Btech Construction Management Assignments Ist Year

Maximum Marks : 100 Course Code : ET101A BTCM/BTWRE Weightage : 30% Last Date of Submission : July

31, 2009

TUTOR MARKED ASSIGNMENT ET 101 (Part A) MATHEMATICS-I

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

Q.1 (a)

If

. Prove that f (x) = x2 −

(b)

1 x

.

1 f (x) = − f   x

2

A function f (x) is defined as for x ≠ 1 f (x ) =

x 2 − 4x + 3 x 2 + 2x − 3 for x = 1

=−

1 2

Show that f (x) is differentiable at x = 1 and find its value. (c)

Find

, when

dy dx (i)

y = tan− 1

cos x − sin x cos x + sin x

(ii) 1

 1 + x 4 1 −1 y = loge   − tan x 1 − x 2  

3

(d) Tangents are drawn from origin to the curve y = sin x. Prove that their point of contact lie on

. 2

x y

(e)

(i)

2

2

=x −y

2

Verify Rolle’s Theorem for the function :

 ( x 2 + ab)  x → ln   , x ∈ [ a, b]  (a + b ) x  (ii)

Explain the failure of the Lagrange’s Mean Value Theorem in the interval [− 1, 1], when

f (x) = Q.2 (a)

.

Evaluate

∫ (b)

1 , ( x ≠ 0), f (0) = 0 x

5

sec x dx

Evaluate (i)

, and π 6

∫ 0

3 cos 2x − 1 dx cos x

(ii) Prove that

. b

∫ a

(c)

sin ( x − a ) − cos ( x − a ) dx = sin ( b − x ) − cos ( b − x )

Find the area common to the circle

b

∫ a

sin ( b − x ) − cos ( b − x ) dx sin ( x − a ) − cos ( x − a )

and the parabola 2

2

x + y = 16a

2

. Hence, y

2

= 6ax

find the larger of the area into which the circle is divided by the parabola. (d)

Solve the different equation :

, given that when x = 0, y = 3. dy

e dx = x + 1

Q.3 (a)

Prove by vector method :

. cos (α + β) = cos α cos β − sin α sin β

(b)

Find a vector of magnitude

which makes equal angles with the vectors

51

a =

1 ˆ 1 ( i − 2 ˆj + 2 kˆ ), b = ( − 4 iˆ − 3 kˆ ) and c = ˆj 3 5

3

(c)

and A = (1, 1, 1)

are two given vectors. Then prove that a vector C = (0, 1, − 1)

B

satisfying the equations

is A × B = C and A . B = 3

(d)

.

5 2 2  3, 3, 3   

A particle is executing uniform circular motion along the circumference of a circle of radius ‘a’ with an angular speed ‘ω ’. Express the radius vector as a function of time and prove that the acceleration of the particle is and that it is perpendicular to the r ( − ω2 r ) velocity.

(e)

It is given that the surface integral of the electric displacement vector

across a closed D

surface ‘S’ enclosing a volume ‘V’ is equal to the total free charge enclosed by the volume. Show that the divergence of is equal to the volume density of free charge. D Q.4 (a) (b)

If a matrix A is non-singular, prove that A and adj A are commutative and that their product is a diagonal matrix, every element of which is det A. Find the characteristic equation of the matrix  2 −1 1    A =  − 1 2 − 1  1 −1 2    and verify that it is satisfied by A. Hence, obtain A– 1.

(c)

(i)

Prove that for every square matrix A, the matrix (A + A′ ) is symmetric.

(ii)

Prove that the inverse of a unitary matrix is unitary.

(d)

If A is skew-hermitian prove that the characteristic roots are either zero or purely imaginary.

(e)

Prove that the matrix given below is orthogonal  cos θ − sin θ     sin θ cos θ  Find the characteristic roots and verify that the modulus of each characteristic root of an orthogonal matrix is unity.

Maximum Marks : 100 Course Code : ET-101B BTCM/BTWRE Weightage : 30% Last Date of Submission : Sept.

30, 2009

TUTOR MARKED ASSIGNMENT ET 101 (Part B) MATHEMATICS-II 4

Note :

All questions given are compulsory. Marks assigned to the questions

Mathematics - II.

Q.1 (a)

unbiased estimator for 2,  being population mean? If not find its bias?

Is X2

(b)

Q.2 (a) (b)

A box A contains 5 white and 2 black balls. Another box B contains 4 white and 5 black balls. A ball is transferred from box A to box B. then a ball is drawn from the box B. Find the probability that it is white. What is the probability of 6 turning up at least once in two tosses of a fair die. A box contains 3 blue and 4 red balls. Two drawing of two balls are made. Find the probability of drawing first 2 red balls and second 2 blue balls if the balls are not returned after the first draw.

Q.3 A population consists of four 0, 2, 4, 6, consider all possible samples of size two which can be drawn with replacement from this population. Find :

Q.4 (a)

(i)

the mean of the population

(ii)

standard deviation of the population

(iii)

means of the sampling distribution of means

(iv)

standard error of means.

20% of the tools produced in a certain manufacturing process turns out to be defective. Find the probability that in a sample of 20 tools chosen at random, (i)

exactly 5 will be defective, and

(ii)

more than one will be defective.

By using Poisson’s approximation. (b)

Assume that the probability of an individual coal miner being killed in a mine accident during a year is . Use appropriate distribution to calculate probability that in a mine

1 2400 employing 200 miners, there will be at least one such accident in a year. Q.5 (a)

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.

(b)

A random sample of 10 boys had the following IQ : 70, 120, 110, 101, 88, 83, 95, 98, 107, 100. Do these data support the assumption of a population mean IQ of 100 (at 5% level of significance)?

Q.6 (a)

A firm sells oil in cans containing 5000 g oil per can and is interested to know whether the mean weight differ significantly from 5000 g at the 5% level, in which case the filling machine has to be adjusted. Set up a hypothesis and an alternative and perform the test, assuming normally and using a sample of 50 fillings with mean 4990 g and standard deviation 20 g.

(b)

If simultaneous measurements of electric voltage by two different types of voltmeter yield the differences (in volts) 0.4, −0.6, 0.2, 0.0, 1.0, 1.4, 0.4, 1.6, can we assert at the 5% level that there is no significant differences in the calibration of the two types of instruments?

Q.7 (a)

(i)

A student gets 85, 76, 82 marks in the three tests for the Mathematics Course. She gets 79 marks in the final examination. What are here average marks if the weightage given to the tests and the final examination are 10?

4

(ii)

(b)

Three cities A, B, C are at equidistant from each other. A motorist travels from A to B at 30 km/h, from B to C at 40 km/h and from C to A at 50 km/h. Determine the average speed.

Students of a class were given an aptitude test. Their marks were found to be normally distributed with mean 60 and standard deviation 5. What percentage of students scored more than 60 marks?

Q.8 In the measurement of temperature it measured 100 times with variation in apparatus and procedure. After applying the corrections the results are Temperature oC

397

398

399

400

401

402

403

404

405

Frequency of Occurrence

1

3

12

23

37

16

4

2

2

Calculate (i) arithmetic mean, (ii) mean deviation, (iii) standard deviation, (iv) probable error of one reading, (v) standard deviations and the probable error of mean, and (vi) standard deviation of standard deviations. Q.9 (a)

X is a discrete random variable having probability mass function : X :

0

1

2

3

4

5

6

7

P (x = x) :

0

k

2k

2k

3k

2k2

2k2

7 k2 + k

(a) determine the constant k; (b) find p (x < ); p (x  6). (b)

Obtain the expectation of the number of tails preceding the first head in an indefinite series of tosses of the same coin.

Q.10 (a)

A dice was thrown 400 times. “SOX” resulted 80 times. Does the data justify the hypothesis of an unbiased die?

(b)

A machine produced 20 defective articles in a batch of 400. After overhauling it produced 10 defectives in a batch of 300. Has the machine improved?

3

Maximum Marks : 100 Course Code : ET105A BTCM/BTWRE Weightage : 30% Last Date of Submission : July

31, 2009

TUTOR MARKED ASSIGNMENT ET 105 (Part A) PHYSICS

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

Q.1 (a)

A particle moves from rest, its initial position being given by x = c with reference to a fixed point O. Its acceleration at a distance ‘x’ from 0 is away from O. Show that its µ x2 velocity is

when it is a distance ‘x’ from O.

µ c (b)

Two particles of equal mass have the same linear momentum. Which one has greater K.E.?

(c)

A bullet of mass ‘m’ traveling horizontally at a speed ‘v’ embeds itself in the centre of a block of wood of mass ‘M’, which is suspended by a light vertical string of length ‘l’. What would be the maximum inclination of the string with the vertical?

(d)

A flywheel with moment of inertia I = 63.6 kg m2 about its axis, rotates with a constant angular velocity, ω = 31.4 rad s– 1. Find the braking moment M which stops the flywheel in t = 20 seconds.

(e)

Had the gravitational force of attraction had not been of the inverse square nature, which one among the Kepler’s laws would have still remained valid?

(f)

Find the period of revolution of an artificial planet if the semi-major axis of the planet’s elliptic orbit is greater than that of the Earth’s orbit by 24  106 km. It is given that the semi-major axis of earth orbit round the sum is 1.5  108 km. (4 + 2 + 4 + 4 + 2 + 4 = 20)

Q.2 (a)

Two bodies are moving under their under mutual force of attraction. If the masses of the bodies are m1 and m2 and their position vectors w.r.t. an origin are and , respectively r r r1 r2 (i)

Write down their equations of motion.

(ii)

Define the co-ordinates of their centre-of-mass and show that its velocity remains constant.

3

(iii)

Define the relative co-ordinate of the system and using the said co-ordinate reduce the two equation mentioned at (i) into a single equation of motion. What is the significance of the ‘mass’ that appears in this single equation?

(iv)

What happens when m1 > > m2, so that

.

m2 →0 m1 (2 + 2 + 4 + 2 = 10) (b)

(i)

Write down the expression for the total mechanical energy of a torsional pendulum, presuming that it has been given a twist, in the form of a pure shear, through an angle θ .

(ii)

Assuming the system to be conservative, use the expression for the total mechanical energy to obtain the differential equation of motion of the to torsional pendulum and hence obtain the expression for the time period of oscillation. (2 + 4 = 6)

(c)

A disc weighing 2 kg rolls without slipping over a horizontal plane with a velocity 4 ms1. Find the kinetic energy of the disc.

Q.3 (a)

The amplitude of an SHM is 2 cm and its total energy is 3 × 10– 7 J. What is its displacement from the position of equilibrium when it is acted upon by a force 2.25 × 10– 5 N?

(b)

Explain the statement: The prongs of a tuning fork execute transverse vibration and its stem executes longitudinal vibration.

(c)

The wavelengths of two notes in are

and

90 m 175

. Each note produces four beats

90 m 173

per second with a third note of a fixed frequency. Calculate the velocity of sound in air. (d)

A parallel beam of sodium light (

) is incident on a thin glass plate of refractive o

λ = 5890 A index 1.5 such that the angle of refraction into the plate is 45º. Calculate the smallest thickness of the plate which will make it dark by a reflector. (e)

Calculate the wave length of light which gives a deflection of 9º32, for the third order spectral lines with a grating of 1012 lines per cm.

(f)

The minimum thickness required so that a quart plate becomes a quarter wave plates, at is 1.6 × 10– 3 mm. If µ 0 = 1.544, find the value of µ e. o

λ = 5890 A Q.4 (a)

An infinite number of changes each equal to q are placed along the x-axis at x = 1, x = 2, x = 4, x = 8, . . . and so on. Find the potential and the esoteric at x = 0 due to this set of changes. What will be the potential and electric field if, in the above set-up, the corrective charges have opposite sign?

(b)

Two metal spheres, each of mass 1 gm and radius 0.5 cm are placed on a smooth, horizontal, insulated plate such that their centres are 15 cm apart. One is charged to a potential 500 volt and the other to 1000 volt. What is the velocity of each sphere when they drift away to a distance of 30 cm. between their centres?

(c)

A uniform electric field E in the x-direction is produced by an appropriate charge configuration. A thin sheet of charge σ per unit area is placed perpendicular to the

4

x-direction at x = 0. If the initial charge configuration is assumed to be undisturbed by the presence of the sheet, what is the total electric field on each side of the sheet? (d)

An ammeter accurately calibrated, indicates 12.2 amperes when it is inserted in a circuit, when an identical ammeter is inserted in series with the first one, the reading of each becomes 11.8 ampere. Find the current in the circuit before the first ammeter was inserted.

(e)

An aluminum of wire resistance 7.30 ohm at 30ºC is placed in the left gap of a metre bridge and the balance is attained at 42.6 cm from the left end of the bridge wire. If the temperature of the aluminum wire be increased to 100ºC without changing anything else, by how much will the balance point shift? Given, the temperature coefficient of resistance of the aluminum wire is 3.8 × 10– 3 oC– 1. (4 5 = 20)

Q.5 (a)

(b)

A straight horizontal rod A of mass 50 gm and length 0.5 m, is placed in a uniform horizontal magnetic field of 0.2 T, perpendicular to A. Calculate the current in A if the force acting on it just balances it weight. A coil of N turns is wrapped around an iron ring of radius ‘d’ and cross-section ‘A’ (d > > A). Assuming a constant permeability, µ > > 1 for the iron. Find the following : (i)

the magnetic flux as a function of the current ‘i’, and

(ii)

the magnetic flux if a gap of width  (δ

2

< < A) is cut in the ring.

(c)

The two rails of a railroad metre gauge track are insulated from each other and from ground and are connected by a mill voltmeter. What is the reading when a train travels at the rate of 100 km h– 1 down the track, assuming that the vertical component of the earth’s magnetic field is 2 × 10– 5 T.

(d)

Consider a parallel LC circuit operated at a frequency ‘’ below its resonant frequency. ‘ω o’. Explain with reasons whether its reactance is capacitive on inductive.

(e)

Find out the magnitude and direction of the Poynting vector at the surface of a long straight wire of circular cross-section carrying a direct current ‘i’. The radius of the wire is ‘b’ and the resistance per unit length is ‘r’. (4 × 5 = 20)

4

Maximum Marks : 100 Course Code : ET105B BTCM/BTWRE Weightage : 30% Last Date of Submission : July

31, 2009

TUTOR MARKED ASSIGNMENT ET 105 (Part B) CHMISTRY

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

Q.1 Explain the following giving reasons : (i)

Usually the first ionization energy of elements increases with the atomic number of elements in a period of the periodic table.

(ii)

Flourine has lower electron affinity than chlorine.

(iii)

Why does ionization energy decreases from Be to B and Mg to Al?

(iv)

Diamond is an insulator while graphite conducts electricity.

(v)

All gases are mono-atomic.

Q.2 (a)

(b)

(i)

Justify the dual nature of matter.

(ii)

List the properties of conductors and insulators.

A photon of wave length 3310

falls on a photocathode and an electron of energy o

A 3 × 10

– 19

J is ejected. If the wavelength of the incident photon is changed to 5000

, the o

A energy of the ejected electron is 7.91 × 10– 20 J. Calculate the value of Plank’s constant and threshold wavelength of the photon. Q.3 (a)

Write down the electronic configuration of the following elements : Ca, Ca2+, Gd, O2–, Cu

5

(b)

A radioactive isotope decays in the following sequence 0

+ 1β α A  → A1  → A2

If the mass number and the atomic number of A2 are the 176 and 71, respectively, find the mass number and the atomic number of A1 and A. Which of the three elements are isobars? Q.4 (a) (b)

Discuss the concepts of enthalpy and internal energy. State and prove the Hess’s law of constant heat summation. Define and explain Second Law of Thermodynamics. Explain Carnot’s cycle.

Q.5 The energy of the electron in the second and third Bohr orbits of the hydrogen atom is – 5.42  10– 19 J and – 241 × 10– 19 J, respectively. Calculate the wave-length of the emitted radiation when an electron drops from the third to the second orbit. Q.6 (a)

(b)

Identify the Lewis acids and bases from the following : (i)

ALCL3

(ii)

BCL3

(iii)

Cu2+

(iv)

F–

(v)

NH3

(vi)

CH3OC2H5

Complete and balance the following nuclear reactions : (i) 81 36 Kr

+

0 − 1e

→?

(ii) 104 47 Ag

→

0 + 1e

+?

(iii) 73 31 Ga

→

0 − 1e

+?

(iv) 104 48 Cd

→

104 47 Ag

+?

Q.7 Calculate reduction potential at the following points for the titration of 50.0 ml of 0.10 M with 0.10 M Ce4+; 25, 49.0, 50.0, 50.2 and 52 ml Ce4+.

Fe (CN)6− 4 Given :

Fe (CN)36− + e − → Fe (CN)64 − ; Eo = 0.36 V

Ce 4+ + e − → Ce3+; Eo = 1.44 V

Give the results in a tabular form of Ce4+ ml added versus potential.

6

Q.8 (a) (b)

What is the difference between a Galvanic cell and a concentration cell? Calculate the solubility product of Ag Br from the following concentration cell set up at 25ºC. B r (1 M) Ag (anode) Ag+ (1 m) , AgBr (s) Ag (cathode)

Q.9 What are the merits of using isolated enzyme over the use of whole organisms in bio-technology. Q.10 Explain in brief the following terms with illustrations : (i)

Structural isomerism ,

(ii)

Stereo isomerism,

(iii)

Position isomerism, and

(iv)

Tautomerism.

Maximum Marks : 100 Course Code : ET-201A BTCM Weightage : 30% Last Date of Submission : Sept.

30, 2009

TUTOR MARKED ASSIGNMENT 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.

Q.1 (a)

Describe briefly the main causes of capillary effect. Calculate the capillary effect of a glass tube of 3 mm internal diameter, for kerosene. The surface tension of kerosene is 0.049 N/m, angle of concrete being 1o, specific weight of kerosene is 8700 N/m3.

(b)

A flat bottom tank 3 m × 1.5 m  2 m in size carries 1.2 m depth of water and slides down an inclined plane of 30o inclination to horizontal ground level at an acceleration of 2 m/sec2. Find the free surface slope and pressure at the bottom of the tank.

7

Ns.3 v3 1 M Q T ∆Mm

(c)

Derive the resultant force in the dam due to a spherical rook projection. State the angle of the same to the horizontal axis (Figure 1). The area of the dam can be had by taking a normal projection (to paper) of 5.5 m.

8

- (1,1) co d b a (-1,-1) (1,-1) (1,1)

Q.2 (a)

Find the circulation around the square enclosed by the lines x = ± 1, y = ± 1 (Figure 2) for a two dimensional flow provided by the equations, u = x2 + 2xy; v = x – 2y2 at the centre O.

Figure 2

(b)

What is Continuity Equation? Why it is termed so? Determine whether the following satisfy the continuity equation : (i) u = 2x 2 + zy

v = − 2xy + 3y 3 + 3zy

w =−

3 2 z − 2 xz − 6 yz 2

(ii) u =x+ y

v =x−y

Q.3 (a)

Describe the importance of dimensionless parameters for a civil engineer. What is Reynolds number? What it signifies and where is it used? Which of the following are not valid combinations of parameters :

4

(i) F g2 ρv 4

,

v 2 ρ2 v 3 , g D gµ

(ii) ρv D v 2 µF , , 2 2.5 5.7 µ gD ρ g D (iii)

F ρv D , µv D µ

20 cm 1 20

(b)

The pressure drop  p generated by a pump of a given geometry is known to depend upon the impeller diameter D, the rotational speed N, the fluid discharge Q, the fluid density ρ and viscosity µ . Obtain dimensionless form of the functional relationships.

(c)

A junior technician of Airport Authority concepts two dies of dissimilar diameters as shown in Figure 3, for carrying ATF (Aviation turbine fuel). Estimate the discharge through the pipe and draw energy and piezometric heads along the pipeline and connection. The pressure at section 1 is p1 = 3 kPa. Pressure difference between sections is

Figure 3

(d)

Explain the propulsion of a fighter bomber jet aircraft with two gas turbines. Calculate the mechanical efficiency when a bomber consumes 2 kg of ATF for 37 kg air and discharge gases at the exhaust at a velocity v2 at 2137 m/sec. Determine the efficiency at the speed of

aircraft at 313 m/sec.

4

Q.4 (a)

(b)

Q.5 (a)

(b)

Which is the most popular method of measurement of gas flow in industries? Discuss various methods in brief and accuracies of gas flow measurement for large volumes. Derive the flow measurement equation for orifice meters. (i)

How Hagen-poiseuille and Couette flows are formed?

(ii)

Derive a combined flow equation for the flows.

(iii)

Discuss the industrial application of such flows.

(i)

Depict main differences between laminar and turbulent flows?

(ii)

What causes transition fram laminar to turbulent flow?

(iii)

Why are most engineering applications have turbulent flows than laminar?

(i)

Gas companies worldwide use more globe than gate valves. Why?

(ii)

Why very high pressure piping (≈ 200 kg/cm2 or more) are made of seamless pipes having smooth surfaces?

(iii)

Do the pipeline losses reduce after the pipelines are in use for 1 year or so?

Q.6 (a)

Define and derive boundary layer velocity distribution adjacent to smooth and rough boundaries.

(b)

Find the elevation of level of reservoir C and distribution of discharge. Take f = 0.023 all pipes (Figure 4).

4

100 L C B A 80 = 1300 M ≅ 800 M 1000 M 0.5 D=1 0.8 MM 3 Q 1 = 3M /s

3

Figure 4

Q.7 (a)

Explain drag and lift of bodies, with specific reference to spheres. For various Re ranges Re = ∈ [0, 1]

Re = ∈ [1, 2 × 10 5]

Re > [2 × 10 5]

(b)

An inclined metallic plate was kept in a wind tunnel with a specific angle of attack where the CL and CD where 0.75 and 0.15 for a flat size of 2 m long and 1.2 m wide. Calculate lift force, drag force, resultant force and its direction and power spent for overcoming resistance to plate, when the wind velocity (in the tunnel) is 50 km/h. Assume density of air is 1.2 kg/m3.

Q.8 (a)

Discuss drag of model of aircraft. For prototype studies, what dimensions are kept in common for model and actual aircraft? Can kinematic and dynamic similarities be taken care in all model testings of aircrafts?

(b)

An oil company has a pipe diameter of 2.5 m for crude oil. Calculate the velocity of propagation of pressure wave in a steel pipe [E = 2.07  105 MPa] carry crude oil with its RD = 0.8 and K = 1.5 × 103 MPa. The pipe thickness is 200 mm.

Q.9 (a)

(b)

Define and discuss the concepts of : (i)

turbulence intensity,

(ii)

apparent shear stresses,

(iii)

effective viscosity,

(iv)

Prandtl mixing length, and

(v)

free turbulence and wall turbulence.

A wing of a small aeroplane is rectangular in plan having a span of 10 m and a chord of 1.2 m. In straight and level flight at 240 km/hour, the total aerodynamic force acting on the wing is 20 kN. If the lift/drag ratio is 10, calculate the coefficient of lift and the total weight that the aeroplane can carry. Assume air density to be 1.2 kg/m3.

Q.10 Select and write the correct answer : (a)

(b)

The viscosity of (i)

liquids increases with temperature

(ii)

gases increases with temperature

(iii)

fluids increases with temperature

(iv)

fluids decreases with temperature

The kinematic viscosity (ν ) is related to dynamic viscosity () as (i) ν=

µ ρ

4

(ii) ν=µρ

(iii) ν=

ρ µ

ν=

µ ρg

(iv)

(c)

(d)

The capillary rise in a 3 mm tube immersed in a liquid is 1.5 cm, if another tube of diameter 4 mm is inserted, the capillary rise would be : (i)

1.125 cm

(ii)

2.0 cm

(iii)

2.667 cm

(iv)

8.44 cm

The pizometric head in a static fluid (liquid) (i)

remains constant only on a horizontal plane

(ii)

increases linearly with depth in the liquid volume

(iii)

remains constant at all points

(iv) decreases linearly with depth below the free surface. (e)

Streamline is a line which (i)

is normal to the velocity vector at every point

(ii)

represent lines of constant velocity potential

(iii)

is normal to the lines of constant stream function

(iv) is tangential to the velocity vector everywhere at a given instant. (f)

If ‘wz’ is the component of rotation of a fluid about z-axis. The vorticity along the z-axis would be (i)

1 wz 2 (ii) 2 wz

(iii)

∂ wz dx (iv)

∫ (g)

w z dz

For Bernoulli’s equation

constant, which of the following is not true : 2

p v + + z= γ 2g

4

(i)

the flow must be steady

(ii)

fluid must be ideal gas

(iii)

flow must be irrotational

(iv) the fluid must be incompressible. (h)

What is the main cause of losses in pipeline fittings (bends, tees, etc.) and valves? (i)

fabrication methods

(ii)

surface roughness

(iii)

flow separation of boundary layers

(iv) none of these. (b)

(b)

The velocity potential is used to define (i)

Unsteady flows

(ii)

Irrotational flows

(iii)

Rotational flows

(iv)

Isothermal flows.

Vorticity is (i)

Limiting value of circulation per unit area

(ii)

Limiting value of circulation per unit volume

(iii)

Circulation around a curve in steamlined flow

(iv)

Circulation around a curve in non-streamlined flow.

3

Maximum Marks : 100 Course Code : ET 201 B BTWRE Weightage : 30% Last Date of Submission : Oct.

31, 2009

TUTOR MARKED ASSIGNMENT ET 201 (Part B) ENGINEERING THERMODYNAMICS

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

Q.1 Define following : (i)

System and Surroundings.

(ii)

Homogeneous and Heterogeneous system.

(iii)

Thermodynamics equilibrium.

(iv)

Reversible and Irreversible process.

Q.2 (a) (b)

Differentiate between open and closed cycle. Differentiate between absolute and gauge pressure.

Q.3 Define enthalpy of a system and prove that change in enthalpy for a non-flow constant pressure process is equal to heat exchange. Q.4 The work and heat exchange involved by a system in a process (say A) are 20 kJ and 16 kJ. Another process (say B) between the same and conditions involves a heat input of 9 kJ. Determine the change in internal energy involved and also the work done in the process B. Prove that if a cycle is formed using process A and B, the first law is obeyed. Q.5 State the second law of thermodynamics as per (i) Kelvin Planck and (ii) Clausius and prove that both statements are equivalent although they appear to be different. Q.6 A closed system undergoes a thermodynamics cycle ABCDA. The heat transfer per minute during processes AB, BC and CD are – 500 kJ, 10,000 kJ and – 1000 kJ, respectively. The

3

work transfers per second during processes AB, BC, CD and DA are – 10,000, zero, 17000, and – 1000 kJ, respectively. Find the rate of heat transfer during the process CD and net rate of work input in kW. Q.7 (a) (b)

What is the difference between wet compression and dry compression? An air compressor takes in air at 1 bar and 20oC and compresses it according to law PV1.2 = constant. It is then delivered to a receiver at a constant pressure of 10 bar. Determine : (i)

Temperature at the end of compression.

(ii)

Work done during compressions per kg of air.

Given : R = 0.287 kJ/kgoK. Q.8 An ice plant working on reversed Carnot cycle heat pump produces 20 tonnes of ice per day. The ice is formed from water at 0oC and maintained at 0oC and heat is rejected to atmosphere at 27oC. The ice plant is run by a Carnot engine which absorbs heat from a source which is maintained at 227oC by burning fuel of 5000 kcal/kg calorific value. Find the consumption of fuel per hour and HP developed by engine. Q.9 (a)

A sample of steam from a boiler drum at 30 bar is passed through a throttling calorimeter in which pressure and temperature are found to be 1 bar and 150oC. What is the dryness fraction of steam taken from the boiler? Given :

At

p = 1 bar, t = 150oC, h = 2776.4 kJ/kg

At

p = 30 bar, hf = 100\8.3 kJ/kg hg = 2802.3 kJ/kg.

(b)

A reversible heat engine is operating between – 13oC and 37oC. Find its COP as : (i)

heat pump and

(ii)

refrigerator.

Q.10 Define compressor? What are the various types of compressor? Describe the working principle of reciprocating compressor with neat sketch of PV diagram.

4

Maximum Marks : 100 Course Code : ET-202A BTCM Weightage : 30% Last Date of Submission : Sept.

30, 2009

TUTOR MARKED ASSIGNMENT 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.

A B 4cm 2cm hole 1cm 60°

Q.1 (a)

Find the c.g. of the plane figure with a hole as shown in Figure 1. Also find its moment of inertia about line A-B.

3

Figure 1

(b)

Determine the moment of inertia of the given I-section (Figure 2) about : (i)

X-X,

2cm A B 2.5cm 2cm xY 3mm

(ii)

Y-Y, and

(iii) A-B.

Figure 2

4

(5 + 5 = 10) Q.2 (a)

(b)

A bar of constant cross-section hangs vertically subjected only to its own weight, W. Determine the strain energy stored within the bar, in terms of its length, area of cross-section, and modulus of elasticity of its material. A simply supported beam is struck at its mid-point by a weight W = 125 kgf falling freely from a height of 12 cm above the top of the beam. The beam is of circular cross-section, 10 cm in diameter, and 5 m long. Determine the maximum deflection of the beam, taking E = 2  106 kfg/cm2. (5 + 5 = 10)

r1=100mm D A C B

3

Q.3 (a)

The surface of a plate of uniform thickness is given by the shaded area ADBC as shown in Figure 3.

Figure 3

If the plate is suspended from a hinge at A, what angle will the line AB make with the vertical? Y 4.10 1.8m 22 xT 35° 1 5°kg rpm Zm

(b)

A rod XYZ is rotating at 150 rpm about a vertical axis through X. It supports a ball of mass 22 kg at the end Z (Figure 4). XYZ is fixed in position by the rod YT. Neglecting the masses of XYZ and YT, determine the force that is experienced by the rod YT, and is nature.

Figure 4

(5 + 5 = 10)

Q.4 A solid uniform circular disc having a diameter equal to 740 mm, and a mass of 270 kg, rolls without slippage down a plane that is inclined at an angle of 25o with the horizontal. Determine the frictional force and acceleration of the mass centre of the disc.

4

(10) Q.5

25 cm 2.5 20 cm

A (a)

Determine the load that the beam can carry per metre of its length, if the allowable stress in the beam = 1000 kg/cm2.

Figure 5

(b)

Determine the load if the both flanges are of length 20 cm.

(c)

Determine the load if the section is simply an inverted T-section, i.e. the upper flange is missing. (5 + 2 + 3 = 10)

120 E 8 C 4 1 A B 50 m kg 40° 0°

3

Q.6 (a)

A truss, with both its ends fixed, carries loads as shown in Figure 6. It is subjected to a system of loads. Drawing the vector diagram, find the magnitude and nature of forces in all the members of the truss.

Figure 6

(b)

Discuss in the detail the following : (i)

perfect frame,

(ii)

imperfect frame,

(iii)

deficient frame, and

(iv) redundant frame. (5 + 5 = 10) 2.5 C D 3 B A 7 2.5 5 2.2 tmtm

4

Q.7 (a)

Construct SF and BM diagram of the beam (Figure 7). Also find the value and position of the maximum BM.

Figure 7

(b)

Given a simply supported beam (Figure 8) loaded as shown. Constant SF and BM diagrams of the beam; and indicate the value and position of maximum BM.

4

Cω t/m sm A B ll/2

3

Figure 8

Q.8 (a)

(b)

(5 + 5 = 10) A solid shaft of 6 cm diameter is running at an rpm of 160. Find the hp which the shaft can transmit, if the permissible shear stress is 800 kgf/cm2, and the maximum torque is likely to exceed the mean by 30%. Determine the appropriate diameter for a circular shaft required to transmit 120 hp at 180 rpm. The shear stress, in the shaft is not to exceed 700 kg/cm2, and the maximum torque exceeds the mean by 40%. Also calculate the angle of twist in a length of 2 m. Take C = 0.9 × 106 kg/cm2. (5 + 5 = 10)

3 1 B A 3.5 10 u.d.l .5 kN/m kN cm 45°

4

Q.9 (a)

For the cantilever shown in Figure 9, determine the reactions (forces and moment), and draw SF and BM diagrams.

Figure 9

(b) (i)

For the figure shown in Figure 10, calculate the moment of area about : X1 – X1,

5 213cm 1500 10 X cmmm

4

(iii)

X3 – X3.

Figure 10

(5 + 5 = 10) Cµost= 0.15 B A 60° 0.30

Q.10 (a)

Figure 11 shows two blocks A and B on rigid surfaces. If the weight of block B = 3 kN, find the minimum value of the weight of block A to maintain the equilibrium as shown.

Figure 11

(b)

Figure 12 shows a flexible belt wrapped around a portion of a drum. For various angles of contact, θ (= 60o, 100o, 215o and 260o) find the tensions in the belt as a result of friction of the torque developed by the belt is 215 Nm and 195 N-m – for each angle of contact, respectively. Take µ = 0.25 and assume that the belt is slipping while the drum rotates.

4

Flexible D T θ 21rum belt

Figure 12

(5 + 5 = 10)

Maximum Marks : 100 Course Code : ET-202B BTCM Weightage : 30% Last Date of Submission : Sept.

30, 2009

TUTOR MARKED ASSIGNMENT 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.

3

Q.1 (a)

Explain the following with reference to 3- systems : (i)

Meaning of phase sequence.

(ii)

Function of neutral wire in the supply system.

(iii)

Distinction between phase and the voltages.

(b)

How and why do we conduct open circuit (O.C.) and short circuit (S.C.) tests on a transformer?

Q.2 (a)

Explain the phenomenon of resonance in parallel RLC circuit and derive the expression for resonant frequency.

(b)

What is power factor of an A.C. circuit? What is the necessity 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 F 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.3 (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)

(c)

Q.4 (a)

Explain the speed-torque characteristics of : (i)

A d.c. series motor, and

(ii)

A d.c. shunt motor.

A 250 V d.c. shunt motor has Rf = 150 Ω and Ra = 0.5 Ω . The motor operates on noload 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. Differentiate between machine language, assembly language and high level language.

(b)

What are the addressing modes available in 8085 microprocessor? Give at least two examples of each.

(c)

What are different types of instruction available in 8085 instruction set? Give and explain at least two examples for each type.

Q.5 (a)

State and explain Thevenin’s theorem. What is the Thevenin equivalent of an ideal d.c. voltage source?

(b)

Find the voltage across R in the following network by mesh analysis :

4

5 10 2 V VV Ω +kΩ

Figure

Q.6 (a) (b) Q.7 (a)

Give advantages of negative feedback over positive feedback. Derive step response of a second order system and find its time constants. 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 400 V, 3-phase supply. Find the readings of the two watt meters.

Q.8 (a) (b)

What are Op-amps? Is the assumption of virtual ground valid in practical op-amps? Explain the working of an ADC and a DAC.

Q.9 (a)

A 50 KVA transformer has primary voltage of 6600 V and a secondary voltage of 250 V. It has 52 secondary turns. Find the number of primary turns and the primary and secondary current neglecting losses.

(b)

A DC motor has 6 poles, flux per pole of 0.05 Wb with lap wound armature of 600 conductors. Motor speed is 500 rpm. Determine the applied voltage and back emf given that, armature resistance is 0.25 , armature current 40 A. Also, determine the torque developed by the motor in N-m.

Q.10 (a)

What are the basic components used in electrical installations? State briefly the function of each component.

3

(b)

What are advantages of using digital indicating instruments vis-à-vis analog instruments?

4

Maximum Marks : 100 Course Code : ET204A BTCM Weightage : 30% Last Date of Submission : July

31, 2009

TUTOR MARKED ASSIGNMENT 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.

Q.1 (a) (b)

What are the various types of special and new materials? Describe each material, with suitable examples. Describe the types of bonding in solids, with neat sketches and suitable examples. (5 + 5 = 10)

Q.2 How do the solids are classified according to their electrical properties? Describe them in detail. (10) Q.3 What are the three most common crystal structures found in metals? Describe them in detail with suitable diagrams. (10) Q.4 (a) (b)

Differentiate between engineering stress and true stress. What is ductility, and how it is measured? Explain. (5 + 5 = 10)

Q.5 (a) (b)

What is TTT diagram? What is its purpose? Explain. What is the purpose of heat treatment? Why is annealing performed? (5 + 5 = 10)

Q.6 (a) (b)

Describe the various types of dislocations with the aid of neat sketches. Describe the various types of surface imperfections in the crystals, with neat diagrams. (5 + 5 = 10)

Q.7 Describe the concept of plasticity in materials, with the aid of stress-time diagrams. (10) Q.8 Describe the phenomenon of superconductivity in metals and alloys. (10) Q.9 A cylindrical specimen of steel having an original diameter of 12.8 mm is tensile tested to fracture and found to have an engineering fracture strength of 460 MPa. If its cross-sectional diameter is 10.7 mm. Determine : (i)

The ductility in terms of percent area reductions, and

3

(ii)

The true stress at fracture. (10)

Q.10 (a) (b)

What is corrosion? Explain the effect of corrosion of steel in concrete structures. Explain the following : (i)

Atmospheric degradation, and

(ii)

Degradation of polymers.

(5 + 5 = 10)

4

Maximum Marks : 100 Course Code : ET-204B BTCM Weightage : 30% Last Date of Submission : Sep.

30, 2009

TUTOR MARKED ASSIGNMENT ET 204 (Part B) ENGINEERING MATERIALS

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

Q1. (a)

What are the structural components of a conventional floorings – give well-defined sketches, and discuss their essential aspects.

(b)

Collect your own (or from other sources) the relevant photographs of the above (a) items, with reference to their construction and place them in your answer sheet.

Q.2 (a)

(b)

Discuss the following : (i)

Terrazo flooring,

(ii)

Magnesium oxychloride flooring, and

(iii)

Bitumen mastic flooring.

Explain the construction procedures of the above mentioned floorings.

Q.3 Using sketches/photographs, discuss and explain the following steel-flooring systems : (i)

Open grid floors,

(ii)

Pressed steel planks, and

(iii)

Embossed plates.

Give their advantages and comparison with other systems. Q.4 (a) (b) Q.5 (a)

Q.6

Explain how superplasticizers act, and how they differ from plasticizers? Outline the preparation of mud phuska. How are these items laid, and paved with brick tiles? Explain the advantages of integral water proofing compounds.

(b)

What is water proofing liquid membrane? Explain its use and function.

(c)

Discuss the role of epoxy resins and compounds in water proofing.

Draw the following on a drawing sheet : (i)

A finish using plaster moulds,

(ii)

Various types of textural form of linear finishes,

(iii)

Exposed aggregate finishes – various types, and

(iv) Mechanical finishing. Discuss their functions and construction.

4

Q.7 Summarise the relevant IS-code and give the important specifications about water proofing materials, and white washing. Q.8 Give detailed manufacturing process of plywood products, fibre borads, straw boards and hard boards. Discuss their use and advantages. Q.9 Draw 3-D views of the following items : (i)

Box conduits – all types,

(ii)

General metallic conduit box, and

(iii)

Solid and inspection type of bends, tee and elbows.

Explain their functions. Q.10 Give 3-D views plan, elevational and sectional elevations of the following items : (i)

Various types of lamp holders;

(ii)

Fluorescent lamp holders – various types,

(iii)

Switches – various types, and

(iv)

Electronic electric meters.

Discuss in brief construction and function of each item.

4

Maximum Marks : 100 Course Code : ET-301A BTCM Weightage : 30% Last Date of Submission : July

31, 2009

TUTOR MARKED ASSIGNMENT ET 301 (Part A) SYSTEMS METHODS

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

Q.1 A company manufacturers two products X and Y using four major departments Q, R, S and T. The capacity limits of those department are given below : Department Q R S T

Capacity for the Production of X Y 4000 Not required 5000 5000 7000 4000 8000 3000

Solve graphically for the optimal production level if both products sell at Rs. 40 per unit and the average costs of the two products X and Y are Rs. 14 and Rs. 20, respectively. (10) Q.2 A company produces two types of products say type A and B. Product B is of superior quality and product A is of lower quality. Profit on the two types of products ae Rs. 30 and Rs. 40, respectively. The data on resource required, availability of resources are given below :

Raw materials (kg) Machining (hours/per piece) Assembly (man hour)

Requirements Product A Product B 60 120 8 5 3 4

Capacity Available per Month 12000 600 500

How should the company manufacture the two types of products in order to have a maximum overall profit? (10) Q.3 A manufacturer has distribution centres at X, Y and Z. These centres have availability 40, 20 and 40 units of his product. His retail outlets at A, B, C, D and E require 25, 10, 20, 30 and 15 units, respectively. The transport cost (in rupees) per unit between each centre outlet is given below : Distribution Centres X Y

A 55 35

Retail Outlets B C 30 40 30 100

3

D 50 45

E 50 60

Z

40

60

95

35

30

Determine the optimal distribution to minimise the cost of transportation. (10) Q.4 A certain equipment needs five repair jobs which have to be assigned to five machines. The estimated time (in hours) that each mechanic requires to compute the repair job is given in the following table : Job

J1

J2

J3

J4

J5

M1

7

5

9

8

11

M2

9

12

7

11

10

M3

8

5

4

6

9

M4

7

3

6

9

5

M5

4

6

7

5

11

Machine

Q.5

Q.6

Q.7

Q.8

Assuming that each mechanic can be assigned to only one job, determine the minimum time assignment. (10) A large service station has a store room from where the service mechanics take the parts for the jobs they work upon. The mechanics wait in the line to get the parts they need. The store is manned by one attendant who can on an average attend 7 mechanics per hour. It is observed that on an average, the mechanics average arrival rate at the store room is 5 per hour. Assuming that the pattern of mechanic arrivals is Poisson distributed and the servicing time is exponentially distributed, determine : (i) the expected numbers of mechanics in the system, that is those waiting in the line and being serviced by the attendant, (ii) the expected number of mechanics waiting in the queue, (iii) the expected time that a mechanic has to spend in the queue, and (iv) the expected time that a mechanic spends in the system, i.e. waiting in the queue and getting service. (10) XYZ manufacturer expects to produce 200,000 widgets during the year ending June 20, 2009 to supply a demand that is uniform throughout the year. The set-up cost for each production run of widgets is Rs. 144 and the available cost of producing each widget is Rs. 5. The cost of carrying one widget in inventory is Rs. 20 per year. After a batch of widgets is produced and placed in inventory, it is sold at a uniform rate and inventory is exhausted when the next batch of widgets is completed. Management wants an equations to describe this situation. Determine the optimal quantity of widgets to produce in each run in order to minimise total production and inventory costs. (10) (a) Describe system diagram. Represent sped control of the pump motor with the help of a system diagram. (b) What do you mean by manual and automatic feed back? Give at least two examples of manual and automatic feed back. (c) How are system classified? Explain causal and non-casual systems with the help of suitable examples. (d) Explain physical and non-physical system with the help of suitable examples. (2.5 × 4 = 10) (a) What do you understand by model of a system? Explain various types of system models. (b) Describe various elements of a electrical system.

3

(c) (d)

What are the various types of mechanical system? Give at least one example of each. Why electrical analogus model is developed for a physical system? (2.5  4 = 10)

Q.9 A civil engineering firm has to bid for the construction of a dam. The activities and time estimates are given below : Activity

Optimistic

Most Likely

Pessimistic

1-2

14

17

25

2-3

14

18

21

2-4

13

15

18

2-8

16

19

28

3-5

15

18

27

4-6

13

17

21

14

18

20

7-9

16

20

41

8-9

14

16

22

3-4 (Dummy)

5-7 (Dummy) 5-9 6-7 (Dummy) 6-8 (Dummy)

The policy of the firm with respect to submitting bids is to bid the minimum amount that will provide a 95% of probability of at best breaking even. The fixed costs for the project are eight lakhs and the variable costs are Rs. 9000 every day spent working on the project. The duration is in days and the costs are in terms of rupees. What amount should the firm bid under this policy? (10) Q.10 (a)

Describe the automatic temperature control system incorporated into the room air-conditioner. Draw a functional diagram for it.

(b)

What do you mean by Electro-mechanical system? Explain the equivalent circuit of a DC machine.

(c)

An 9 kW, 230 DCD shunt motor has armature resistance of 0.60 ohms. Its no load speed is 1250 rpm : (i)

calculate the speed, torque and armature current at full load, and

(ii)

compare the speed when the motor drives a centrifugal load having torque characteristics of TP = 0.6 × 10– 4 N2/Nm, where N = speed in rpm. (2 + 2 + 6 = 10)

3

Maximum Marks : 100 Course Code : ET301B BTCM Weightage : 30% Last Date of Submission : July

31, 2009

TUTOR MARKED ASSIGNMENT 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.

Q.1 (a) (b) Q.2 (a) (b)

What is an operating system? Explain the various functions of the operating system. Explain ROM, RAM, PROM and EPROM. Draw a worksheet of LOTUS 1-2-3. Label the sketch. Describe the components of spreadsheet with emphasis on control panel and mode indicator. Explain different date related functions in LOTUS 1-2-3.

Q.3 Explain the following dBase commands : (i)

MODIFY COMMAND

(ii)

SET TALK ON/OFF

(iii)

USE

(iv)

DISPLAY ALL

(v)

ACCEPT

Q.4 What are the different hardware and software requirements for making a Computer Aided Drawing? Q.5 Write short notes on the following AutoCAD commands : (i)

MIRROR

(ii)

PEDIT

(iii)

SCALE

(iv)

LAYER

(v)

PAN

(vi)

SNAP

Q.6 (a) (b) Q.7 (a) (b)

Explain different types of memories used in a computer. How many types of graph does “Types” item on the graph menu provide? What is the restriction about data ranges for a pie chart in Lotus 1-2-3? What technology was used in third generation and fourth generation computers? Describe the following MS-DOS commands : (i)

FORMAT

(ii)

XCOPY

3

(iii)

MKDIR

(IV) DEL Q.8 A database file called EMPLOYEE contains the fields NAME, BASIC, HRA. Write a set of commands to print a report with employee name and total salary for those emp0loyees whose total salary is more than Rs. 30,000 per month. Total salary = BASIC + HRA In the end of the program, it should also print the total number of employees with total salary more than Rs. 30,000. Q.9 (a) (b) Q.10 (a) (b)

What is computer-aided drafting? What are the advantages and disadvantages of computer-aided drafting? What is graphics editor? What are the advantages of having graphics editor? Mention the differences between RAM and ROM. Write down MS-DOS commands. (i)

To delete the file IGNOU.TXT from the root directory in drive A.

(ii)

Format a new floppy for use with system files transferred into it.

4

Maximum Marks : 100 Course Code : ET-501A BTCM/BTWRE Weightage : 30% Last Date of Submission : July.

31, 2009

TUTOR MARKED ASSIGNMENT ET 501 (Part A) SOIL MECHANICS

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

Q.1 (a)

Draw and explain the USBPR textural classification chart of soil (triangular chart) giving clearly the size-limits of the various soil components.

(b)

The results of particle size analysis of two soil samples A and B are given below. Draw the particle size distribution curves and find the percentages of gravel, sand, silt and clay in each sample according to the (i) MIT, (ii) USDA and (iii) BIS classifications. Particle Size (in mm)

Percent Finer A

B

1.000

100.0

100.0

0.842

96.7

99.5

0.592

88.2

92.3

0.420

75.5

77.8

0.251

65.6

51.4

0.075

54.9

39.6

0.040

46.5

28.7

0.020

35.8

19.3

0.005

30.7

17.5

0.002

25.5

14.0

Q.2 (a)

What is the role of hydrometer analysis in determination of soil particle size? Explain the various corrections made in the readings of a hydrometer analysis.

(b)

In a hydrometer analysis 50 g of oven-dried soil is mixed with 1000 cm3 of water. For a reading of 0.0080 (corrected value) taken after 120 minutes, the depth of the centre of the hydrometer bulb is 142.5 mm (all corrections applied). What is the particle size and its percentage corresponding to this reading? Special gravity of soil grains = 2.65 Viscosity of water = 0.001 Ns/m2.

Q.3 (a)

Explain a field method of measuring permeability of a soil layer.

3

(b)

Q.4 (a)

In a field permeability test, steady state conditions are reached under a pumping rate of 6830 cm3/sec from the test well, which is bored up to the impervious stratum. A and B are two observation wells situated at 22 m and 31 m from the test well. The elevation of water in A is 9.83 m and in B is 9.94 m, calculate the coefficient of permeability of the soil layer. What are the various engineering classifications of soil and what is their basis?

(b) The following data were obtained from the liquid limit test on a soil sample : No. of Blows

Moisture Content %

36

43.2%

32

47.8%

20

51.5%

12

59.8%

Draw the flow curve and find the liquid limit and flow index. If the plastic limit of the soil is 17.9%, what is the plasticity index? Classify the soil according to the Unified Soil Classification system. Q.5 (a) (b)

Explain the phenomenon of ‘compaction’ of soil. How is it different from ‘consolidation’. In a Standard Proctor Test the following data were obtained : Moisture Content (%)

14.0

16.0

18.0

20.0

22.0

24.0

Wet Unit Weight of Soil (kN/m3)

16.75

17.80

18.95

19.45

19.25

19.00

Plot the moisture content – dry unit weight curve and obtain the maximum dry unit weight of soil and the optimum moisture content. Also plot the zero air-void line and 10% constant percentage air-void line. Given Special gravity of soil = 2.67 Unit weight of water (w) = 10 kN/m3 Q.6 Write short explanatory notes on the following : (i)

Flow-nets,

(iii) Seepage force, (iii) Uplift pressure under a hydraulic structure, (iv) Critical hydraulic gradient, and (v) Pore-water pressure. Q.7 (a) Explain Boussinesq’s theory of stress distribution under a point load ‘P’ acting on a soil mass, stating clearly the assumptions made. Are these assumptions strictly valid? Plot graphically the distribution of vertical stress in a soil mass with depth. (b) Explain how the above idea is extended in case of a uniformly loaded square plate resting on a soil mass. Plot again the isobars for vertical stress in such a case. Q.8 (a) (b)

What are the factors that affect the shear strength of soil? Explain. In a consolidated undrained test, a sample of saturated sand was consolidated under a 3-dimensional pressure of 300 kPa. The axial stress was then increased without allowing

3

drainage. Failure occurred when the deviator stress reached 250 kPa. The proe-water pressure at failure was 220 kPa. Find the shear parameters of the consolidated undrained test, both in terms of total and effective stress. Q.9 (a)

What are the various methods of determining the coefficient of consolidation of a soil specimen?

(b)

The following compression dial readings were obtained in an oedometer test on a saturated doubly-drained clay specimen for the pressure increment from 1 kg/cm2 to 2 kg/cm2. Time (in minutes)

0

0.25

0.50

1.0

2.25

4

6.25

9

16

Reading (in mm)

8.13

7.74

7.63

7.52

7.30

7.08

6.91

6.80

6.67

Time (in minutes)

25

36

49

64

81

100

300

1440

−

Reading (in mm)

6.60

6.55

6.52

6.49

6.47

6.46

6.40

6.32

−

The thickness of the specimen measured at the end of 24 hours was 18.12 mm and the moisture content was 24.8%. The specific gravity of clay is 2.67. For this pressure range calculate : (i)

the coefficient of compressibility,

(ii)

the coefficient of volume change,

(iii)

the coefficient of consolidation of the clay, and

(iv)

the compression ratios.

Both by (a) the square root method (b) the log-time method, and compare. Q.10 (a)

(b)

Explain briefly how the stability of slopes are affected by : (i)

the water-table,

(ii)

sudden draw-down conditions, and

(iii)

earthquake forces.

A clay embankment 6 m wide at top slopes on both sides at 1.5 H to 1.0 V. The height of the embankment is 5 m, and it carries a surcharge load of 2 t/m2 over its full top area. Determine the factor of safety against failure along a slip circle passing through the foundation soil, which is of sand having φ = 33o and γ = 1.0 t/m3. For the clay embankment C = 2 t/m2 and γ = 1.8 t/m3. Assume water table at top of foundation soil level.

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Maximum Marks : 100 Course Code : ET-501B BTCM/BTWRE Weightage : 30% Last Date of Submission : Sep.

30, 2009

TUTOR MARKED ASSIGNMENT ET 501 (Part B) FOUNDATION ENGINEERING

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

Q.1 (a) (b) Q.2 (a) (b)

Q.3 (a) (b)

Q.4 (a) (b)

Q.5 (a)

Q.6

Explain standard penetration test. How the bearing capacity and settlement are estimated by using SPT value? Explain with neat sketches – auger boring and wash boring. Discuss the factors affecting depth and location of foundation. Determine the net ultimate bearing capacity of a rectangular footing of size 2 m  4 m foundated at 2 m below the ground surface. The water table is located at 2.5 m below ground surface. The properties of soil are  = 18 kN/m3, C′ = 15 kN/m3, φ = 25o, NC = 20.7, Nq = 10.7 and Nγ = 10.4. Explain immediate settlement, consolidation settlement and secondary settlement. A square footing carrying a load of 200 t from a column is proposed to be founded on sand. The corrected average value of SPT for the soil is 20. If the maximum settlement of the footing is 40 mm and the factor of safety against shear failure is 3. Determine the size of footing if the depth of footing is 2.5 m and depth of ground water is 3.5 m. Discuss the plate load test and its limitations. A footing 5 m × 3 m in plan transmits a pressure of 200 kN/m2 on a cohesionless soil having E = 6  104 kN/m2 and  = 0.5. Determine immediate settlement at the centre of footing. The influence factor is 1.5. Classify the pile foundation.

(b)

A RCC pile weighing 50 kN (including self weight helmet, dolly and cushion) is driven by a drop hammer weighing 60 kN and having effective fall of 1 m. The average set per blow is 1.5 cm. The total elastic compression is 1.5 cm. Assuming coefficient of restitution on as 0.25 and factory of safety as 2.5, determine the allowable load for the pile.

(a)

Discus pile load test. What is integrity of pile.

(b)

250 mm diameter, 8 m long piles are used as foundations for a column in a uniform deposit of medium clay (c = 50 kN/m2). The spacing between the piles is 600 mm. There are 9 piles in the group arranged in a square pattern. Calculate the ultimate load capacity of the group. Assume adhesion factor as 0.7.

Q.7 Write short notes on following : (i)

Foundation on expansive soil,

(ii)

Group action of pile,

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(iii)

Types of sampler, and

(iv)

Dynamic cone penetration test.

Q.8 (a) (b)

Explain active earth pressure, passive earth pressure and earth pressure at rest. A retaining wall with smooth vertical back is 12 m high and retains a two layer sand backfill with following properties 0-6 m depth :

c = 0

φ

′

= 30,

6-12 m depth :

c = 0

φ

′

= 35o,

γ = 19 kN/m3 γ = 20 kN/m3

Show the active earth pressure distribution, assuming that water table is far below the base of the wall. Q.9 (a) (b)

Discuss various types of mat foundation. When such type of foundation is provided. Calculate the settlement of pile group shown in Figure 1.

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Area 500 600 2/3 8 3 L Middle 0GL m L63 = mm kN Stratum m × =of9 Clay PilesLayers γDiameter = 20 of kN/m Pile3 = 200 sat mm LL = 40% PL = 26% e = 1.06

3

Figure 1

Q.10 (a) (b)

Explain Culmann’s graphical method for the estimation of active earth pressure. A 8 m high retaining wall with smooth vertical back, retains a day backfill with C′ = 15 kN/m2, φ  = 15o, γ = 18 kN/m3. Find the total active thrust on the wall, assuming that tension cracks may develop to the full theoretical depth.

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Maximum Marks : 100 Course Code : ET 531 A BTWRE Weightage : 30% Last Date of Submission : July

31, 2009

TUTOR MARKED ASSIGNMENT ET 531 (Part A) EARTH AND ITS ENVIRONMENT

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

Q.1 (a)

Q.2 (a) (b) (c) (d)

Discuss the different types of slow and rapid mass movements and engineering aspects of mass movements. Write short notes on : (i) Revolution and rotation of the earth, (ii) Mohorovicic discontinuity, (iii) Erosion and denudation, and (iv) Meanders. Why silicates are the most abundant minerals in the earth crust? What are the causes of colouration in quartz? Give examples. What are the uses of study of texture of an igneous rock? What is the meaning of soil in agricultural sense?

Q.3 (a)

State the important types of deserts and give one example of each.

(b)

(b)

Prepare a map (on a A4 size drawing sheet) showing earthquake zones of India.

(c)

Which properties of the atmosphere make long distance communication?

(d)

Temperature is very high (1100-1650oC) in the thermosphere and yet its total heat content is very low. Why?

Q.4 (a) (b) Q.5 (a)

Write an essay (of about 300 words) on the “The importance of atmosphere to the man”. Why is trekking in Himalayas more difficult than at see level? Name the two processes responsible in making loose, soft, unconsolidated sediment into compact, hard, consolidated sedimentary rock.

(b)

What is the difference between mudstone and shales?

(c)

What are the major types of foliation?

(d)

What is the importance of study of lineation?

Q.6 (a)

Write short notes on : (i)

Living fossils,

(ii)

Principles of stratigraphy,

(iii)

Fold morphology, and

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(b) Q.7 (a)

(iv) Significance of study of faults. Distinguish between a fault zone and a shear zone. Compare the lower indogangetic alluvium with the upper indogangetic alluvium.

(b)

What suggests that warm and humid climate in premian gave place to arid climate during Triassic?

(c)

Give the geographical distribution of Cuddapah Supergroup.

(d)

State the three principles of stratigraphy.

Q.8 (a)

Define sustainable development.

(b)

Discuss the remedial measures for wastelands.

(c)

Make a list of toxic metallic pollutants found in aquatic and terrestrial ecosystems.

(d)

Enlist any four methods of soil conservation.

Q.9 (a)

Discus the biogeographical regions of India and prepare a map (on an A4 size drawing sheet) showing these regions in India.

(b)

Prepare a short note on ecological niche.

(c)

List fundamental structure displayed by rocks in field.

(d)

Explain why ecotone may have more diverse community.

Q.10 (a)

What is meant by biogeochemical cycles? Represent any one cycle.

(b)

Write general characteristics of minerals of Feldspar group.

(c)

On Moh’s Scale of hardness, graphite, a form of elemental carbon shows a hardness of 1-2; whereas the other form diamond shows 10. What could be the reason?

(d)

Prepare a map showing distribution of the Proterozoic Rocks in Peninsular India.

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Maximum Marks : 100 Course Code : ET-531B BTWRE Weightage : 30% Last Date of Submission : Sep.

30, 2009

TUTOR MARKED ASSIGNMENT ET 531 (Part B) SOIL SCIENCES

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

Q.1 What is a soil pedon? How are soils classified? Explain the properties of soils of your state to which you belong. Q.2 Explain, how micro-organisms affect each other and how do they affect higher plants? Q.3 Write short notes on the following : (i)

Carbon-nitrogen ratio,

(ii)

ESP of salt-affected soils,

(iii)

Soils of humid regions, and

(iv)

Soil-plant-atmosphere continuum (SPAC).

Q.4 What do you mean by nitrogen fixation? Differentiate between symbiotic and non-symbiotic nitrogen fixation. Q.5 Differentiate between the following :

Q.6

(i)

Vertisol and Ultisol,

(ii)

Soil Microfauna and Soil Microflora

(iii)

pH and pF,

(iv)

Land Grading and Land Evaluation, and

(v)

Fertilisers and Bio-fertilisers.

What are soil moisture constants? Explain each of them with the help of a diagram.

Q.7 Write step-by-step procedure to determine soil texture. Q.8 List the essential plant nutrients? Explain, how will you identify nitrogen deficiency in plants? Q.9 Describe the role of bio-fertilisers in the background of ill effects of heavy doses of chemical fertilisers. Q.10 What is integrated part management? Explain its role in providing safe food.

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