IGNOU BTCM-BTWRE First Year Assignments December 2012

3

Q.1 (a) Solve the differential equation :

(i) 2 2( )dy

x y xydx

− =

(ii) 2x y ydye x e

dx

− −= +

(b) A function f (x) is defined as follows :

2

1

( ) 2 1 2

2 3 2

x x

f x x x

x x x

<

= − ≤ ≤ − + − >

Q.2 (a) A particle moving in a straight line is subjected to a resistance kv3 where v is the velocity. If u is the velocity at any time t when the distance is S. Prove that :

21,

1 2

u Sv t KS

kuS u= = +

+

u, being the initial velocity.

(b) A motor boat of weight w is moving at 25 m/sec, when the motor is stopped. If the

resistance to the motion is K v and the boat comes to the rest after moving

100 meters. Find the time taken by it to cover these 100 m.

Q.3 (a) A particle moves along a circle r = 2a cos θ in such a way that its acceleration towards origin is always zero. Prove that :

22 cotθ = − θ θɺɺ ɺ

(b) A particle is describing a plane curve. If the tangential and normal acceleration are constant throughout the motion then prove that :

log (1 )A Btψ = +

where ψ is the angle through which the direction of motion turn in time t.

Q.4 (a) Find the total work done in moving a particle in a force field given by ˆ ˆ ˆ3 5 10xy i z j x k= − +F along the curve 2 2 31, 2 ,x t y t z t= + = = from t = 1 to t = 2.

(b) Show that the vector field defined by 3 2 3 2 2ˆ ˆ ˆ2 3xyz i x z j x yz k= + +A is irrotational.

Find scalar potential ψ such that = ∇ ψA .

TUTOR MARKED ASSIGNMENT

ET 101 A

MATHEMATICS-I

Note : All questions are compulsory and carry equal marks.

Maximum Marks : 100 Weightage : 30%

Course Code : ET 101 A Last Date of Submission : July 31, 2012

BTCM/BTWRE

4

Q.5 (a) Evaluate the following limits, if they exist

(i)

1

2

115

1Lim

1x

x

x

−

→ −

−

−

(ii) 2

2 20

1 cosLim

sinx

x

x x→

−

(b) If 2ln ( 1 )y x x= + − , prove that

2

2 1(1 ) 0x y xy+ + =

Hence, find yx + 2, using Leibhitz’s theorem.

Q.6 (a) If 1 1cos cotx y

uy x

− − = +

Show that 0u u

x yx y

∂ ∂= + =

∂ ∂

(b) (i) Solve 1 cos ( ) sin ( )dy

x y x ydx

= + + +

(ii) Find the costant ‘a’ so that A is a conservative vector field, where

3 2 2ˆ ˆ ˆ( ) ( 2) (1 )A a xy z a x a x z= − + − + −i j k

Calculate its potential and work done in moving a particle from (1, 2, − 3), to

(1, − 4, 2) in the field.

Q.7 (a) The position vector of a particle at time t is 3ˆ ˆ ˆcos ( 1) sinh ( 1)r t i t j t k= − + − + α

. Find

the condition imposed on α by requiring that at time t = 1, the acceleration is normal to the position vector.

(b) A particle moves along the curve x = t3 + 1, y = t2, z = 2t + 3 where t is the time. Find the

components of its velocity and acceleration at t = 1 in the direction ˆ ˆ ˆ3i j k+ + .

Q.8 (a) Find the directional derivative of the function xyz2 in the direction of the vector ˆ ˆ ˆ2i j k+ − at the point (2, 3, 1).

(b) If the vector ˆ ˆ ˆ( 3 4 ) ( 2 3 ) (3 2 )ax y z i x y z j x y z k= + + + − + + + −

P is solenoidal,

then determine the constant a.

Q.9 (a) Find the eigen values and eigen vectors of the matrix

5 1 0

0 5 9

5 1 0

A

− = − −

(b) Find the inverse of the matrix

1 0 0

0 cos sin

0 sin cos

A

= θ θ θ − θ

5

Q.10 (a) Express the matrix

2 2 4

1 3 4

1 2 3

A

− − = − − −

as the sum of a Symmetric and a

skew-symmetric matrix.

(b) Find the inverse of

2 1 1

1 2 1

3 1 4

A

= − − −

and hence solve the equations.

2 8x y z+ + =

2 1x y z− + =

3 4 15x y z− − = −

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ET 101 (Part B)

MATHEMATICS-II

Note : All questions given are compulsory. Marks assigned to the questions have been shown in brackets. This assignment is based on all Blocks of Mathematics-II.


Course Code : ET-101B Last Date of Submission : July 31, 2012

BTCM/BTWRE

Q.1 (a) The probability of n independent events is P1, P2, . . . Pn. Find the probability that at least one of the events will happen. Using this, find the probability of obtaining at least one 6 in a throw of four dice :

(b) Suppose an assembly plant receives its voltage regulators from three different sources, 60% from B1, 30% from B2 and 10% from B3. Let 95%, 80% and 65% of the supply received respectively from the source B1, B2 and B3 perform as per specifications laid. If A is the event that a voltage regulator received at the plant performs as per specifications then find P (A).

Q.2 (a) Two cards are drawn from a pack of 52 cards. Find the probability that draw includes an ace and a ten.

(b) In a production of iron rods the diameter X can be approximated to be normally distributed with mean 2 inches and S.D. 0.008 inches.

(i) What percentage of defectives can we expect if we set the acceptance limit at 2 ± 0.02 inches?

(ii) How should we set the acceptance limits to allow for 4% defectives?

Q.3 (a) Following data gives 11 measurements of the same object in the same instrument 2.7, 2.5, 2.3, 2.4, 2.3, 2.5, 2.7, 2.5, 2.6, 2.6, 2.5 at 1% level. Test the hypothesis that the variance of the instrument is no more than 0.16.

(b) The test runs with six models of an experimental engine showed that they operated respectively for 24, 28, 21, 23, 32 and 22 minutes with a gallon of fuel. Obtain a 99% confidence interval for the average run time of engine with a gallon of fuel.

Q.4 (a) A problem of mechanics is given to three students A, B and C whose chances of solving

it are 1 1 1

, and2 3 4

respectively. What is the probability that the problem will be solved.

(b) If events A and B are independent and ( ) 0.15, ( ) 0.45P A P A B= ∪ = then find P (B).

Q.5 (a) A machine contains a component C that is vital to its operation. The reliability of component C is 80%. To improve the reliability of a machine, a similar component is used in parallel to form a system. The machine will work provided that one of these components functions correctly. Calculate the reliability of the system.

(b) India plays two matches each with West Indies and Australia. In any match the probability of India getting points 0, 1 and 2 are 0.45, 0.05, and 0.50, respectively. Assuming that the outcomes are independent, find the probability of India getting at least 7 points.

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Q.6 (a) A class consists of 80 students, 25 of them girls and 55 boys. While 10 of them are rich and the remaining poor, it is found that 20 are fair complexioned. What is the probability of selecting a fair complexioned rich girl or a poor boy who is not fair complexioned?

(b) Suppose the probability for A to win a game against B is 0.4. If A has an option of playing either a “best of 3 games” or a “best of 5 games” match against B, which option should A choose so that the probability of his winning the match is higher? (No game ends in a draw).

Q.7 (a) The chances that doctor A will diagnose a disease X is 60%. The chances that a patient will die by his treatment after correct diagnosis is 40% and the chances of death by wrong diagnosis is 70%. A patient of doctor A who had disease X, died. What is the chance that his disease was diagnosed correctly?

(b) Three urns A, B, C contain 6 red, 4 black balls, 2 red and 6 black balls and 1 red and 8 black balls respectively. An urn is chosen at a random and a ball is drawn from the urn. If the ball drawn is red, find the probability that the ball was drawn from urn A.

Q.8 (a) If 20% of the bolts produced by a machine are defective, determine the probability the out of 4 bolts chosen at random.

(i) 1

(ii) zero

(iii) at most 2 bolts will be defective.

(b) In a certain factory producing cycle tyres there is a small chances of 1 in 500 tyres to be defective. The tyres are supplied in lots of 10. Using Poisson distribution, calculate the approximate number of lots, containing no defective, one defective, and two defective tyres respectively, in a consignment of 10,000 lots.

Q.9 (a) The diameter of an electric cable is assumed to be continuous random variate with

probability density function ( ) 6 (1 ), 0 1f x x x x= − ≤ ≤

(i) Verify the above is probability density function, and

(ii) Also find the mean and variance.

(b) The mean life time of a sample of 100 fluorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation of 120 hours. The company claims that the average life of the bulbs produced by it is 1600 hours. Using the level of significance of 0.05, is the claim acceptable.

Q.10 (a) A machinist is making engine parts with axle diameter of 0.70 inch. A random sample of 10 parts shows mean diameter 0.742 inch with standard deviation of 0.04 inch. On the basis of this sample, would you say that the work is inferior?

(b) The means of simple samples of sizes 1000 and 2000 are 67.5 cm and 68.0 cm respectively. Can the samples be regarded as drawn from the same population of SD 2.5 cm?

8


ET 105 (Part A)

PHYSICS

Note : All questions are compulsory and carry equal marks. This assignment is based on all Blocks of Physics.


Course Code : ET105A Last Date of Submission : July 31, 2012

BTCM/BTWRE

Q.1 Attempt all questions of the following :

(a) If the mean distance of Mars from the Sun is 1.525 times that of Earth from the Sun. Calculate the number of years in which Mars will complete one revolution about the Sun.

(b) Calculate the moment of inertia of a circular disc (i) about an axis through its centre and perpendicular to its plane (ii) about a diameter.

(c) If the earth receives 2 cal min– 1cm– 2 solar energy, What are the amplitudes of electric and magnetic fields of radiation?

(d) A circuit consists of an accumulator of EMF 2 volts and negligible internal resistance, a resistor of 2 ohms, two resistances of values 4 ohms and 8 ohms connected in parallel and an ammeter to record the current through the accumulator. The resistance of the ammeter is 1/3 ohms. Calculate the reading of the ammeter and the power expended in the 4 ohms resistor.

(4 × 4 = 16)


(a) State and prove the Work-Energy theorem. Using this theorem calculate the speed of the bob of a simple pendulum when the bob is passing through the equilibrium position.

(b) Find the maximum numbers of orders available with a grating and show that only first order is possible if the width of the grating element is less than twice the wavelength of light.

(c) A solenoid of 1200 turn is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. Find the strength of the magnetic field at the centre of the solenoid, when a current of 2 amp flows through it.

(d) Show that the frequency of beats is equal to the difference in frequencies of the sounding bodies.

(4 × 5 = 20)


(a) Calculate the minimum number of lines in a grating which will just resolve the lines of wavelengths 5890 Ǻ and 5896 Ǻ in second order.

(b) Determine the intensity of electric field due to a dipole at an equatorial and axial point.

(c) Deduce Gauss’s law in differential form i.e. 2

0

. Eρ

∇ =∈

.

(d) Two spheres are identical in mass and volume, but one is hollow and the other is solid. How will you identify them experimentally?

(4 × 4 = 16)

9


(a) Explain the concept of Maxwell’s displacement current and show how it led to the modification of the Ampere’s law.

(b) Explain the concept of free body diagram. A mass ‘m’ is released from the top of a smooth vertical track of radius R with negligible speed. Show that if leaves contact with the track at an angle θ = cos– 1(2/3).

(c) Calculate the electric intensity required to just support an ion of mass 10– 4 g and having a charge of 1.44 coulomb in air.

(d) Define group velocity and phase velocity. Show that the phase velocity is half of group

velocity, i.e. 1

2p gV V= .

(4 × 4 = 16)


(a) Define moment of inertia. What is its physical significance? Show that in rotatory motion, moment of inertia plays the same role as mass does in linear motion.

(b) Prove that the electromagnetic wave equation in free space for the electric field E

is

given by 2

20 0 2

EE

t

∂∇ = µ ∈

∂

.

(c) A small sphere of mass 10– 3g and charge 4 × 10– 8 C, hangs from silk thread at 60o with a large charged conducting sheet. Calculate the surface charge density for the sheet.

(d) Derive an expression for time period of a simple harmonic motion.

(4 × 4 = 16)


(a) Assuming that all the energy from a 1000 watt lamp is radiated uniformly; calculate the average values of the intensities of electric and magnetic fields of radiation at a distance of 2 m from the lamp.

(b) Show that the velocity of escape of the body from the earth’s surface is √2 times the velocity for a circular orbit just above the earth’s surface.

(c) A thin metallic sheet of radius R carries a charge Q. At its centre is another point charge Q. Find the electric fields at distance of 2 R and R/2 from the centre of the shell.

(d) Define the intensity of sound waves. Show that when they propagate in air their intensity varies inversely as the square of the distance.

(4 × 4 = 16)

10


ET 105 (Part B)

CHMISTRY

Note : All questions are compulsory and carry equal marks. This assignment is based on all Blocks of Chemistry.


Course Code : ET105B Last Date of Submission : July 31, 2012

BTCM/BTWRE

Q.1 Give IUPAC name of the following structures :

(i) OH O ||

CH3― CH―CH2―C― CH3

(ii) (CH3)2 C = CHCOCH3

(iii) [PtCl (NH2CH3) (NH3)2] Cl

(iv) CH3OCH2 CH2O CH3

(v) CH3

CH3―CH2―C―CH2―CH3

COOH

Q.2 (a) The λ of Hα line of Balmer series is 6500 o

A . What is the λ of Hβ line of Balmer series?

(b) The ionisation energy of a H like Bohr’s atom is 4 Rydberg :

(i) Calculate the wavelength radiated when electron jumps from the first excited state to ground state

(ii) What is the radius of 1st orbit of this atom? Given that 1 Rh = 2.18 x 10– 18 J.

Q.3 (a) State Heisenberg’s uncertainty principle. An electron has a speed of 50 m s-1 accurate

upto 99.99%. What is the uncertainty in locating its position?

[Mass of electron = 9.1 x 10– 31 kg; h = 6.6 x 10– 34 J s]

(b) What do you mean by “plasticizer” and thermosetting plastics?

Q.4 (a) Ten moles of an ideal gas at 10 bar (10 atm) pressure 27oC are expanded isothermally to 1 bar pressure. Calculate the work done :

(i) if the expansion is reversible and

(ii) if it is irreversible against an external pressure of 1 bar.

(b) Write short note on Heat capacity and Enthalpy.

Q.5 (a) Explain the working of devices for change of free energy into electrical energy under the process of redox reaction.

(b) Write note on types of electrodes and convenient notation for the representation of electrodes and cells.

11

Q.6 (a) What are the main reasons of corrosions? What are the protective measures required for an iron rod to be used in civil work?

(b) In order to protect steel structures from corrosion, which among Ni, Na, Pb, Cd, Zn, Mg and Al will be more useful and why?

Q.7 (a) Write down the electronic configuration of 29Cu+ and 78Pt+, 58Ce4+. Explain the reasons for

these charged elements in respect of changes in their Ionisation Energy and Stability.

(b) How can the similarity in the chemical properties of lanthanides be explained?

Q.8 (a) Give details of the commercial production of HNO3, its properties and various uses.

(b) Why Mn2+ is more stable than Mn3+? Does same argument stand for the stability of Fe2+

and Fe3+?

Q.9 (a) Describe the chief uses of fluorine, chlorine and their compounds.

(b) Give reasons :

(i) Why inert gases do not react with other elements to form compound?

(ii) All inert gases are monoatomic.

Q.10 (a) Describe the activated sludge method to treat wastewater.

(b) Explain any two :

(i) Are all the five bonds in PCl5 molecule equivalent? Justify your answer.

(ii) Why electron affinity of fluorine is less than that of chlorine?

(iii) Why graphite is a conductor but diamond is not?

12


ET 201 (Part A)

MECHANICS OF FLUIDS

Note : All questions are compulsory and carry equal marks. This assignment is based on all

Blocks of Mechanics of fluids.


Course Code : ET-201A Last Date of Submission : July 31, 2012

BTWRE

Q.1 (a) If the equation of a velocity distribution over a plate is given by v = 2y – y2, in which v is

the velocity in m/s at a distance y, measured in meters above the plate, what is the velocity gradient at the boundary and at 7.5 cm and 15 cm from it? Also determine the

stress at these points if absolute viscosity µ = 8.60 poise.

(b) An iceberg weighing 8976 N/m3 floats in the ocean with a volume of 600 m3 above the surface. Determine the total volume of the iceberg if specific weight of ocean water is 10 055 N/m3.

Q.2 (a) The Velocity components in the x- and y-directions are given as 3

22

3

xyu x y

= −

and

32 2

3

yxv xy

= −

. Indicate whether the given velocity distribution is a possible field of

flow or not.

(b) If the expression for the stream function is described by 3 23x xyψ = − , indicate whether

the flow is rotational or irrotational. If the flow is irrotational determine the value of the velocity potential.

Q.3 (a) If the volume of a liquid decreases by 0.2 per cent for an increase of pressure from 6.867 MN/m2 to 15.696 MN/m2, what is the value of the bulk modulus of the liquid?

(b) Oil of specific gravity 0.90 flows in a pipe 300 mm diameter at the rate of 120 litres per second and the pressure at a point A is 24.525 kPa (gage). If the point A is 5.2 m above the datum line, calculate the total energy at point A in terms of metres of oil.

Q.4 (a) A circular orifice of area 6.45 × 10– 4 m2 is provided in the vertical side of a large tank. The tank is suspended from a knife edge 1.53 m above the level of the orifice. When the head of water is 1.22 m, the discharge is 1161.5 N/min and a turning moment of 14.421 N-m has to be applied to the knife edges to keep the tank vertical. Determine Cv, Cd and Cc of the orifice.

(b) Water under a constant head of 3 m discharge through an external cylindrical mouthpiece 50 mm diameter, for which Cv = 0.82, determine (i) the discharge in cumec and (ii) absolute pressure at vena-contracta; and the maximum head for the mouthpiece to flow full.

Q.5 (a) Derive an expression for mean velocity for laminar flow (i) through a pipe and (ii) between parallel plates.

(b) What do you understand by hydro dynamically smooth and rough pipes.

13

Q.6 (a) The population of a city is 800 000 and it is to be supplied with water from a reservoir 6.4 km away. Water is to be supplied at the rate of 140 liters per head per day and half the supply is to be delivered in 8 hours. The full supply level of the reservoir is R. L. 180.00 and its lower water level is R. L. 105.00. The delivery end of the main at R. L. 22.50 and the head required there is 12 m. Find the diameter of the pipe. Take f = 0.04.

(b) A compound piping system consist of 1800 m of 0.50 m, 1200 m of 0.40 m and 600 m of 0.30 m new cast iron pipes connected in series. Convert the system to (i) an equivalent length of 0.40 m pipe and (ii) and equivalent size pipe 3600 m long.

Q.7 (a) The velocity distribution in the boundary layer is given as 23 1

2 2

v

V= η − η in which

y η = δ

compute *δ

δ and

θ δ

.

(b) Given that a laminar boundary layer at zero pressure gradient over a flat plate is

described by the velocity profile 0

sin2

y

V

ν π = δ

.

Determine the momentum correction coefficient (or factor) and the energy correction coefficient (or factor).

Also show that boundary layer thickness δ, wall shear stress τ0 and coefficient of drag CD

are given by 20

0

0.3284.795 1.312; ;

Re Re ReD

x x x

VxC

ρδ = τ = = , where symbols have their usual

meaning.

Q.8 (a) Find the ratio of skin friction drag on the front two-third and rear one-third of a flat plate kept in a uniform stream at zero incidence. Assume the boundary layer to be turbulent over the entire plate.

(b) For laminar flow of an oil having dynamic viscosity µ = 1.766 Pa.s in a 0.3 m diameter pipe, the velocity distribution is parabolic with a maximum point velocity of 3 m/s at the centre of the pipe. Calculate the shearing stresses at the pipe wall and within the fluid 50 mm from the pipe wall.

Q.9 (a) Show by method of dimensional analysis that the resistance R to the motion of a sphere

of diameter D moving with uniform velocity V through a fluid having density ρ and

viscosity µ may be expressed as :

2( )R D Vv D

µ= ρ φ ρ

Also show that the above expression reduces to R = k µ VD when the motion is through viscous fluid at low velocity, where k is a dimensionless constant.

(b) Find the viscosity in poise of a liquid through with a steel ball of diameter 1 mm falls, with a uniform velocity of 20 mm/s. The specific gravity of the liquid is 0.91 and that of the

steel is 7.8. Given that k = 3π.

(b) Assuming that rate of discharge Q of a centrifugal pump is dependent upon the mass

density ρ of fluid, pump speed N (rpm), the diameter of impeller D, the pressure p and

the viscosity of fluid µ, show using the Buckingham’s π-theorem that it can be represented by

3

2 2 2( ) ,

gHQ ND

N D ND

υ = φ

where H = head and ν = kinematic viscosity of the fluid.

14

Q.10 (a) An oil having viscosity of 1.43 poise and specific gravity 0.9 flows through a pipe 25 mm diameter and 300 m long at 1/10 of the critical velocity for which Reynolds number is 2500. Find (i) the velocity of flow through the pipe; (ii) the head in metres of oil across the pipe length required to maintain the flow and (iii) the power of the flow.

(b) Two parallel plates kept 75 mm apart have laminar flow of glycerine between them with a maximum velocity of 1 m/s. Calculate the discharge per metre width, the shear stress at the plates, the difference in pressure in pascals (or N/m2) between two points 25 m apart, the velocity gradients at the plates and velocity at 15 mm from the plate. Take viscosity of glycerine as 8.35 poise.

15

Q.1 (a) A fish freezing plant of 100 tonnes capacity is to be maintained at – 50oC when the outside atmosphere temperature is 40oC. The actual C.O.P. of the refrigeration system used is 1/5 of the theoretical Carnot refrigerator working between the same temperature limits. Calculate the power required to run the plant.

(b) A reversible engine is supplied with heat from two constant sources at 900 K and 600 K and rejects heat to a constant temperature sink at 300 K. If the engine executes of complete cycles while developing 100 kW, and rejecting 3600 kJ of heat per min. Determine the heat supplied by each source per minute and efficiency of the engine.

Q.2 (a) A heat pump working on the Carnot cycle takes in heat from a reservoir 5oC and delivers heat to a reservoir 60oC. The heat pump is driven by a reversible heat engine which takes heat from a reservoir at 840oC and rejects heat at 60oC. The reversible heat engine also drives a machine that absorbs 36 kW. If the heat pump extracts 17 kJ/sec from 5oC reservoir, determine,

(i) The rate of heat supply from 840oC source.

(ii) The rate of heat rejection to 60oC sink.

(b) Threee Carnot engines R1, R2, R3 operate in series between two heat reservoirs which are at temperatures of 1000 K and 300 K.

Calculate intermediate temperautres if amount of work produced by these engines is in the, peoportions of 5 : 4 : 3.

Q.3 (a) A reversible engine works between three thermal reservoirs A, B and C. The engine absorbs an equal amount of heat from the thermal reservoirs A and B kept at temperatures TA and TB respectively, and rejects heat to the thermal reservoir C kept at

temperature TC. The efficiency of the engine is α times the efficiency of the reversible engine, which works between the two reservoirs A and C. Prove that

( ) ( )2 1 2 1A A

B C

T T

T T= α − + − α

(b) A heat pump is used to maintain an auditorium hall at 24oC when the atmospheric temperature is 10oC. The heat lost from the hall is 1500 kJ/min. Calculate the power required to run the heat pump if its COP is 30 percent of Carnot machine, working between the same temperature limits.


ET 201 (Part B)

ENGINEERING THERMODYNAMICS


Blocks of Engineering Thermodynamics.


Course Code : ET 201 B Last Date of Submission : July 31, 2012

BTWRE

16

Q.4 (a) A piston and cylinder machine contains 1 kg of air, initially v = 0.8 m3/kg and T = 290 K. The air is then compressed in a slow frictionless process to a specific volume 0.2 m3/kg and a temperature 580 K. The law for compression is PV1.5 = 0.75 with P in bar and v in m3/kg. Determine work done and heat transferred during the process. Assume for air Cp = 1.00 kJ/kg-K and Cv = 0.743 kJ/kg-K and R = 0.287 kJ/kg-K.

(b) 3 kg of air at a pressure of 150 kPa and temperature 360 K is compressed polytropically to 750 kPa according to law PV1.2 = constant. The air is then cooled to initial temperature at constant pressure. The air is then brought to state (1) by following PV = C. Draw the cycle on PV-diagram and determine net work done and heat.

Q.5 (a) 1 m3 of gas is filled in a closed tank. The initial condition of the gas is 3 bar and 50oC. The gas is heated until the pressure becomes 5 bar. Find the change in internal energy, work done, heat supplied, change in entropy.

Take R = 0.287 kJ/kg-K and Cv = 0.743 kJ/kg-K.

(b) Find the work done, in kilojoules by an ideal gas in going from state A to state C along the path shown in the PV diagram as shown in Figure 1.

Figure 1

Q.6 (a) A cylinder contains 0.12 m3 of air at 1 bar and 100oC. the air is compressed to 0.03 m3. The final pressure is 6 bar.

Determine :

(i) The value of index n

(ii) Mass of air in the cylinder

(iii) Increase in internal energy

Take γ = 1.4, R = 0.287 kJ/kg-K and Cv = 0.72 kJ/kg-K.

(b) Determine pressure of 1 kg of oxygen at 100oC if the specific column is 0.2. m3/kg using. (i) Van der Waals equation and (ii) Ideal gas laws.

Take for O2, a = 13.93 × 104 N.m4 (kg mole)2; b = 0.0314 m3/kg mole, and R = 8314 J/kg mole K.

Q.7 (a) Steam at 20 bar and 360oC expands in a steam turbine to 0.08 bar. It is then condensed in a condenser to saturated water. The pump feeds back the water to the boiler. Assume ideal Rankine cycle and determine.

(i) The net work done/kg of steam

(ii) Efficiency of the Rankine cycle

(b) Steam at 20 bar and 360oC is expanded in a steam turbine to 0.08 bar. It then enters a condenser where it is condensed to saturated liquid. It is then fed back to the boiler. Determine :

(i) Net work (shaft work) per kg of steam.

(ii) Dryness fraction of steam entering the condenser.

T = Constant

A

0 1 2 3

100

k Pa

P

V, m3

17

Q.8 (a) A single stage, single acting reciprocating air compressor has a bore of 200 mm and a stroke of 300 mm. It runs at a speed of 500 rpm. The clearance volume is 5% of swept volume and polytropic index is 1.3 throughout. Intake pressure and temperature are 97 kPa, 20oC and the compression pressure is 550 kPa. Determine :

(i) FAD in m3/min

(ii) Air deliver temperature

(iii) Cycle power

(iv) ηiso Neglecting clearance volume

(b) Calculate the volumetric efficiency of the compressor having a cylinder diameter 410 mm and stroke 610 mm. Compressor makes 420 rpm and delivers 30 kg/min of air at 1.01325 bar and 15oC.

Q.9 (a) In an air standard Diesel cycle, compression begins at 103 KPa and 300 K. After compression heat addition is of 545 kJ/kg of air, the peak pressure reached in the cycle is 4.7 MPa. Calculate :

(i) Fuel cut-off ratio

(ii) Compression ratio

(iii) Maximum temperature in the cycle

(iv) Air standard efficiency

Take γ = 1.4, and Cp = 1.004 kJ/kg-K.

(b) A vapour absorption cycle has generator temperature 120oC, evaporator temperature – 10oC and the ambient temperature 30oC. Estimate the maximum possible COP. The actual COP is 0.5 of the maximum COP. If the capacity of the plant is 100 TR, calculate the fuel consumption of the plant. The calorific value of the fuel is 40 MJ/kg.

Q.10 (a) A dense air machine operates on reverse Brayton cycle and is required for a capacity of 10 TR. The cooler pressure is 4.2 bar and refrigerator pressure is 1.4 bar. The air is cooled in the cooler at a temperature of 50oC and temperature of air at inlet to compressor is – 20oC. Determine for the ideal cycle :

(i) C.O.P.

(ii) Mass of air circulated per min.

(iii) Theoretical piston displacement of compressor and expander.

(iv) Net power per tonne of refrigeration.

(b) 28 tonnes of ice from and at 0oC is produced per day in an ammonia refrigeration plant. The temperature range in the compressor is from 25oC to – 15oC. The refrigerator is dry and saturated at the end of compression. If actual COP is 60% of the theoretical COP, calculate the power supplied or required to drive the compressor. Assume latent heat of ice = 335 kJ/kg. Use properties of refrigerant given below :

Temperature oC hf kJ/kg Hg kJ/kg sf kJ/kg-K Sg kJ/kg-K

25 100.04 1319.22 0.3473 4.4852

− 15 − 54.56 1304.99 − 2.1338 5.0585

18

Q.1 (a) Two forces of 10 kg and 15 kg act simultaneously at a point. Find the resultant force, if the angle between the two forces be (i) 30o, (ii) 45o, (iii) 60o, (iv) 90o, and (v) 180o. Draw the force diagram for each situation.

(b) Find the angle between two equal force P, when their resultant is equal to (i) P, (ii) P/2,

(iii) 2 P, (iv) 3 P, and (v) √2 P. Draw the force diagram for each case.

Q.2 (a) A particle is acted upon by three forces equal to 5 kg, 10 kg and 13 kg, along the sides of an equilateral triangle taken in order. Find graphically the magnitude and direction of the resultant force. Find the magnitude and direction of the resultant force if forces are acting along the sides of right angle triangle when one of the angle is 45o.

(b) Four forces of 2, 2.5, 1, and 3 kg are acting simultaneously along straight lines OA, OB,

OC and OD, such that ∠ OAB = 40o, ∠ BOC = 100o and ∠ COD = 125o. Find graphically the magnitude and direction of the resultant force.

Q.3 A body weighing 10 kg, is suspended by two strings AC and BC at the point C. The lengths of the strings AC and BC are 3 metres and 4 metres respectively and the horizontal distance BC is also 4 metres. Find the tensions in the strings AC and BC.

Q.4 (a) A fly wheel of weight 200 N and diameter 20 cm is made to rotate at 10 rotation per second. Determine the K.E. of the wheel. If the frictional couple at its bearing is 10 Nm, determine the number of revolution it will make before coming to rest. If the frictional couple at bearing is double, determine the numbers of revolutions it will make before coming to rest.

(b) A mass of 4 kg moving with a velocity of 10 m/sec along x direction follows another mass of 10 kg moving with 5 m/sec in the same direction. Determine the final velocities of the two masses (i) if e = 0.6, (ii) if the impact is fully plastic, determine also the loss in KE, and (iii) the impact is perfectly elastic, determine the final velocities of the two bodies.

Q.5 A metal rod A of 25 cm length expands by 0.05 cm when its temperature is raised from 0oC to 100oC. Another rod B of a different metal of length 40 cm expands by 0.04 cm for the same rise in temperature. A third rod C of 50 cm length, made up of pieces of rod A and B placed end to end, expands by 0.03 cm on heating from 0oC to 50oC. Find the lengths of each portion of the composite rod C.

Q.6 A shell of weight 7 kN is fired horizontally from a gun weighing 400 kN, with a velocity 450 m/sec. With what velocity will the gun recoil? What will be the average force of resistance to bring it to rest in a distance of 2 meters.


ET 202 (Part A)

ENGINEERING MECHANICS

Note : All questions are compulsory and carry equal marks. This assignment is based on all Blocks of Engineering Mechanics.



BTCM

19

Q.7 (a) Consider a simply supported beam subjected to a uniformly distributed load on the left half of the span as shown in Figure 1.

Figure 1

Determine SF and BM diagrams for the beam and find the location of the magnitude of maximum BM.

(b) Find the forces in all the members of the truss shown in Figure 2.

Figure 2

Q.8 A boy throws a ball so that it may just clean a wall 3.6 m high. The boy is at a distance of 4.8 m from the wall. The ball was found to hit the ground at a distance of 3.6 m on the other side of the wall as shown in Figure 3. Find the least velocity with which the ball can be thrown.

Figure 3

Q.9 Locate the centroid for plane section shown in Figure 4 and determine the moment of inertia about AB.

Figure 4

4 m 4 m

A B

3 m

3 m

A

B

C

D

E

150 kN

6 m 6 m

A O X

B

α

V

4.8 m 3.6 m

3.6 m

C

A B

12 cm

4 cm

4 cm 4 cm

φ 2 cm

Hole

20

Q.10 Calculate the force required, P, to cause a block of weight W1 to slide under the another block

of weight W2. What will be the tension in the string AB. W1 = 2000 N, W2 = 1000 N, µ = 0.3.

Figure 5

W1

W2

P

A

30o

21


ET 202 (Part B)

PRINCIPLES OF ELECTRICAL SCIENCES

Note : All questions are compulsory and carry equal marks. This assignment is based on all Blocks of Principles of Electrical Sciences.



BTCM

Q.1 (a) Define the terms electrical energy and electrical power. Give their symbols and units for measurement.

(b) Explain the following terms :

(i) Linearity

(ii) Active circuit

(iii) Depended energy sources

(c) Find the resistance at 20oC of 5 km of copper wire of cross-sectional area 0.5 cm2, if the

specific resistance of copper at this temperature is 17.3 × 10– 9 Ω-m. What would be its

resistance at 40oC if α = 0.0043 peroC?

Q.2 (a) State and explain Thevenin’s Theorem. What is the Thevenin equivalent of an ideal DC voltage source?

(b) State and explain the following :

(i) Superposition theorems

(ii) Maximum power transfer theorems

(c) Explain the working of :

(i) PMMC instrument

(ii) Induction type energy meter.

Q.3 (a) Explain the phenomenon of resonance in series RLC circuit and derive the expression for resonant frequency.:

(b) Explain the terms ‘power factor’. What is the need for power factor correction?

(c) An inductive load draws 1000 W from a 200 V, 50 Hz single phase source. A capacitor

of 25.3 µF connected in parallel with the impedance raises the overall p. f. of the combination to unity. What is the p. f. of the inductive load?

Q.4 (a) Give advantages of negative feedback over positive feedback.

(b) Derive unit step response of a second order system and find its time constants.

(c) Why is the B-wave in a synchronous machine nearly sinusoidal? How is this achieved in a salient pole machine?

22

Q.5 (a) Explain the following with reference to 3-φ systems :

(i) Meaning of phase sequence, and

(ii) Function of ground wire in the supply system.

(b) Explain the following test in a transformer :

(i) Open circuit (O. C.), and

(ii) Short circuit (S. C.) tests.

(c) The following data were obtained on a 20 kVA, 50 Hz, 2000/200 V distribution transformer

Voltage Current Power

(V) (I) (P)

OC test with HV open circuited 200 4 120

SC test with LV short circuited 60 10 300

Draw the approximate equivalent circuits of the transformer referred to HV and LV sides, respectively.

Q.6 (a) Explain the construction and working of a CRO. What are its applications?

(b) How is power measured in a 3-phase circuit using 2-watt meter method?

(c) A balanced 3-phase capacitive load of power factor 0.9 draws 10 A from a 400V, 3-phase supply. Find the readings of the two watt meters.

Q.7 (a) What is the effect of reversing the polarity of supply voltage on the direction of rotation in the case of shunt, series and compound d. c. motors? Comment.

(b) Explain the torque-armature characteristics of :

(i) A d. c. series motor

(ii) A d. c. shunt motor

(c) A 250 V d. c. shunt motor has Rf = 150 Ω and Ra = 0.6 Ω. The motor operates on no-load with a full field flux at its base speed of 1000 rpm with Ia = 5 A. If the machine drives a load requiring a torque of 100 N-m, calculate armature current and speed of motor. If the motor is required to develop 10 kW at 1200 rpm, what is the required value of external series resistance in the field circuit? Neglect saturation and armature reaction

Q.8 (a) Explain construction and working principle of full wave rectifier.

(b) Give an account of numerous applications of semiconductor diodes.

(c) Explain the characteristic of ideal OP-AMP? Is the assumption of virtual ground valid in practical op-amps? Explain the concept of CMRR.

Q.9 (a) What are different kinds of gate and flip-flop? Explain their operation.

(b) What are registers, counters and memories?

(c) Explain the working of an ADC and a DAC.

Q.10 (a) What is bus and bus interface unit?

(b) Classify the various 8085 instructions microprocessor.

(c) How stack is used in 8085 microprocessor?

23


ET 204 (Part A)

MATERIALS SCIENCE

Note : All questions are compulsory and carry equal marks. This assignment is based on all Blocks of Materials Science.



BTCM

Q.1 (a) Describe the simple classification of materials with suitable examples.

(b) Distinguish between the following :

(i) Metals and Alloys

(ii) Ceramics and Glasses

(iii) Polymers and Rubbers.

Q.2 (a) Describe the effects of variables on mechanical properties of materials.

(b) When a steel wire 2.5 m long and of cross-sectional area 15 mm2 was subjected to a

tensile force of 4.0 kN, it stretched elastically by 3.2 mm. Calculate Young’s modulus of elasticity for the wire.

Q.3 What are the various types of bonding in solids? Explain each bonding structure with suitable example.

Q.4 What are the three most common crystal structures in metals? Explain with neat sketches and give some examples of metals, which consists of these structures.

Q.5 Discuss about the types of defects in solids. Describe the significance of Burgers Vector and Burgers circuit.

Q.6 (a) Explain the phenomenon of superconductivity.

(b) Define semiconductor. Describe the various types of semiconductors with neat sketches.

Q.7 (a) Explain about the factors, which accelerate the corrosion in processes.

(b) Explain about the techniques used in preventing corrosion of metals.

Q.8 (a) Copper has a FCC structure and an atomic radius of 1.278 o

A . Calculate the lattice constant of the unit cell and its density. The atomic weight of Cu is 63.546.

(b) The unit cell of alpha iron is BCC with lattice constant of 2.86 o

A . Calculate the density of iron. The atomic weight of iron is 55.84.

Q.9 (a) If the average modulus of elasticity of the steel used in 205,000 MPa, by how much will a wire 2.5 mm in diameter and 3 m long be extended when it supports a load of 500 kg?

(b) A piece of copper originally 305 mm long is pulled in tension with a stress of 276 MPa. If deformation is entirely elastic, what will be the resultant elongation? Take E for

copper = 11.0 × 104 MPa.

24

Q.10 Write short notes on :

(i) Electronic Materials

(ii) Recyclability

(iii) Semiconductors

(iv) Spinel Crystal Structure

(v) Burgers Circuit

(vi) Drift Velocity

(vii) Tensile Test

(viii) Degradation of Polymers.

25


ET 204 (Part B)

ENGINEERING MATERIALS


Blocks of Engineering Materials.



BTCM

Q.1 (a) Give and discuss the functional and qualitative requirements of flooring materials, in general. Discuss each aspect in 100 words (at least).

(b) Collecting present market data about the latest flooring material products (give the source of your data), discuss these in the light of above discussed criteria.

Q.2 (a) Discuss in detail the role of aggregates in granolithic concrete wear-resistant surface.

(b) Outline how will you lay wear resistant surface, giving sketches/photographs of each stage/step?

Q.3 (a) Explain what an Epoxy Resin flooring is? Discuss its various types, and the method of its construction.

(b) Write an exhaustive report about its commercial formulation with their respective advantages collect your own data from the market.

Q.4 With regard to water proofing work, write an essay touching on the following aspects : (i) admixtures and their functions, and (ii) types of admixtures.

Bring out the action and advantages of super-plasticizers.

Q.5 Giving photos and sketches discuss damp proofing treatment with regard to : (i) basement, (ii) ground floor level as such, (iii) plinth level top of buildings, and (iv) compound wall plinth.

Q.6 Draw on a full drawing sheet, neatly labeled 3-D sketches of the following :

(i) Finish using plaster moulds,

(ii) Textured form of linear finishes – including all the types that are in use,

(iii) Exposed aggregate finishes, and

(iv) Mechanical finishes.

Explain the tems in detail.

Q.7 Summarizes the important specifications (from IS Codes) regarding various types of paints and painting work.

Q.8 Giving sketches and photographs, discuss and explain foamed sections for doors and windows, plastic sections in buildings, and PVC pipes and fittings.

Give the respective advantages and disadvantages.

26

Q.9 Take a full drawing sheet and give 3-D sketches (fully labeled) of the following :

(i) Slip socket joint coupler,

(ii) Slip socket with a gland nut at the top coupler,

(iii) Two-screw flexible coupling,

(iv) Conduit coupler, and

(v) Conduit fittings.

Explain every item that you draw.

Q.10 Draw on a full drawing sheet, and give 3-D view of the following items :

(i) Lamp holders – all the types,

(ii) Ceiling rose

(iii) Fluorescent lamp holder, and

(iv) Various types of switches

Explain their features.

27


ET 301 (Part A)

SYSTEMS METHODS


Blocks of Systems Methods.



BTCM

Q.1 Give short answers to the following questions :

(i) Define ‘system model’. Give the names of different types of system models.

(ii) Explain ‘biological systems’ with examples.

(iii) Can we consider a window or a door as a system? If yes, what are its components and how are they put together?

(iv) Give the block diagram of the system for controlling the temperature within a refrigerator with thermostat. Is it an open-loop or closed-loop system?

(v) What is Kirchoff’s current law for an electric circuit? Explain with an example.

(vi) Give the equations and Laplace transforms of the five basic standard input signals used for system analysis.

(vii) Define the terms Reference input signal, Feedback signal, Error signal, Controller, Plant, Output signal and Feedback element.

(viii) Give disadvantages of closed-loop systems.

(ix) Cite at least one example each with block diagram of hydraulic, mechanical, thermal and electro-mechanical control systems.

(x) What are the methods of controlling the speed of :

(a) separately excited

(b) shunt and

(c) series d. c. motor? (20)

Q.2 (a) Explain the concepts of ‘duality’ and ‘sensitivity analysis’ in linear programming. For a given maximization primal problem how will you write the dual in following cases :

(i) All constraints of ‘less than or equal to’ type

(ii) One or more constraints of ‘greater than or equal to’ type

(iii) One or more constraints of ‘equal to’ type.

(b) Solve the following problem using Simplex Method :

Minimise C (Total Cost) = 3X + 4Y

Subject to

20 + 60Y ≥ 80

30 + 40Y ≥ 100

X, Y ≥ 0 (10)

28

Q.3 (a) What are second order systems? Give examples of second order system. Derive equations of time response of a second order system to a periodic inputs like impulse, step and ramp.

(b) What is transfer function? Derive the closed-loop transfer function of a second order system?

(10)

Q.4 (a) What is linear programming? What are its industrial applications? What are the limitations of linear programming?

(b) A scrap metal dealer has received an order from a customer for at least 2000 kg of scrap metal. The customer requires that at least 1000 kg of the shipment metal must be of a high quality metal called Alpha that can be melted down and used to produce metal tubings. Furthermore, the customer will not accept delivery of the order if it contains more than 175 kg of metal that he deems unfit for commercial use, i.e. metal that contains an excessive amount of impurities and cannot be melted down and refined profitably.

The dealer can purchase scrap metal from two different suppliers in unlimited quantities with following % ages (by weight) of Alpha and unfit :

Table : Scrap

Supplies A Supplies B

Alpha 25% 75%

Unfit Scrap 5% 10%

The costs per kg of metal purchased from supplies A and B are Re 1 and Rs. 4, respectively. By graphical method, determine optimum quantities of metal for the dealer to purchase from each of the two suppliers.

(10)

Q.5 (a) A company has factories at A, B and C which supply warehouses at D, E, F and G. Monthly factory capacities are 160, 150 and 190 units, respectively. Monthly warehouse requirements are 80, 90, 110 and 220 units, respectively. Unit shipping costs (in rupees) are as follows :

To From

A B C D

A 42 48 38 37

B 40 49 52 51

C 39 38 40 43

Determine the optimum distribution for this company to minimize shipping costs using Vogel’s Approximation Method.

(b) A company has factories at A and B which supply warehouses at C and D. Monthly factory capacities are 500 and 400 units, respectively. Monthly warehouse requirements are 300 and 600 units, respectively. Unit shipping costs (in rupees) are as follows :

To From

C D

A 2 2

B 1 3

Determine the optimal distribution for this company to minimize shipping costs using Stepping-store method

(10)

29

Q.6 (a) A foreman has four mechanics and four jobs to be performed. The mechanics differ in efficiency and the jobs differ in their intrinsic difficulty. His estimates of the time (in hours) each mechanic would take to perform each job is given in the effectiveness matrix below. How should the jobs be allocated, one to a mechanic, so as to minimize the total time taken? Solve using Hungarian method.

(b) Arrival of machinists at a tool crib are considered to be Poisson distributed at an average rate of 6 per hour. The service time at the tool crib is exponentially distributed with an average of 3 minutes

(i) What is the probability that a machinist arriving at the tool crib will have to wait?

(ii) What is the average number of machinists at the tool crib?

(iii) The company will install a second tool crib when convinced that a machinist would have to wait atleast six minutes before being served. By how much the flow of machinists to the tool crib must increase to justify the addition of a second tool crib?

(10)

Q.7 (a) Derive the formula for EOQ and total inventory cost for the following cases :

(i) EOQ model with uniform demand

(ii) EOQ with different rates of demand in different cycles

(iii) EOQ when shortages (back orders) are allowed

(iv) EOQ with uniform replenishment

(v) EOQ with price (or quantity) discounts

Also, give characteristics and limitations of each of the above models.

(b) XYZ company buys in lots of 500 boxes which is a 3-month supply. The cost per box is Rs. 125 and the ordering cost is Rs. 150. The inventory carrying cost is estimated at 20% of unit value

(i) What is the total annual cost of the existing inventory policy?

(ii) How much money could be saved by employing the economic order quantity?

(10)

Q.8 (a) With reference to PERT and CPM network models explain the following concepts : (i) Activities, (ii) Events, (iii) Predecessor, successor, concurrent and dummy activities, (iv) Rules for constructing network diagrams, (v) Project duration and critical path, (vi) Earliest expected completion time of event, (vii) Latest allowable completion time of an event, (viii) Probability of completing the project on or before a specified time, (ix) PERT algorithm and (x) Float of an activity :

(b) A truck can carry a total of 10 tons of commodity. Three types (A, B and C) of commodities are to be carried. These commodities have the characteristics as shown in the following table

Commodity Unit Weight

(Tons) Profit per Ton

(Rs.)

A 4 100

B 5 130

C 3 80

Given the total allowable weight, determine the number of units of each of the three commodities to carry so as to maximize the total profit. Use dynamic programming approach.

(20)

30


ET 301 (Part B)

COMPUTER APPLICATIONS

Note : All questions are compulsory and carry equal marks. This assignment is based on all Blocks of Computer Applications.


Course Code : ET301B Last Date of Submission : July 31, 2012

BTCM

Q.1 Attempt all parts of the question and all parts have equal marks.

(a) What is difference between the software and hardware? Mention different type of software.

(b) What technology is used in third and fourth generation computers?

(c) Describe the layout of a Lotus 1-2-3 Spreadsheet.

(d) What is an operating system? Explain the various functions of the operating systems.

(e) In word star which command is used to :

(i) Underline a block of text,

(ii) Print a document,

(iii) Write a block to another file, and

(iv) Save a document.

(5 × 4 = 20)

Q.2 Attempt all parts of the question.

(a) How do you view the structure of a database? How do you modify it?

(b) Briefly explain the following commands :

COPY, PATH, DISKCOPY, TREE, XCOPY, MODE.

(c) What is the difference between digitizers and mouse?

(d) What is computer virus? Mention different ways of preventing the virus attack.

(4 × 4 = 16)


(a) What is a mail merge operation? What are the files that you have to prepare for mail merge operation? Explain with the help of an example.

(b) How are formulas useful in a spreadsheet? What is precedence of operation in a formula?

(c) What are the different functions of a word processor? What are the common applications of word processors in the work place?

(d) What are dot commands in word star? Explain any four dot commands with examples.

(4 × 4 = 16)

31


(a) What are functions in LOTUS 1-2-3? Describe the structure of a functions and Date related functions.

(b) How many types of graphs can be drawn in Lotus 1-2-3? Explain any one of them with example.

(c) In an opening menu of Word Star, what do D, L, X and R mean?

(d) What do you mean by dimensioning in Auto CAD? Explain different types of dimensioning with examples.

(4 × 4 = 16)


(a) Which coordinate systems are available in Auto CAD? What is a relative coordinate?

(b) What are the special characters used to print the date and page numbers in footer or header?

(c) Write short notes on the usage sequence of the following Auto CAD commands :

(i) Line,

(ii) Scale,

(iii) Move,

(iv) Pan, and

(v) Ortho.

(d) What are layers? Explain their advantages in practical drafting work.

(4 × 4 = 16)


(a) How would you describe utility of Computer Aided Designing in routine work?

(b) Explain the application of absolute, relative and polar coordinate systems in Auto CAD.

(c) Explain the application of absolute, relative and polar coordinate systems in Auto CAD.

(d) What is a key in a record? How do you sort the records? Explain with an example.

(4 × 4 = 16)

32


ET 501 (Part A)

SOIL MECHANICS


Blocks of Soil Mechanics.



BTCM/BTWRE

Q.1 (a) Define Consistency Limit. Determine Liquid Limit and Flow Index using following data on a soil :

No. of Blows 32 27 22 18 16

Water Content (%) 51.2 55.0. 58.9 61.4 66.6

(b) A natural soil deposit has a bulk unit weight of 19 kN/m3 and water content of 6 percent. Calculate the amount of water required to be added to 1.2 cum of soil to raise the water content to 15%. Assume the void ratio to remain constant. What will then be the degree of saturation?

Q.2 The data from a typical hydrometer analysis on a clay sample is given below :

(i) Compute the particle sizes and the percent finer corresponding to the time intervals given, and

(ii) Plot the gradation curve.

The basic data is :

Weight of oven dried soil = 50 g

Specific Gravity of solids = 2.65

Area of x-section of cylinder = 19.61 cm2

Volume of suspension = 1000 cc

Volume of hydrometer bulb = 65 cc

Hydrometer reading in clear water = 0.9900

Room temperature = 27oC

Viscosity of water at room temperature = 0.008545 poise

Dispersing agent correction = − 0.0004

Meniscuss correction = + 0.0004

Volume correction = − 1.657 cm

Time (min) 0.5 1 2 5 15 30 60 120 1440

Hydrometer Reading

1.0150 1.0130 1.0120 1.0090 1.0075 1.0060 1.0030 1.0020 1.0010

33

Q.3 From the sieve analysis, the following grain size distribution data is obtained. Plot grain size distribution curve for the soil and calculate Cu and Cc.

Sl. No. Sieve Size Weight Retained (g)

I 4.76 101.48

II 2.399 33.98

III 1.201 60.48

IV 0.592 32.55

V 0.420 28.34

VI 0.296 44.86

VII 0.151 98.01

VIII 0.075 100.30

Q.4 (a) Describe the procedure of permeability tests (constant and variable head methods on soils. Discuss their limitations and deduce formulae of permeability used.

(b) The profile of a soil deposit in which there is a 4 m thick sand layer underlain by clay layer, the water table is present at a depth of 2 m from ground level. Above water table, the unit weight of sand is 17 kN/m3 and below water table, its standard unit weight is 19.81 kN/m3. The saturated unit weight of clay is 16.91 kN/m3. Draw the variation of effective stress, pore water pressure and total stress upon a depth of 7 m. Ignore capillary effect. Take unit weight of water as 9.81 kN/m3.

Q.5 (a) The water table in a certain area is at a depth of 4m below the ground surface. To a depth of 12 m, the soil consists of very fine sand having an average void ratio of 0.7. Above the water table the sand has an average degree of saturation of 50%. Calculate the effective pressure on a horizontal plane at a depth of 10 m below the ground surface. What will be the increase in the effective pressure if the soil gets saturated by capillarity upto a height of 1 m above the water table? Assume G = 2.65.

(b) Discuss various methods of compaction of granular and cohesive soils. How the degree of compaction is checked in the field?

Q.6 Following data is obtained from Standard and Modified Proctor Compaction Tests on a clayey sand in the laboratory :

Bulk Unit Weight kN/m3 Moisture

Content (%) Standard Test Modified Test

6.8 16.98 18.37

8.9 17.86 20.15

11.9 19.47 21.37

14.4 20.48 21.74

15.9 20.40 21.09

18.4 19.42 20.48

21.3 18.20 19.41

Take G = 2.65 and

(i) Plot graphs of moisture content vs dry unit weight for both tests.

(ii) Plot zero air void line, and

(iii) Compare the magnitudes of OMC and maximum dry density obtained from both tests and comment on the differences observed.

34

Q.7 (a) What do you mean by Potential Function and Stream Function? Discuss their significance.

(b) A foundation trench is to be excavated in a stratum of stiff clay, 8 m thick, underlain by a bed of sand. In a trial borehole, the ground water is observed to rise to an elevation 2 m below the ground surface. Find the depth to which the excavation can be safely carried out without the danger of the bottom becoming unstable under uplift pressure of ground water. The specific gravity of clay particles is 2.72 and void ratio 0.72. If excavation is to be carried safely to a depth of 6 m, how much should the water be lowered in the vicinity of trench?

Q.8 (a) A rectangular area 2 m × 4 m caries a uniform load of 100 kN/m2 at ground surface. Determine vertical stress at a point A 2 m below the center of loaded area. If a circular

area of same intensity of diameter of 2√5 m is applied on the ground, what will be vertical stress at same point A.

(b) A clay deposit 3 m thick and resting on rock has undergone consolidation under a deposit of sand 18 m thick. The water table was at top of the sand. Due to erosion, 10 m of sand has been eroded. Compute the pre-consolidation pressure at the center of the clay layer.

If a load is applied so that vertical stress on the clay layer is increased by 0.5 kg/cm2, compute the settlement of the clay layer. The following are the properties of the soil :

Clay Sand

Bulk density 2 g/cc 2.2 g/cc

Moisture content 31.1% 20%

Specific gravity of solids 2.9 −

Coefficient of consolidation 2 × 10– 4

cc/sec −

Cc (normally loaded) 0.25 −

Cc (over consolidated) 0.05 −

σu (unconfined) kg per cm2 2.0 −

Q.9 (a) Discuss various methods to improve the stability of slope.

(b) In order to determine shear strength parameters of a saturated clay deposit in a field, a Vane shear test is carried out. The failure torque is found to be 35 Nm. The size of Vane

is 50 mm × 100 mm. The vane is completely pushed into the clay deposit. Find the shear strength parameters of the clay deposit.

Q.10 (a) A canal, 3 m deep runs through a soil having the following properties : Cu = 10 kN/m2,

φu = 10o, e = 0.8 and G = 2.72. The angle of slope of the banks is 45o. Determine the factor of safety with respect to cohesion when the canal is full upto the top of banks. What will be the factor of safety in case of sudden draw down?

(b) Discuss Taylor’s Stability Number. How the stability of a slope is checked with this, explain with an example?

35


ET 501 (Part B)

FOUNDATION ENGINEERING


Blocks of Foundation Engineering.



BTCM/BTWRE

Q.1 (a) Discuss different types of foundation with their suitability for different type of structures

with your justification?

(b) Discuss the different methods of site exploration by boring.

Q.2 Why stabilization of bore holes are needed? Explain various stabilization techniques with application to the field situations.

Q.3 (a) What do you understand by the term “Ultimate Bearing Capacity”?

(b) What are the bearing capacity factors for computing ultimate bearing capacity of shallow foundations?

(c) Explain the significance of each of the three terms in the Terzahi’s equation for the ultimate bearing capacity of a strip footing.

Q.4 Estimate the load carrying capacity of rectangle footing 1.75 × 2.75 m to be placed at a depth of 1.2 m below ground surface. The unit weight of soil is 18 kN/m3 and the shear parameters

are c′ = 23 kN/m2, φ = 23. The ground water table at 2.7 m depth below ground surface?

Q.5 (a) Discuss the effect of size of the footing on settlement.

(b) What are the alternative methods for computing settlement?

Q.6 Two tube wells, each of 20 cm diameter are spaced to 100 m distance. Both the wells penetrate fully a confined aquifer of 12 m thickness. Calculate the discharge if only one well is discharging under a depression head of 3 m. What will be the percentage decrease in the discharge of this well if both the wells are discharging under the depression head of 3 m? Take the radius of influence of each well equal to 250 m, and the co-efficient of permeability of the aquifer as 60 m/day.

Q.7 (a) What is the significance of direct shear test? Explain the test procedure by discussing the advantages and disadvantages for using different soil conditions.

(b) Consolidated undrained triaxial tests are performed on two identical specimens of saturated, remoulded clay with pore pressure measurements. The observations are recorded in the table below :

Test No.

Consolidation pressure (kg/cm

2)

Cell pressure at failure (kg/cm

2)

Deviator stress at failure (kg/cm

2)

Pore pressure at failure (kg/cm

2)

1 2.65 2.25 1.67 1.21

2 3.27 3.25 2.28 1.37

Determine the values of the shear strength parameters, cohesion and friction, for the clay both in terms of total and effective stresses. If in the consolidated undrained test, an identical specimen is first consolidated under a cell pressure of 3.75 kg/cm2, what would be the deviator stress at failure?

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Q.8 A 25 pile square group has to be proportional in a uniform pattern in clay with equal spacing in all directions. Taking C = 0.7, determine the optimum value of spacing. Neglect end-bearing effect of the group. Each pile is square in cross-section, with sides of length a. If the major and minor principal stresses through a mass of soil at the instant of failure are 6 kg/cm2 and 2 kg/cm2 respectively. Calculate the values of normal and shear stress on a plane making an angle of 300 with the direction of minor principal stress.

Q.9 A retaining wall 6 metres high with a sloping back at 12o to the vertical supports a cohesion-less backfill rising from the crest at an angle of 5o with the horizontal. The backfill weighs 1.89 t/m3 and carries a uniformly distributed load of 0.65 t/m3. The angle of shearing resistance of the backfill is 32o and the angle of wall friction is 23o. Find the total active pressure per metre and point of application.

Q.10 (a) Discuss various classifications of pile foundation with their application in the field situations and explain why it is being adopted.

(b) Explain under what conditions an under-reamed pile foundation used? Give reasons to support your answer. Explain their advantages and disadvantages with respect to other deep foundations.

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ET 531 (Part A)

EARTH AND ITS ENVIRONMENT


Blocks of Earth and its Environment.


Course Code : ET 531 A Last Date of Submission : July 31, 2012

BTWRE

Q.1 Describe the main constituents of atmosphere. How the interaction of radiant energy on earth, apace system get influenced. Describe green house effect.

Q.2 Describe advances in weather forecasting. Why weather forecasting in India has tremendous criticism. Suggest ways to improve the situation.

Q.3 You have to establish a weather observatory in your area. Prepare a list of instruments, their specifications with brief description and availability.

Q.4 How the intensity of earthquake is measured. Prepare a chart of major earthquake zones of India. Describe the areas lying in seismic zone-V. What are the main specifications of earthquake resistance buildings?

Q.5 Differentiate among structure of major types of rocks. On a natural map of India delineate major rock groups.

Q.6 How do you classify faults? Describe seismic faulting with suitable examples.

Q.7 Give distribution of important rock formation of India. Give detailed features of Gondawana sequence along with its importance.

Q.8 With proper examples explain process ecological succession. How environmental factors influence ecological succession?

Q.9 On a map of India, delineate nine bio-geographical regions of India. Give salient features of each of the regions.

Q.10 Describe estuarine ecosystems. How is it different from marine ecosystems? Substantiate your answer with suitable examples, preferably from Indian sub-continental. Also discuss the menaces of environmental pollution.

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ET 531 (Part B)

SOIL SCIENCES


Blocks of Soil Sciences.



BTWRE

Q.1 What are the various soil physical properties affecting plant growth? Prepare a chart indicating optimum soil physical conditions and moisture requirements for selected crops grown in India.

Q.2 Explain dynamics of moisture uptake in plant root? How do plants differ in adaption to various agro-climatic conditions with varying degree of water available? Support your answer with specific examples from Indian condition.

Q.3 Discuss the role of infiltration in ground water recharge. Compare different methods to determine the infiltration characteristics of soil under field conditions. With the help of sketches explain the construction and functioning of different types of infiltrometers. Prepare a chart of infiltration characters of major soils of India.

Q.4 Prepare a detailed account of land evaluation system in India. Compare it with international systems. How does land evaluation helps in land use planning?

Q.5 Enlist harmful effects of acidity and alkalinity of soil in plant growth. On a natural map of India, show the regions affected by these maladies. Suggest measures to reclaim such soils.

Q.6 What are major and minor nutrients to improve soil fertility? How the soil fertility has declined in the post green revolution era? What are the major recommendations to improve soil fertility on sustainable basis?

Q.7 Write an essay “role of micro-organism and green manure in improving biological health of soils”. “In the race of increasing productivity we have ignored the soil health” justify the statement giving examples.

Q.8 Describe environmental factors influencing microbial activities in soil. What is nitrogen fixation? How does cropping patterns influence this process?

Q.9 Write a detailed account on effect of cultural practices on soil organisms. Prepare a table showing plant pathogenic micro organisms and their control measures.

Q.10 With specific examples, write a detailed note on soil born plant diseases, their symptoms and control measures.

Documents

IGNOU BTCM-BTWRE First Year Assignments December 2012