses at a temperature of 602/ mmkN

Sketch the shear force and bending moment diagrams showing the salient values for the

below figure.

aA horizontal beam of the section shown in below Figure is 3m long and is simply

supported at the ends. Find the maximum uniformly distributed load it can carry if the

compressive and tensile stresses must not exceed 50 N/mm2 and 30 N/mm

2 respectively.

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Max Marks: 80

e of stresses at temperature of 200C.

es at a temperature of 600C.

showing the salient values for the

Figure is 3m long and is simply

distributed load it can carry if the

respectively.

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Code No: X0323/R07

4. Show that the maximum shear stress intensity for a rectangular section of a beam is 1.5

times the average shear stress.

5. Find the forces in the members of the truss.

6. a) A girder of uniform section and constant depth is freely supported over a span of 2.5

meters. Calculate the central deflection and slopes at the ends of the beam under a central

load of 25 kN. Given: I XX = 7.807 × 10-6

m4 and E = 200 GN/m

2 .

b) A simply supported 6 meters long rolled steel joist carries a uniformly distributed load of

9.5 kN/meter length. Determine slope and deflection at a distance of 3 meters from one end

of the beam.

7. a) Derive expression for hoop and longitudinal stresses in a cylinder subjected to an internal

pressure ‘P’.

b) A cylindrical shell is 500mm internal diameter and 10mm thick and I meter long. Find

the change in the internal diameter and the length, when the cylinder is charged with an

internal pressure of 10N/mm2. Take young’s modulus of elasticity, E=2x10

5N/mm

2 and

Poisson’s ratio =0.3.

8. A steel tube of external diameter 200mm is to be shrunk on to another steel tube of 60mm

int, dia. After shrinking, the dia, at the junction is 120mm. Before shrinking on, the

difference in diameter at the junction is 0.08mm. Find the hoop stresses developed in the

two tubes after shrinking on and the radial pressure at junction E=200GPa.

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Code No: X0421/R07

II B.Tech I Semester (R07) Supplementary Examinations, May- 2011

PROBABILITY THEORY AND STOCHASTIC PROCESSES

(Com. to ECE, ECC)




1. a) Explain the following

i) Probability as a Relative Frequency

ii) Conditional probability

iii) Total probability

iv) Bayes’ Theorem. (8M)

b) A missile can be accidently launched if two relays A and B both have failed. The

probabilities of A and B failing are known to be 0.01 and 0.03 respectively. It is also known

that B is more likely to fail (Probability 0.06) is A has failed.

i) What is the probability of an accidental missile launch

ii) What is the probability that A will fail if B has failed

iii) Are the events ‘A’ fails and ‘B’ fails statistically independent (8M)

2. a) Find a value for constant A such that

.1,

11

1,

),2/(cos)1(

0

0

)( 2

x

x

x

xxAxf X

<

≤≤−

−<

−��

��

�

= π

is a valid probability density function. (8M)

b) Write shoes notes on “ Bionomial distribution (8M)

3. a) A random variable X has a pdf

xinelsewhere

xxxf X

22,0

),(cos)()(

21 ππ <<−

��

=

Find the mean value of the function 24)( XXg = (8M)

b) Show that the second moment of any random variable X about an arbitrary point a is

minimum when Xa = (8M)

4. a) Define Joint distribution and state the properties of Joint distribution. (8M)

b) Find the marginal densities of X and Y using the Joint density

��

��

��

��

�+−=

24exp)()(2),(

xyyuxuyxf XY

(8M)

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Code No: X0421/R07

5. a) Statistically independent random variables X and Y have moments m10 = 2, m20 = 14,

m02=12 and m11 = - 6 Find the moment 22µ (8M)

b) Show that the Joint characteristic function of N independent random variables xi , having

characteristic function )(xi i

ωφ is

)(

1

).....1

(.....

1i

iX

i

N

NN

xxωφωωφ

=

Π=

(8M)

6. a) Given the random process

)()()( 00 tSinBtCosAtX ωω += where 0ω is a constant and A and B are uncorrelated zero

mean random variables having different density functions but the same variances 2σ .

Show that X(t) is wide sense stationary but not strictly stationary (8M)

b) Distinguish between Auto correlation and cross correlation. State the properties of auto

correlation function (8M)

7. a) A random process has the power density spectrum

41

26

)(ω

ωωξ

+=XX find the average power in the process (8M)

b) Write short notes on “cross power density spectrum” (8M)

8. a) White noise with power density2

0N is applied to a network with impulse response

)(exp)()( tttuth ωω −= where ω > 0 is a constant. Find the cross correlation of the input

and output (8M)

b) Write short notes on “ Average Noise Figure” (8M)

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Code No: X0421/R07



(Com. to ECE, ECC)




1. a) Distinguish between Joint probability and conditional probability (8M)

b) A coin is tossed an infinite number of times, show that the probability that k heads are

observed at the nth

toss but not earlier equals knk

qpk

n −

��

��

�

−

−

1

1

(8M)

2. a) Define probability density function. State its properties (8M)

b) For a gaussian random variable with 0a = and 1=σ

What is [ ]2x� > and [ ]2>xq (8M)

3. a) Given the Rayleigh random variable from the density function

eb

ax

axb

xf

2)(

)(2

)(

−−

−= )( axu −

Show that the mean and variance are

[ ]4baXE π+=

and 4

42 πσ

−= bx

(8M)

b) Show that any characteristic function )(ωφx satisfies

1)0()( =≤ XX φωφ (8M)

4. a) State and prove the center limit theorem (8M)

b) Find the marginal densities of X and Y using the Joint density function

)()(.2),( .)

24(

yuxuyxf e

xy

XY

+−

= (8M)

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Code No: X0421/R07

5. a) Random variables X and Y have the Joint density

60,40

0),( 24

1 <<<<

��

=y

elsewhere

xyxf XY

Find the expected values of E [ ]2)(XY (8M)

b) Two random variables have a uniform density on a circular region defined by

elsewrere

ryxryxf XY

2222

0

1),(

≤+

��

��

= π

Find the mean value of the function 22),( YXYXg += (8M)

6. a) Explain stationarity and Ergodic random processes (8M)

b) stationary process has an auto correlation function given by

425.6

3625)(

2

2

+

+=

τ

ττR

Find the mean value, mean square value and variance of the process (8M)

7. a) The power spectral density of Random process x(t) is given by

otherwise

forS XX

1

0

1)(

2 <

�� +

=ωω

ω

Find out the auto correlation function R τ (8M)

b) What is cross power density spectrum? State the properties of cross power density

spectrum (8M)

8. a) A random process n(t) has a psd G(f) = 10-4

for .α≤≤− fa The random process is

passed through an LPF whose transfer function is

otherwise

ffffH

MM ≤≤−

��

=0

100)(

Find the psd of the waveform at the 0/p of the filter (8M)

b) Explain the concept of Effective input noise temperature (8M)

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Code No: X0421/R07



(Com. to ECE, ECC)




1. a) Define the probability and state the axioms of probability (5M)

b) State and prove the Baye’s theorem (6M)

c) A letter is taken out at random out of ‘ASSISTANT’ and a letter out of ‘STATISTICS’.

What is the chance that they are same letters (5M)

2. a) A random variable X has a pdf

�� ≤≤−−

=otherwise

xifxcxf X

11

0

)1()(

4

i) Find C

ii) Find [ ]21<Ρ x

iii) Find FX(x) (8M)

b) Define conditional density and state the properties of conditional density (8M)

3. a) For poission distribution, prove that variance is equal to λ . (8M)

b) Find the characteristic function for the following probability density function

��

+=

)()(

22 xxf X

λπ

λ

(8M)

4. a) A joint probability density function is byand

elsewhere

axyxf

ab

XY

<<<<

��

=00

0),(

1

Find and sketch FXY(x,y) (8M)

b) Statistically independent Random variables X and Y have respective densities

)5(exp)(5)( xxuxf X −=

)2(exp)(2)( yyuyfY −=

Find the density of the sum w = X+Y (8M)

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Code No: X0421/R07

5. a) Random variables X and Y have the Joint density

4060

0),( 24

1 <<<<

��

=yand

elsewhere

xyxf XY

Find the expected value of the function

( ) ( )2, XYYXg = (8M)

b) For two zero mean Gaussian random variables X and Y, show that their Joint

characteristic function is ��

��

��

� ++−= 2

22

21yx�22

12

2

1exp)

2,

1( ωσωσσωσωωφ

ywxXY

(8M)

6. a) Assume that an Ergodic random process x(t) has an auto correlation function

�)12(cos416

218)(

2τ

ττ +

++=XXR

i) find X

ii) Does this process have a periodic component

iii) what is the average power in x(t) (8M)

b) What is cross correlation function and state the properties of cross correlation function

(8M)

7. A random process has a power density spectrum

[ ]32

2

1

6)(

w

wwS XX

+=

Find the average power in the process (8M)

b) Power spectrum and auto correlation function are Fourier transform pair. Prove this

statement (8M)

8. a) What is system Response and Discuss the spectral characteristics of system Response

(8M)

b) An amplifier has 3 stages for which Te1 = 200 K(First stage), Te2 = 450 K and

Te3 = 1000 k (Last stage). If the available power gain of the second stage is 5, what gain

must the first stage have to guarantee an effective input noise temperature of 250 K?

(8M)

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Code No: X0421/R07

II B.Tech I Semester (R07) Supplementery Examinations, May- 2011


(Com. to ECE, ECC)




1. a) Explain the following.

i) Probability

ii) Joint probability

iii) Bayes’ theorem

iv) Independent Events (8M)

b) In a factory 4 machines A1, A2, A3, A4 Produce 10%, 20%, 30%, 40% of the items

respectively. The percentage of defective items produced by them is 5%, 4%, 3%, and 2%

respectively. An item selected at random is found to be defective what is the probability that

it was produced by the machine A2 (8M)

2. a) Let x be a continuous random variable with distribution function

60;9

)( ≤≤+= xkx

xf

= otherwise0

i) Find the value of k

ii) Find [ ]5x2.� ≤≤ (8M)

b) Write short notes on “ Rayleigh distribution” (8M)

3. Let X be a continuous random variable with pdf

a) 51;12

)( <<= xx

xf

= elsewhere0

Find the probability density function of Y=2X-3 (6M)

b) If X is a random variable, show that

var (ax+b) =a2 var (x) (5M)

c) A random variable x has pdf

nxxfx

...3,2,1;2

1)( ==

Find the moment generation function. M(t) (5M)

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Code No: X0421/R07

4. a) The Joint pdf of two random variables X and Y

α

α

≤<

≤≤

++

++=

y

x

yx

yxyxf XY

0

0

)1()1(2

)1((9),(

44

Find the marginal distribution of x and y (8M)

b) If x and two random variables which are Gaussian, if new random variable is defined as

z = x + y, find fZ(z). (8M)

5. a) Two random variables x and y have the density function

��

��

�+

=elsewhere

yxyxf YX

0

)5.0(43

2

),(2

, 3020 <<<< yandx

i) Find the first and second order moments

ii) Find the convanice

iii) Are X and Y uncorrelated (8M)

b) For N random variables show that 1)0......,0(......

1

)......1

(.....

1

=≤N

xxNN

xxφωωφ

(8M)

6. a) Explain the following

i) Wide sense stationary Random process

ii) Correlation Ergodic Random process (8M)

b) A stationary ergodic random process has the Autocorrelation function with the periodic

components is 261

425)(

ττ

++=XXR

Find the mean and variance of X(t) (8M)

7. a) State and prove the properties of cross correlation function (8M)

b) The Auto correlation of periodic random process is

.2

exp)(2

2

��

��

−=

σ

ττXXR Find the power spectres density and the average power of the signal

(8M)

8. a) X(t) is a stationary random process with zero mean and Auto correlation eRXX

ττ

2)(

−=

is applied to a system of function 2

1)(

+=

ωω

jH . Find the mean and PSD of its output

b) Show that the effective noise temperature of ‘n’ networks in cascade is given by

12121

3

1

21

....,.....

−

++++=n

eggg

Ten

gg

Te

g

TeTeT

(8M+8M)

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Code No: X0522/R07


MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

(Com. to CSE, IT)




�

1. a) Using the statements: (8M)

R: Mark is rich

H: Mark is happy

Write the following statements in symbolic form:

i) Mark is poor but Happy

ii) Mark is rich or unhappy

iii) Mark is neither rich nor happy

iv) Mark is poor he is both rich and unhappy

b) Show that ( ) ( ) ( ) RQPQVRPRQP →Λ⇔¬→⇔→→ (8M)

2. a) Explain the two rules of interference. Using rules of interference demonstrate that

R is a valid inference from the premises ,QP → RQ → and P (8M)

b) Let ( ) xxP : is a person

( ) xyxF :, is the father of y.

( ) xyxM :, is the mother of y.

Write the predicate

i) “x is the father of the mother of y”

ii) “x is the mother of the father of y” (8M)

3. a) Explain the properties of binary relations in a set. (8M)

b) Show that the function ( ) yxyxf +=, is primitive recursive. (8M)

4. a) Define the following: (8M)

i) Homomorphism

ii) Epimorphism

iii) Monomorphism.

iv) Isomorphism.

b) Prove that every row or column in the composition table of a group >∗< ,G is a

permutation of the elements of G. (8M)

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5. a) Find the number of 5–digit integers that contain the digit 6 exactly once. (6M)

b)State and prove the principle of Inclusion – Exclusion for n sets. (10M)

6. a) Obtain the generating function for the sequence arwhere ar = 0 for

)1(0 −<< nr and ��

��

�

−

−=

1

1

n

rar

for nr ≥ (8M)

b) Solve the recurrence relation an = 7an-1, where n ≥ 1, given that a2 = 98. (8M)

7. With an example explain the working of Prim’s algorithm to find the minimal spanning tree.

(16M)

8. a) When do we say two graphs are isomorphic? Give an example (8M)

b) Prove that “A connected graph G has an Euler circuit if and only if all vertices of G are of

even degree.” (8M)

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Code No: X0522/R07



(Com. to CSE, IT)




�� a) Give the truth tables for conjunction and disjunction. (4M)

b) State whether the following is a well formed formula or not. If not state why. (4M)

i) ( ) ( )QQP ∧→→ ii) ( ) )QQP →∧

c) Obtain the principal disjunctive normal form of ( ) ( ) ( )RQRPQP ∧∨∧¬∨∧ (8M)

�� a) Derive the following, using rule CP if necessary. (8M)

.,, SPSRRQQP →�→∨¬∨¬

b) Indicate the variables that are free and bound. Also show the scope of the Quantifiers.

i) ( )x ( ) ( )( ) ( ) ( ) ( )xQxPxxRxP ∧→∧

ii) ( )x ( ) ( ) ( ) ( )( ) ( )xSxRxxQxP ∧∃∧⇔ (8M)

�� a) If relations R and S are reflexive, symmetric and transitive, show that R ∩ S is also

reflexive, symmetric and transitive. (8M)

b) If yxf →: and zyg →: and both f and g are onto, show that g o f is also onto. Is g o f

one-to-one if both g and f are one-to-one? (8M)

�� a) Define

i) Semigroup

ii) Monoid

iii) Abelian group (6M)

b) Let G be the set of all non-zero real numbers and let abba2

1* = . Show that ∗,G is an

abelian group. (10M)

�� a) How many positive integers n can we form using the digits 3,4,4,5,5,6,7, if we want n to

exceed 5,000,000? (8M)

b) Find the number of integer solutions of the equation

20321

=++ xxx such that 92,74,52321

≤≤−≤≤≤≤ xxx (8M)

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�� a)Determine the co-efficient of

i) x12

in ( )10321 xx −

ii) x5 in ( ) 7

21−

− x

iii) x20

in ( )565432

xxxxx ++++ (8M)

b) Solve the recurrence ration aa nnn

1−= for 1≥n given that 1

0=a (8M)

� Explain with an example Kruskal’s method to find the minimal spanning tree. (16M)

� a) Show that two graphs need not be isomorphic even if they have equal number of vertices,

equal number of edges and equal number of vertices with the same degree (8M)

b) Prove if the complete graph with n vertices, where n is an odd number ,3≥ three are

( )2

1−n edge – disjoint Hamiltonian cycles. (8M)

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Code No: X0522/R07



(Com. to CSE, IT)




1. a) What are the rules for generating a well formed formula? Give an example for wff.

(6M)

b) Obtain the principal conjunctive and disjunctive normal forms of the following formula

( ) ( )(( )RQPRQP ¬∧¬→¬∧∧→ (10M)

2. a) Show the following (use indirect method if needed)

( ) ( ) ( )( ) QPRRPQSRQP ⇔�¬∨→∨¬→→¬ ,, (8M)

b) Symbolize the expressions:

i) “All the world loves and lover”

ii) “x is the father of the mother of y” (8M)

3. a) Let R denote a relation on the set of ordered pairs of positive integers such that

vuRyx ,, iff xv = yu. show that R is an equivalence relation. (8M)

b) Let RRf →: be given by ( ) 23−= xxf find f

1−

(8M)

4. a) Show that the set N of naturel numbers is a semigroup under the operation (8M)

{ }yxyx ,max=∗ . Is it a monoid.

b) Prove that H is a subgroup of G if and only if, for all a,b � H, we have

ab-1

� H (8M)

5. a)Find the number of committees of 5 that can be selected from 7 men and 5 women if the

committee is to consist of at least 1 man and at least 1 woman. (8M)

b)State and prove multinomial Theorem. (8M)

6. a) Find the recurrence relation and the initial condition for the sequence 2,10,50,250…

Hence find the general term of the sequence. (8M)

b)Solve the recurrence relation 21,,0201

2=≥=− − aa nann

(8M)

7. Explain DFS algorithm for graph traversal with an example. (16M)

8. a) A Define

i) Edge –disjoint sub graphs

ii) Vertex – disjoint sub graphs

iii) isomorphic graphs (6M)

b) Define Euler circuit. Prove that “A connected graph G has Euler circuit if and only if G

can be decomposed into edge-disjoint cycles.” (10M)

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Code No: X0522/R07



(Com. to CSE, IT)




1. a) What is tautology? Check whether the following formula is tautology or contradiction.

( )( ) ( ) )( )( )RPQPRQP →→→→→→ (8M)

b) Obtain the product of sums canonical form of the following formula. (8M)

( ) ( ) ( )RQPQRPRQP ¬∧¬∧¬∨∧∧¬∨∧∧

2. a) Derive the following, using rule CP if necessary

( )( ) SQSRQPP →�∧→→, (8M)

b) Explain the rules to obtain a well formed formula of predicate calculus. (8M)

3. a) Give a covering of the set { }nAAAS ,.....,, 21= , show how we can write a compability

relation which defines the covering. (8M)

b) Show that if any eight positive integers are chosen, two of them will have the same

remainder when divided by 7. (8M)

4. a) Define:

i) Group, ii) Abelian group, iii) Sub group. (6M)

b) Prove that every finite group of order n is isomorphic to a permutation group of degree n.

(10M)

5. a) Find the number of ways of selecting 4 persons out of 12 persons to a party if two of them

will not attend the party together. (8M)

b) Determine the number of integer between 1 and 300 (inclusive) which are

i) Divisible by exactly two of 5,6,8, and

ii) Divisible by atleast two 5,6,8 (8M)

6. Solve the following recurrence relations.

i) 5,0,043 11 =≥=−+

anaa nn

ii) 1,0,52 01=≥=−

+ananna

iii) 81,1,032 41 =≥=−−

anaa nn (16M)

7. Explain BFS graph traversal technique with an example. (16M)

8. a) What is chromatic number? Prove that every connected simple planar graph G is 6 –

colorable (10M)

b) Prove the following (6M)

i) A path n vertices is of length n-1

ii) If a cycle has n vertices, it has n edges.

iii) The degree of every vertex in a cycle is two.

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Code No: W0821/R07


MOMENTUM TRANSFER

(CHEMICAL ENGINEERING)




1. In the orifice meter, a flat disk with a central opening of diameter D0 is set across a pipe of

diameter D, and the pressure drop �p is a function of the average fluid velocity in the pipe

V, the density of the fluid �, the fluid viscosity µ, and the diameters of the pipe and the

opening, D and D0, respectively. Thus �p = � (V, �, µ, D, D0), find an acceptable set of

dimensionless groups which relate these various factors. 16M)

2. Derive equation of motion for Newtonian fluid and write assumptions made to derive the

equation. (16M)

3. a)Explain the terms

i)Pipes in parallel

ii) Equivalent pipe (6M)

b) A single pipe of 30 cm diameter, 300m. long conveys a discharge of 0.1 m3/sec. What

length of another 40 cm diameter pipe is required to be placed in parallel with the existing

pipe in order to augment the discharge by 30%? Take = f =0.015 and neglect the minor

losses. (10M)

4. Write a short note son the

a)Isentropic expansion

b)Adiabatic friction flow

c) Isothermal friction flow (5M+6M+5M)

5. a) Explain briefly drag forces (4M)

b) Explain creeping flow (4M)

c) Calculate the terminal velocity of the spherical droplets of coffee extract 450 microns

diameter falling through the air specific gravity of coffee extract is 1.06 and air is at a

temperature of 1500c. Assume free settling conditions viscosity of air is 0.028cp. (8M)

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6. To clean a sand bed filter it is fluidized at minimum conditions using water at 240C.The

round sand particles have a density of 2550 kg/m3 and an average size of 0.40mm.The sand

has �s=0.86 and �M is taken as 0.42.

i)The bed diameter is 0.40 m and the desired height of the bed at these minimum fluidizing

conditions is 1.75 m. Calculate the amount of solids needed.

ii)Calculate the pressure drop at these conditions and the minimum velocity for fluidization.

iii)Using 4.0 times the minimum velocity, estimate the porosity and height of the expanded

bed. (16M)

7. A liquid is pumped from a reservoir to the top of the mountain through a pipe of ID of

0.1396 meter at an average velocity of 3.048 m/s the pipe discharges into the atmospheres at

a level of 1219 meters above the level in the reservoir. The pipe line itself is 1524 m long if

the efficiency of the pump is 70 percent and if it costs 50 paisa/kW-hr. What is the hourly

energy cost for pumping? Assuming entrance and exit losses negligible. (16M)

8. a) Explain in detail about positive displacement blower with neat sketch. (8M)

b) A pitot static tube having a coefficient of 0.98 is used to measure the point velocity of

water flowing through a pipe. The stagnation pressure recorded is 3 m and the static pressure

is 2m. Evaluate the point velocity. (8M)

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Code No: W0821/R07


MOMENTUM TRANSFER





1. A steady stream of liquid in turbulent flow is heated by passing it through a long, straight,

heated pipe. The temperature of the pipe is assumed to be greater by a constant amount than

the average temperature of the liquid. Therefore, the rate of heat transfer is function of

diameter, velocity, density, viscosity, heat capacity, thermal conductivity and difference

temperatures. It is desired to find relationship that can be used to predict the rate of heat

transfer from the wall of the liquid using Buckingham dimensionless analysis. (16M)

2. a) Water at room temperature flows through a smooth straight pipe A of internal diameter

4cm at an average velocity of 42cm/sec. Oil flows through another pipe B of internal

diameter 12.5 cm at such a velocity that dynamic similarity exists between the two streams.

Calculate the velocity through pipe B. (Specific Gravity of oil = 0.85, viscosity of oil = 2 cp

and viscosity of water = 1 cp.) (10M)

b) Write Navier stoke’s equation and Euler equation in vector form (6M)

3. a) Water is flowing in a smooth pipe of diameter 20 cm. Determine at what radius the point

velocity is equal to the average velocity when the flow is laminar. (6M)

b) A liquid is flowing in a closed conduit having a rectangular cross section with sides 0.03

and 0.02.m.the flow rate of the liquid is 43.2 kg/min. calculate the pressure drop per meter

length of the conduit. Kinematics viscosity = 1.0x10 6− m 2 /s ; Density = 1000 kg/m

Friction factor f = 16/NRe ,for NRe < 2000

F = 0.079 25.0

Re

−N , for NRe> 2000 (10M)

4. a) Explain briefly isentropic flow through convergent – divergent nozzles with neat sketch.

(8M)

b) Explain briefly about critical pressure ratio (4M)

c) Write the effect of cross section on Mach number for isentropic flow (4M)

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Code No: W0821/R07

5. a) What do you mean by Drag and Drag coefficient? How do you estimate Drag coefficient

for Stoke’s law regime? (8M)

b) What is Ergun equation? How do you estimate pressure loss in a packed bed? (8M)

6. a) Write short notes on continuous fluidization (8M)

b) Derive an expression for minimum fluidization velocity (8M)

7. Water at 15.56°C (600 F) is pumped from a reservoir to a top of a mountain through a 2.5

cm I.D. pipe at an average velocity of 3.048 m/sec the pipe discharges into atmosphere at a

level of 1500 m above the reservoir. The pipeline itself is 1600 m long. If the overall

efficiency of the pipe is 70% and if the cost of electrical energy to the motor is 2 Rs./kWh.

What is the hourly energy cost for pumping this water? (16M)

8. a) Explain briefly centrifugal blower with neat sketch (6M)

b) A pitot tube having a coefficient of 0.95 is inserted in the central line of a long smooth

pipe of 250mm diameter in which crude oil of density 0.9 g/cc. and viscosity 16.3 c.p. is

flowing .Calculate the maximum velocity of oil in the pipe if the differential pressure in the

manometer is 5 cm of water. (10M)

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Code No: W0821/R07


MOMENTUM TRANSFER





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1. a) Explain briefly applications of dimensional analysis

b) Determine the dimension less groups formed from the variables involved in the flow of

fluid external to a solid. The force exacted on the body is a function of velocity of the fluid,

density of the fluid, viscosity of the fluid and characteristic length L. Use Buckingham �

method (8M+8M)

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2. a)(i)Estimate the Reynolds number for flow in an entrance to a 15mm tube through which

100%glycerol at 600C is flowing at a velocity of 0.3 m/s. The density of glycerol is 1240 kg/

m3

(ii) Repeat part (i) for 100% n-propyl alcohol entering a 3 inch pipe at 300C and a

velocity of 7ft/s .The density of propyl alcohol is 50lb/ft3

(8M)

b) Define substantial derivative (4M)

c) Write equation of continuity for incompressible fluids (4M)

3. A liquid having a density of 801 kg/m3 and a viscosity of 1.49x10

-3 pas is flowing through a

horizontal straight pipe at a velocity of 4.57 m/s. The commercial steel pipe is 1.5 inch

nominal pipe size, schedule 40. For a length of pipe of 61 m, do as follows.

i) Calculate the friction loss

ii) For a smooth tube of the same inside diameter, calculate the friction loss. What is the

percent reduction of the friction loss for a smooth tube?

(Friction factor versus Reynolds number charts should be provided) (16M)

4. a)A gas at pressure 75 kN/m2 and temperature 313 K is flowing through a horizontal pie

with a velocity 300 kN/m2. Find the velocity of the gas at this section of flow. (10M)

b) Differentiate sonic and subsonic velocities. (6M)

5. a) Explain briefly about wake formation for the flow of fluid over sphere with neat sketch

b) What you understand about stagnation pressure

c) Explain briefly the concept of terminal velocity (8M+4M+4M)

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�

6. a) Write short notes on applications of fluidization? (6M)

b) Derive an expression for bed height for given bubbling fluidization velocity? (10M)

7. a) Explain the effect of any three types of pipe fitting on the discharge of a fluid flowing

through a pipe line. (8M)

b) A theoretical head of 10.6 m is produced by the impeller of a centrifugal pump rotating at

570 rpm. If its larger diameter is 38 cm and vanes are set at 40 0 to its external periphery,

what is the radial velocity of flow? (8M)

8. a) Explain in detail about positive displacement blower with neat sketch. (6M)

b) A rotameter has a 30 cm long tube with ID of 2.5 cm at the top and 1.8 cm at the bottom.

The float has 1.8 cm diameter with specific gravity 5.8 and a volume of 60 cm3. If the co-

efficient of the motor is 0.72, at what height will the float be when metering water at 0.1

lit/sec (10M)

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Code No: W0821/R07


MOMENTUM TRANSFER





�

1. a) Explain the merits and demerits of dimensional analysis. (6M)

b) Show that in a simple inclined tube manometer:

P∆ = Ri (PA-PB ) sin θ , Where ∆ P is the pressure difference, Ri is the level difference of

liquid in the manometer measured along the inclined tube, PA�and PB �are the densities of

the manometric fluid and fluid flowing respectively and θ is the angle of inclination of the

tube to horizontal. (10M)

2. a) Differentiate between time dependent and time independent fluids with suitable examples

(6M)

b) A liquid as a kinematic viscosity of 0.052 stokes and a density of 970kg / m 3 . It fills the

space between two parallel plate 0.1cm apart. What force, expressed in Newton’s, is

required to move 1plate past the another stationery with velocity of 0.2cm /sec? The moving

plate has area of 10000cm 2 (10M)

3. Prove that the flow of a liquid in laminar flow between infinite parallel flat plates in given

by Pa-Pb = [(12µV L)/ a2gc] where L = length of plate in direction of flow, a=distance

between plates , V is the average velocity Neglect end effects. (16M)

4. What is friction parameter? Derive relation to friction parameter for adiabatic friction flow.

(16M)

5. a) Write a brief note on hindered settling and explain how it is different from free settling

(8M)

b) What is the drag on a 0.012 m diameter sphere that drops at a rate of 0.08 m/s in oil of

viscosity 0.1 NS/m2 and specific gravity 0.0852 Assume the drag coefficient as 5.3 (8M)

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6. a) A tower having a diameter of 0.1524 m is being fluidized with water at 20.20

C. The

uniform spherical beads in the tower bed have a diameter of 4.42 mm and a density of 1603

kg/m3

. Estimate the minimum fluidizing velocity and compare with the experimental value

of 0.02307 m/s (8M)

b) Write different types of fluidization with their advantages (8M)

7. a) A solution of density 1.25 g/cc and viscosity of 0.63 cp is pumped from an open tank at

the rate of 200 lit/min through a straight pipe of 25 mm ID and 80 m long. Calculate the

H.P. required. Given that overall efficiency of the pump is 60% and f is equal to 0.079 Re-

0.25 for turbulent flow and f=16/NRe for laminar flow. Neglect fittings. (10M)

b) Write advantages and disadvantages of welding (6M)

8. a) Derive an expression for work compression for adiabatic compressor. (6M)

b) Dry air at 20oC and 1 atm pressure flows through a pipe of ID 320mm.A Pitot-Prandtl

tube is installed at the middle of the pipe. Its differential manometer with water shows a

level difference of H=5.8 mm. Calculate the mass flow rate of air. (10M)

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Code No: W1021/R07


ELECTRO MAGNETIC WAVES AND TRANSMISSION LINES (Electronics and Instrumentation Engineering)




Smith Chart may be supplied.

1. a) Derive expression for electric field intensity E at any point in space due to a finite line

charge placed on the z – axis.

b) Three sides of an equilateral triangle have uniform line charges 2�C/m, 1�C/m, and 1�C/m.

Find E at the centre of the triangle if each side is 50cm long.

2. a) Derive the expressions for magnetic field intensity H in different regions of long co-axial

transmission line.

b) A circular loop located on x2 + y

2 = 9, z = 0 carries a direct current of 10 A along a��.

Determine magnetic field intensity H at (0, 0, 4) and (0, 0, -4).

3. a) What are the boundary conditions of the magnetic field? Explain.

b) Medium 1 (z < 0) is filled with a material whose relative permeability is six, and medium 2

(z > 0) is filled with a material whose relative permeability is 4. If the interface carries current

of ay/µ0 mA/m, and B2 = 5ax + 8az mWb/m2, find H1 and B1.

4. a) Prove that for a good conductor the intrinsic impedance of a plane wave δσ

η

11 j+=

b) In certain medium E = 10 cos(2�107t – �x) (ay + az) V/m. If � = 2�0, � = 50�0, and � = 0,

find � and H.

5. a) State and prove the Poynting’s theorem with regard to EM wave propagation.

b) At frequencies of 1, 100, and 3000 MHz, the dielectric constant of ice made from pure

water has values of 4.15, 3.45, and 3.20 respectively, while the loss tangent is 0.12, 0.035, and

0.0009, also respectively. If a uniform wave with an amplitude of 100 V/m at z = 0 is

propagating through such ice, find the time-average power density at z = 0 and z = 10 m for

each frequency.

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6. a) Can there be any difference between TE and TM modes with regard to guided wavelength,

phase velocity, and wave impedance? Justify your answer.

b) In an air filled rectangular waveguide with dimensions 2.286 × 1.016 cm, the y-component

of the TE mode is given by Ey = sin(2�x / a) cos(2�x / b) sin(10� × 1010

t – �z) V/m. Find the

propagation constant and the intrinsic impedance.

7. a) State and explain the terms: Lossless line and distortion-less line.

b) A distortion-less line has the following parameters: Characteristic impedance Z0 = 60 ohms,

attenuation constant � = 20 mNp/m, wave velocity u = sixty percent of velocity of light. Find

the primary constants of the transmission line at 100 MHz.

8. a) Using Smith chart, calculate the position and length of a short circuited stub designed to

match a 200 ohm load to a transmission line whose characteristic impedance is 300 ohms.

Also calculate the SWR on the main line when the frequency is increased by ten percent,

assuming that the load and line impedances remain constant.

b) Describe the characteristics and importance of quarter and half-wave transmission lines in

detail.

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1. a) A parallel plate capacitor with free space between the plates is connected to a constant source of

voltage. Determine how electrostatic energy WE, capacitance C, total charge Q, and surface charge

density �s change as dielectric of �r = 2.0 is inserted between the plates.

b) In spherical co-ordinates, potential V = 0 for r = 0.1m and V = 100 V for r = 2.0 m. Assuming free

space between these concentric spherical shells, find E and D.

2. a) With suitable sketches, derive the expression for magnetic field intensity H of finite current element.

b)The magnetic vector potential of a current distribution in free space is given by

φρ sin15 −= eA az Wb/m. Find H at (3, �/4, -10). Also find the flux through � = 5, ,2/0 πφ ≤≤

100 ≤≤ z .

3. a) Write the Maxwell’s equations for time varying fields in

i) point form,

ii) integral form, and

iii) differential form. Give word statement of each equation.

b) The surface y = 0 is a perfectly conducting plane, while the region y > 0 has �r =5, �r = 3, and � = 0.

Let E = 20 cos(2× 1010t – 2.58z) ay V/m for y > 0, and find at t = 6 ns;

i) H at point P (2, 0, 0.3);

ii) linear current density K at P.

4. a) Show that the phase relationship (in time) between the electric and magnetic fields depends on the

medium.

b) A lossy dielectric has an intrinsic impedance of 200 ∠ 300 at a particular frequency. If at that

frequency, the plane wave propagating through the dielectric has the magnetic field component

)5.0cos()exp(10 xtx −−= ωαH ay A/m, find E and �. Also determine the skin depth.

5. a) Derive an expression for reflection coefficient � when a plane wave incident normally on an

interface between two different media.

b) In free space (z 0), a plane wave with H = 10 cos(2� ×108t -�z) ax mA/m is incident normally on

a lossless medium (� = 2�0, � = 8�0) in region z 0. Determine the reflected and transmitted waves

(both Electric and magnetic fields).

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6. a) Obtain expressions for the cut-off frequency and phase velocity in the rectangular waveguide

starting from the field expressions of TE modes.

b) A rectangular air-filled waveguide has a cross section of 80 × 40 mm. Find cut-off wavelength for

dominant mode. How many modes are passed at 2.5 times cut-off frequency?

7. a) Derive the expression for characteristic impedance of a transmission line in terms of primary

constants of the line.

b) A telephone line has R = 30 ohms/km, L = 100 mH/km, C = 20µF/km, and G =0. At frequency of 1

kHz, determine the characteristic impedance of the line, the propagation constant and the phase

velocity.

8. a) Show that a lossy transmission line of length ‘l’ has an input impedance of Z0 tanh�l when shorted

and Z0 coth�l when open.

b) A quarter-wave lossless 100 ohm line is terminated by a load of 210 ohms. If the voltage at the

receiving end is 80 V, what is the voltage at the sending end?

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Smith Chart may be supplied.

1. a) State and prove Gauss’s law. Give three applications of Gauss’s law with suitable examples.

b) Given that electric flux density D = z ρ cos2φ az C/m

2, use Gauss’s law to calculate the

charge density at (1, 4/π , 3) and the total charge enclosed by the cylinder of radius of 1 m with

-2 2≤≤ z .

2. a) What is magnetic dipole? Determine magnetic field at any point P in a free space due to a magnetic

dipole.

b) A small current loop L1 with magnetic moment 5 az A/m2 is located at the origin while another

small loop current L2 with magnetic moment 3 ay A.m2 is located at (4, -3, 10). Determine the torque

on L2.

3. a) Describe the concept of displacement current density with suitable example and derive the

Maxwell’s equation which incorporates the displacement current.

b) A conducting circular loop of radius 20 cm lies in the z = 0 plane in a magnetic field B = 10

cos(377t) az mWb/m2. Calculate the induced voltage in the loop.

4. a) Show that in a good conductor, the skin depth is always much shorter than the wavelength.

b) Perfectly conducting cylinders with radii of 8 mm and 20 mm are coaxial. The region between the

cylinders is filled with a perfect dielectric for which � = 10-9/4� F/m. and �r = 1. If E = (500/�) cos(�t –

4z) a� V/m in this region, find H, � with the help of Maxwell’s equations in cylindrical coordinates.

5. a) Illustrate the power balance for EM fields with suitable sketches. Get the expression for time

average power crossing from a given surface S and time average Poynting vector.

b) A uniform plane wave in air with H = 4sin(�t – 5x) ay A/m is normally incident on a plastic region

with parameters � = 4�0, � = �0, � = 0. Obtain the total electric field in air, and calculate the time

average power density in the plastic region.

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6. a) Can there be any difference between TE and TM modes with regard to guided wavelength, phase

velocity, and wave impedance? Justify your answer.

b) In an air filled rectangular waveguide with dimensions 2.286 × 1.016 cm, the y-component of the

TE mode is given by Ey = sin(2�x/a) cos(2�x/b) sin(10� × 1010t – �z) V/m. Find the propagation

constant and the intrinsic impedance.

7. a) Discuss about the primary and secondary parameters of the transmission line.

b) A 600 ohm transmission line is 150 m long, operates at 400 kHz with attenuation constant of 2.4 m

Np/m, and phase shift constant of 0.0212 rad/m, and supplies a load impedance ZL = 424.3 450 ohms.

Find the length of the line in wavelengths, and impedance at sending end Zs. For a received voltage

VR = 50 V, find Vs, the portion on the line where the voltage is maximum and find maximum voltage.

8. a) What is a Smith chart? What are its applications?

b) Using a Smith chart, calculate the position and length of a stub designed to match a 100 ohm load to

a 50 ohm line, the stub being short circuited. If this matching is correct at 63 MHz, what will be the

SWR on the main line at 70 MHz? Note that the load is a pure resistance.

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1. a) Give the general procedure in solving a given boundary value problem involving Poisson’s

equation.

b) In free space, V = 6xy2z + 8. At point P(1,2,-5), find the electric field intensity E and volume charge

density.

2. a) Determine magnetic field intensity H at any point in free space due to any straight filamentary

conductor of finite length directed along z – axis.

b) A circular loop located on x2 + y

2 = 9, z = 0 carries a direct current of 10 A along a��. Determine

magnetic field intensity H at (0, 0, 4) and (0, 0, -4).

3. a) Write the Maxwell’s equations for time varying fields in

i) point form,

ii) integral form, and

iii) differential form. Give word statement of each equation.

b) A parallel plate capacitor with plate area of 5 cm2 and plate separation of 3 mm has voltage 50

sin(1000t) V applied to its plates. Calculate the displacement current assuming � = 2�0.

4. a) Draw the time-phase relationship between conduction current density and displacement current

density.

b) What is loss tangent? Deduce the expression for the loss tangent.

5. a) Obtain the expression for reflection coefficient when a uniform plane wave is obliquely incident

and parallel polarized.

b)In a non-magnetic medium, given an electric field intensity E = 4sin(2� ×107t -0.8x) az V/m find

time averaged power carried by the EM wave and the total power crossing 100 cm2 of plane 2x +y = 5.

6. a) Prove that the wave propagates through rectangular waveguide in its dominant mode is combination

of two uniform plane waves.

b) A rectangular air-filled waveguide has a cross section of 80 × 40 mm. Find cut-off wavelength for

dominant mode. How many modes are passed at 2.5 times cut-off frequency?

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7. a) What is the condition for eliminating frequency distortion on the line? Derive the expression.

b) A simulated line is composed of T sections of pure resistance Z1 = Z2 = 50 ohms, Z3 = 4000 ohms. If

a line composed of 50 such sections in series is terminated in its characteristic impedance, and a

generator of 1V, 400 ohms internal resistance is connected at the sending end, find sending and

receiving currents.

8. a) Show that a transmission coefficient is 2ZL/( ZL + Z0), where ZL, and Z0 are load & characteristic

impedances of the line respectively.

b) Find the transmission coefficient when the line is terminated by

i) short circuit

ii) open circuit

iii) Z0 (matched line).

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II B.Tech I Semester Supplementary Examinations, April/May 2011ANATOMY AND PHYSIOLOGY

(Bio-Medical Engineering)Time: 3 hours Max Marks: 80


? ? ? ? ?

1. What are cranial bones? What is a suture and discuss its types? [16]

2. What are semi-circular ducts? Discuss about cochlea. [16]

3. Write a detailed note on the blood vessels? [16]

4. Write short notes on

(a) Trachea

(b) Pharynx

(c) Pulmonary ventilation. [5+5+6]

5. Describe the histology, location, hormones and functions of the pituitary gland?[16]

6. How does the gastrointestinal tract differ from accessory structures of digestion?[16]

7. Write short notes on:

(a) Spleen

(b) Lymphatic modules. [8+8]

8. Write the structure and the functioning of the renal corpuscle and renal tubule?[16]

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1. Discuss about the anatomy of muscles. What is tubercle? [16]

2. Explain the structure and functions of neuron? [16]

3. Write about the major blood vessels? Discuss about Aorta? [16]

4. Illustrate the physiology of lung with a neat sketch. [16]

5. Write the effect of Iodine on thyroid gland. What are gigantism and Dwarfism?[16]

6. Describe the composition of the saliva and the role of each of its components.[16]

7. What are Lymph Nodes? Discuss about the spleen with a neat structure. [16]

8. Describe the urinary tract with the help of a neat diagram? Write the functions ofthe kidney? [16]

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1. What is sliding filament mechanism occurring in muscle fiber? What is musclebone? [16]

2. Explain how each of the following events related to the phsiology of vision

(a) Refraction of light

(b) Accomodation of the lens

(c) Construction of pupil. [5+5+6]

3. Write briefly on:

(a) Blood plasma

(b) R.B.C [8+8]

4. Discuss about the lung volumes and capacities. What is pulmonary ventilation?[16]

5. Describe the location, histology, hormones and functions of the following endocrineglands:

(a) Parathyroid

(b) Adrenal Gland. [8+8]

6. What are the functions of liver? Write the structure of the liver? [16]

7. What are Lymph Nodes? Discuss about the spleen with a neat structure. [16]

8. What is chronic renal failure? Explain the blood and nerve supply to the kidney?Sketch kidney and label it? [16]

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1. What is a motor unit? Explain the phases of Twitch contraction with musclecontraction? Specify the abnormal contractions of skeletal muscles? [16]

2. Describe the external anatomy of spinal cord in detail? Define Pia-meter? [16]

3. Discuss the external and internal anatomy of the chambers of the heart? [16]

4. What is Spirometer? Define and explain the various lung capacities and volumesin detail. [16]

5. Explain the working of endocrine regulatory system? [16]

6. What are the functions of liver? Write the structure of the liver? [16]

7. Write short notes on:

(a) Spleen

(b) Lymphatic modules. [8+8]

8. Explain the counter current mechanism in detail? Write a short notes on Bowmenscapsule? [16]

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II B.Tech I Semester Supplementary Examinations, April/May 2011MECHANICS OF FLUIDS(Aeronautical Engineering)

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

All Questions carry equal marks? ? ? ? ?

1. (a) Calculate the specific weight, specific mass, specific volume and specific gravityof a liquid having a volume of 6 m

3 and weight of 44 kN.

(b) Distinguish between simple manometer and a differential manometer. [8+8]

2. (a) For a three-dimensional flow the velocity distribution is given by u = -x,v =3-y and w= 3-z. What is the equation of a streamline passing through (1,2,2)

(b) A steady flow can be non-uniform. Discuss. [10+6]

3. An open circuit wind tunnel draws air from the atmosphere through a well con-toured nozzle. In the test section, where the flow is straight and nearly uniform,a static pressure tap is drilled into the tunnel wall. A manometer connected tothe tap shows that the wall pressure within the tunnel is 45 mm of water be-low atmospheric. Assume that air is incompressible and at 250 C, pressure is 100Kpa(absolute). Calculate the velocity in the wind tunnel section. Density of wateris 999kg/m3 and characteristic gas constant for air is 287 J/Kg K. [16]

4. (a) A venturimeter is installed in a pipeline carrying water and is 30cm in diame-ter. The throat diameter is 12.5. The pressure in pipeline is 140 KN/m2 andthe vacuum in the throat is 37.5 cm of mercury. 4 % of the differential headis lost between the gauge. Working from first principle find the rate of flow inthe pipeline in lit/sec, assuming the venturimeter to be horizontal.

(b) Write short notes in [9+7]

i. venturimeter

ii. Orificemeter

iii. Notches & weirs.

5. (a) What are different types of drag? What is streamlining? What is its effect onthe Different types of drag?

(b) A cylinder 15 cm in diameter and 10 m long, is made to turn 1500 revolu-tions per minute with its axis perpendicular in a stream of air having uniformvelocity of 25 m/sec. Assuming ideal fluid flow, find [8+8]

i. Circulation

ii. Lift force experienced by the cylinder and

iii. The position of stagnation points Take density of air as 1.2 kg/m3.

6. (a) What do you mean by ‘pipes in parallel’? When pipes are connected in par-allel? What is the loss of head in the system.

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(b) A pumping plant forces water through a 50 cm diameter main, the frictionalhead being 30 m. It is proposed to lay another main of appropriate diameteralongside the existing one so that the two pipes may work parallel for theentire length and reduce the friction head to 10 m only. Find the diameterof the new main if, with the exception of the diameter, it is similar to theexisting one in every other aspect. [8+8]

7. (a) What do you meant by viscous flow? Mention various forces to be consideredin Navier Stroke’s equation.

(b) Through a horizontal circular pipe of diameter 100 mm and of length 10m,an oil of dynamic 0.097 poise and relative density 0.9 is flowing. Calculatethe difference of pressure at the two ends of the pipe, if 100 Kg. of the oil iscollected in a tank in 30 seconds. [10+6]

8. (a) Show the velocity of sound is in terms of Bulk modulus?

(b) Calculate the stagnation pressure, temperature at stagnation point on the noseof a plane, which is flying at 800 km/hr through still air having a pressure 8N/Cm2(abs) and temperature -100. Take R = 287 J/Kg. K and K=1.4. [8+8]

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1. (a) What do you mean by the term ‘Viscosity’?

(b) What is the force of buoyancy? Is it a body force or surface force?

(c) Show the center of pressure is always below the center of gravity. [6+4+6]

2. (a) In a three dimensional incompressible flow, the velocity components in y andz-direction are v = ax3

−by2+cz2;w = bx3−cy2+az2x. Determine the missing

component of velocity distribution such that continuity equation is satisfied.

(b) How is the continuity equation based on the principle of conservation of massstated? And explain how the control volume approach will help indevicingcontinuity equation. [8+8]

3. (a) Mention the different forces in a fluid flow. For the Euler?s s equation ofmotion, which force are taken into consideration.

(b) A conical tube of length 2m is fixed vertically with its smaller end upwards.The velocity of flow at the smaller end is 5m/s, while at the lower end it is2m/s. The pressure head at the smaller end is 2.5m of liquid. The loss of headin the tube is 0.35 (V 1− V 2)2 / 2g, where V1 is the velocity at the smallerend and V2 at the lower end respectively. Determine the pressure head at thelower end. Flow takes place in downward direction. [6+10]

4. (a) What is the significance of the following non dimensional numbers in thetheory of Similarity?

i. Reynolds number

ii. Froude number and

iii. Mach Number.

(b) A venturimeter its axis vertical, the inlet and throat diameters being 90 mmand 45 mm respectively. The throat is 150 mm above inlet and Cd =0.96, oilof specific gravity 0.8 flows up through the meter at a rate of 0.01 m3/s. Findthe pressure difference between inlet and throat. [6+10]

5. Water of kinematic viscosity 1.02 ×10−6m2/sec is steadily flowing over a smoothflat plate at zero angle of attack with a velocity 1.6 m/sec. The length of the plateis 0.3m. Calculate

(a) The thickness of boundary layer at 15 cm from the leading edge and

(b) Shear stress at trailing edge of the plate.Assume a parabolic profile. Take density = 1000 kg/m3 [16]

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6. (a) Derive Darcy-Weisbach equation for loss of head in a pipe.

(b) Two tanks are connected by a 300 mm diameter 1000 m long pipe. Find therate of flow if the difference of water level in the tank is 10 m. Take 4f = 0.04and ignore minor losses. [10+6]

7. Two reservoirs are connected by a pipeline of diameter 600 mm and length 4000M.The difference of water level in the reservoirs is 20 M. At a distance of 1000M fromthe upper reservoir, a small pipe is connected to the pipeline. The water can betaken from the small pipe. Find the discharge to the lower reservoir, if

(a) No water is taken from the small pipe, and

(b) 100 lit/s of water is taken from small pipe. Take f=0.005 and neglect minorlosses. [16]

8. (a) what is the relation between pressure and density of a compressible fluid for?

i. Isothermal process

ii. Adiabatic process.

(b) A gas is flowing through a horizontal pipe at a temperature of 40C. Thediameter of the pipe is 8cm and at a section I in the pipe, the pressure is30.3N/cm2 (gauge). The diameter of the pipe changes from 8cm to 4cm at thesection II, where pressure is 20.3N/cm2 (gauge). Find the velocities of the gasat these sections assuming an isothermal process. Take R=287.14Nm/Kg.Kand atmosphere pressure=10N/ cm2. [6+10]

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1. (a) A lubricating oil of viscosity µ undergoes steady shear between a fixed lowerplate and an upper plate moving at speed V. The clearance between the platesis t. Show that a linear velocity profile results if the fluid does not slip at eitherplate.

(b) Describe with a neat sketch a micro-manometer used for very precise mea-surement of small pressure difference between two points. [8+8]

2. (a) If φ=3xy, find x and y components of velocity at (1,3) and (3,3). Determinethe discharge passing between streamlines passing through these points.

(b) Define one-dimensional, two-dimensional and three-dimensional flows? [10+6]



i. Reynolds number


iii. Mach Number.


5. (a) Explain with a neat sketch the boundary layer characteristics when a fluid isflowing over a flat plate.

(b) A thin flat plate 0.3 m wide and 0.6 m long is suspended and exposed parallelto air flowing with a velocity of 3 m/sec. Calculate drag force on both sidesof the plate when the 0.3 m edge is oriented parallel to free stream. Considerflow to be laminar and assume for air kinematic viscosity is 0.18 stokes anddensity is 1.2 kg/m3. [10+6]

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6. (a) What is a compound pipe? How would you determine the equivalent size of acompound pipe?

(b) Two pipes each 120 m long, one of diameter 120 mm and other of diameter90 mm are provided in parallel connecting two tanks, the difference of waterlevels of which is 18 m. Find the discharge to the lower tank. If however asingle pipe 120 m long is provided connecting the two tanks and the dischargeto the lower tank is to be increased by 30%, find the diameter of this pipe.For all pipes take 4f = 0.032 and ignore minor losses. [8+8]

7. (a) Derive an expression for the velocity distribution for viscous flow through acircular pipe.

(b) An Oil of viscosity 0.1 Pascal - sec and specific gravity 0.9 is flowing througha circular pipe of diameter 50 mm and of length 300 m. The rate of flow offluid through the pipe is 3.5 lit / sec. Find the pressure drop in a length of300 m and also the shear stress at the pipe wall. [8+8]

8. Find the mass flow rate of air through venturimeter having inlet diameter as 400mm and through diameter 200mm. The pressure at the inlet of the venturimeteris 27.468 N/ cm2 (abs) and temperature of a air at inlet is 200C. The pressure atthe throat is given as 25.506 N/ cm2 (abs ).Take R=287 J/Kg-K and K=1.4. [16]

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1. (a) Discuss factors which affect the viscosity of a liquid.

(b) What do you mean by a single column manometer?

(c) What are the laws of floatation? [6+6+4]

2. (a) If φ=3xy, find x and y components of velocity at (1,3) and (3,3). Determinethe discharge passing between streamlines passing through these points.

(b) Define one-dimensional, two-dimensional and three-dimensional flows? [10+6]



i. Reynolds number


iii. Mach Number.


5. (a) The velocity distribution in the boundary layer is given by the equationuu∞

= 3

2

(

y

δ

)

−1

2

(

y

δ

)2

Determine the displacement thickness and momentum thickness in terms ofthe nominal boundary layer thickness δ.

(b) Air flows at 10 m/sec past smooth rectangular flat plate 0.3 m wide and 3m long. Assuming that the turbulence level in the on coming stream is lowand that transition occurs at Rex = 5×105, calculate the ratio of the totaldrag when the flow is parallel to the length of the plate to the value when theflow is parallel to the width. Assume for air kinematic viscosity as 15 ×10−6

m2/sec. [8+8]

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6. A pipeline ABC 180 m long is laid on an upward slope of 1 in 60. The length ofportion AB is 90 m and its diameter is 0.15 m. At B the pipe section suddenlyenlarges to 0.30 m diameter and remains so for the remainder of its length BC, 90m. A flow of 50 litres per second is pumped into the pipe at its lower end A and isdischarged at the upper end C into a closed tank. The pressure at the supply endA is 137.34 kN/m2. Sketch [16]

(a) the total energy line

(b) the hydraulic gradient line and also find the pressure at discharge end C. Take

f = 0.02 in hf=flV 2

2gD

7. (a) Derive an expression for the velocity distribution for viscous flow through acircular pipe.

(b) An Oil of viscosity 0.1 Pascal - sec and specific gravity 0.9 is flowing througha circular pipe of diameter 50 mm and of length 300 m. The rate of flow offluid through the pipe is 3.5 lit / sec. Find the pressure drop in a length of300 m and also the shear stress at the pipe wall. [8+8]

8. (a) Derive Bernoulli’s equation for compressible flow undergoing adiabatic pro-cess?

(b) Find the Mach number when an aero plane is flying at 1100Km/hr throughstill air having a pressure of 7 N/ cm2 and temperature -50C. Wind velocitymay be taken as zero. Take R=287.14J/KgK. Calculate the pressure, tempand density of air at stagnation point on the nose of the plane. Take K=1.4.

[8+8]

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Code No: W2323/R07


CELL BIOLOGY

(Bio-Technology)




�

1. Give a detailed account of a photosynthetic eukaryotic cell.

2. Discuss the structure of mitochondria , chloroplast and golgi apparatus also

relate them to their function.

3. Explain facilitated diffusion by giving example of transport of sugars in the

red blood cells.

4. Discuss the sequence of vesicle budding and docking in transport of vesicles.

5. Write on the series of events that take place during G2 phase of the cell

division.

6. Define cell differentiation and discuss in detail about the genetic basis of

cellular differentiation.

7. Write notes on the following :

a) Signal transduction by hormones

b)Receptor tyrosine kinases

8. Discuss the process of transformation of normal cell to cancer cell.

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Code No: W2323/R07


CELL BIOLOGY

(Bio-Technology)




1. Discuss in detail chemosynthetic eukaryote.

2. What do you understand by cytosol, describe the process that takes place in

cytosol.

3. Discuss diffusion & osmosis. Explain how diffusion can be explained by

fick’s first law.

4. Write notes on the following:

a) Molecular chaperons

b)Protein targeting

5. Write a detailed note on S phase. Explain how the transition from G1 phase

to S phase occurs with initiation of cell division.

6. Give an overview of general characteristics of cell differentiation.

7. What is signal transduction discuss the steps that occur during the process.

8. Give an overview of the properties of cancer cells that give them an ability

to metastatize. �

�

�

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�

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�

Code No: W2323/R07


CELL BIOLOGY

(Bio-Technology)




�

�

1. Elucidate prokaryotic cell organization and give examples of prokaryotic

phototroph and prokaryotic chemotroph.

2. Write notes on the following and elucidate their function

i) Lysosomes

ii) Peroxisomes

iii) Endoplasmic reticulum

iv) Golgi complex

3. Describe passive transport and also discuss how it is different from active

transport.

4. Describe the role of ER in posttranslational modifications of proteins.

5. Give a detailed account of the commitment of to chromosome replication taking

place in G1 phase. Explain why cell takes longest time in G1 phase for its

division.

6. Describe how nucleocytoplasmic interactions determine cellular differentiation.

7. What do you understand by cell signaling explain the role of G protein in a

signaling pathway.

8. Discuss physiological and biological characteristics of cancer cells. How their

metabolic activity differs from the normal cell. �

�

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Code No: W2323/R07


CELL BIOLOGY

(Bio-Technology)




�

�

1. Discuss various cell types and their shapes and sizes.

2. Describe major organelles of eukaryotic cell also mentioning their functions.

3. Elucidate active transport. Also mention the source of energy involved in the

process.

4. What do you understand by posttranslational modifications. Explain in detail.

5. Describe the importance of interphase in cell cycle and the series of events

during the period between the end of one mitosis to the start of next.

6. What are the cytoplasmic determinants of cellular processes leading to cell

differentiation.

7. Write notes on the following

a)Protein kinases

b) G protein

8. Define oncogenes, discuss the role of oncogenes as possible cause of cancer.

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4

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