MAT201 PARTIAL DIFFERENTIAL EQUATIONS &COMPLEX …

Question Bank

THIRD SEMESTER (2020)

MAT201 PARTIAL DIFFERENTIAL EQUATIONS &COMPLEX ANALYSIS(FOR

EEE,ECE,CE&ME)

MODULE I

1 Solve (𝑦 − 𝑧)𝑝 + (𝑥 − 𝑦)𝑞 = (𝑧 − 𝑥) 3 KTU JULY 2017

2 Form the partial differential equation from 𝑧 = 𝑥𝑔(𝑥) + 𝑦𝑓(𝑥) 3 KTU JULY 2017

3 Solve (𝑚𝑧 − 𝑛𝑦)𝑝 + (𝑛𝑥 − 𝑙𝑧)𝑞 = 𝑙𝑦 − 𝑚𝑥 5 KTU JULY 2017

4 Find the partial differential equation representing the family of spheres whose centre lies on z- axis

3 KTU JULY 2018

5 Find the general solution of (𝑦2 + 𝑧2)𝑝 − 𝑥𝑦𝑧𝑞 = −𝑥𝑧 6 KTU JULY 2018

6 Find the partial differential equation z=xf(x) +y 𝑒2 3 Model qp 2020

7. Solve 3z=xp+yq 3 Model qp 2020

8. Solve (𝑝2+𝑞2)y=qz 7 Model qp 2020

9 Derive pde from thebrelation z=f(x+at)+ g(x+at) 3 Model qp 2020

10 Solve 𝜕2𝑧

𝜕𝑥𝜕𝑦=𝑥2y 3 Model qp 2020

11 Use Charpit’s methods to solve 𝑞 + 𝑥𝑝 = 𝑝2 7 Model qp 2020

12 Solve 𝑥(𝑦 − 𝑧)𝑝 + 𝑦(𝑧 − 𝑥)𝑞 = 𝑧(𝑥 − 𝑦) 7 Model qp 2020

13 Find the differential equation of all spheres of fixed radius having their centers in the xyplane.

7 Model qp 2020

14 Using the method of separation of variables, solve 𝜕𝑢𝜕𝑥 = 2 𝜕𝑢𝜕𝑡 + 𝑢, where (𝑥, 0) = 6ⅇ−3𝑥 .

7 Model qp 2020

MODULE II

1 Write any three assumptions involved in the derivation of the one dimensional wave equation.

3 KTU July 2018

2 A string of the length l fastened at both ends . The midpoint of the string is taken to a height h and the released from the rest in that position .Write the boundary condition and the initial conditions of the string to find the displacement function y(x,t) satisfying the one dimensional wave equation.

3 KTU July 2018

3 Using method of separation of variables ,solve𝜕𝑢

𝜕𝑥= 2

𝜕𝑢

𝜕𝑡− 𝑢, 𝑢(𝑥, 0) =

5𝑒−3𝑥.

2 KTU July 2018

4 A tightly stretched string of length l fastened at both ends is initially in a position given by y = k x,0< 𝑥 < 𝑙. if it is released from the rest from this position ,find the displacement y(x,t) at any time t and any distance x from the end x=0

5 KTU July 2018

5 Solve the one dimensional wave equation 𝜕2𝑢

𝜕𝑡2 = 𝑐2 𝜕2𝑢

𝜕𝑥2 with boundary 10 KTU

conditions 𝑢(0, 𝑡) = 0, 𝑢(𝑙, 𝑡) = 0 for all t and the initial conditions

𝑢(𝑥, 0) = 𝑓(𝑥),𝜕𝑢

𝜕𝑡

May-2017

6 A string of length 20 cm fixed at both ends is displaced from its position of equilibrium ,by each of its points an initial velocity given by 𝑓(𝑥) =

{𝑥 , 0 ≤ 𝑥 ≤ 10

20 − 𝑥, 10 ≤ 𝑥 ≤ 20 ,x being the distance from one end.Determine the

displacement at any subsequent time

10 KTU May-2017

7 A tightly stretched string of length ‘a’ with fixed ends is initially in equilibrium position. Find the displacement u(x,t) of the string if it is set

vibrating by giving each of its points a velocity 𝑣0 sin(𝜋𝑥

𝑎 ).

10 KTU June -2016

8 A tightly stretched string of length ‘a’ with fixed ends is initially in equilibrium position. Find the displacement u(x,t) of the string if it is set

vibrating by giving each of its points a velocity 𝑣0 sin3(𝜋𝑥

𝑎 ).

10

KTU Aug-2016

9 A tightly stretched string of length L is fixed at both ends. Find the displacement u(x,t)if the string is given an initial displacement f(x) and an initial velocity g(x).

10

KTU Dec-2018

10 A tightly stretched string with fixed endpoints x=0 and x=l is initially in a

position given by u =𝑣0 sin3(𝜋𝑥

𝑎 ),0 ≤ 𝑥 ≤ 𝑙.If it is released from rest

from this position ,find the displacement function u(x,t).

10

KTU Dec-2018

11 Solve one dimensional heat equation when k>0 3 KTU May-2017

12 Write down possible solutions of one dimensional heat equation 3 KTU May-2017

13 Derive one dimensional heat equation 10 KTU May-2017

14 Find the temperature in a laterally insulated bar of length L whose ends are kept at temperature 0℃ , assuming that the initial temperature is

𝑓(𝑥) = {𝑥 , 0 < 𝑥 < 𝐿/2

𝐿 − 𝑥 , 𝐿/2 < 𝑥 < 𝐿

10

KTU May-2017

15 Write down the fundamental postulates used in the derivation of one dimensional heat equation.

3 KTU July- 2018

16 Write down the fundamental postulates used in the derivation of one dimensional heat equation.

7

MARCH2107

17 Find the temperature distribution in a rod of length 3m whose end points are maintained at temperature zero and the initial temperature is f(x)= 100 (2x - 𝑥2),0≤ 𝑥 ≤ 2

10

KTU Dec-2018

MODULE III

1. Show that 𝑢 = 𝑦3 − 3𝑥2𝑦 is harmonic and hence find its harmonic conjugate.

8 DEC 2016

2. Define an analytic function and prove that an analytic function of constant modulus is constant.

8 DEC 2016

3. Check whether the following functions are analytic or not. Justify your answer i) 𝑓(𝑧) = 𝑧 + 𝑧 ̅

ii) 𝑓(𝑧) = |𝑧|2

4+4 MARCH2017

4. Show that 𝑓(𝑧) = 𝑠𝑖𝑛𝑧 is analytic for all z. Find 𝑓’(𝑧) 7 MARCH2017

5. Show that 𝑣 = 3𝑥2𝑦 − 𝑦3 is harmonic and find the corresponding analytic function

8 MARCH2017

6. . Let 𝑓(𝑧) = 𝑢(𝑥, 𝑦) + 𝑖 𝑣(𝑥, 𝑦) be defined and continuous in some neighbourhood of a point z = x+ iy and differentiable at z itself.Then

prove that the first order partial derivatives of u and v exist and satisfy Cauchy- Reimann equations

7 ARIL 2018

7. Prove that 𝑢 = 𝑠𝑖𝑛𝑥𝑐𝑜𝑠ℎ𝑦 is harmonic.Hence find its harmonic conjugate.

8 ARIL 2018

8. Check whether the function f(z) = 𝑅𝑒 (𝑧2)

|𝑧|2 if z ≠ 0

= 0if z = 0 is continuous at z=0

7 ARIL 2018

9. Let f (z) = u+iv is analytic ,prove that u = constant,v=constant are families of curves cutting orthogonally.

7 JULY2017

10 Prove that the function u(x, y) = 𝑥3 − 3𝑥𝑦2 − 5𝑦 is harmonic everywhere . Also find the harmonic conjugate of u.

7 JULY2017

11 Find the points, if any, in complex plane where the function f(z)=2𝑥2 +𝑦 + 𝑖(𝑦2 − 𝑥)is (i) differentiable( ii) analytic

8 JULY2017

12 Find the analytic function whose imaginary part is v(𝑥,𝑦) = 𝑙og( 𝑥2 + 𝑦2 ) + 𝑥 – 2𝑦.

7 MAY 2019

13. Find the image of |𝑧 −1

2| ≤

1

2 under the transformation 𝑤 =

1

𝑧 .Also find the fixed points of the transformation 𝑤 =

1

𝑧

7 DEC2016

14. Find the image of the lines x = c and y = k where c and k are constants under the transformation w = 𝑠𝑖𝑛𝑧

7 DEC2016

15 Find the image of 0 < 𝑥 < 1 ,1

2< 𝑦 < 1 under the mapping

w = 𝑒𝑧

7 MARCH2017,SEPT2020

16. Find the image of the rectangular regio𝑛 − 𝜋 ≤ 𝑥 ≤ 𝜋 , 𝑎 ≤ 𝑦 ≤ 𝑏 under the mapping 𝑤 = 𝑠𝑖𝑛𝑧

8 MARCH2017

17. Find the image of the region |𝑧 −1

3| ≤

1

3under the

transformation 𝑤 = 1

𝑧

8 APRIL 2018

18. Under the transformation 𝑤 = 𝑧2, find the image of the triangular region bounded by = 1, 𝑦 = 1 and𝑥 + 𝑦 = 1.

8 MAY 2019,SEPT 2020

19 Find the image of the half plane Re(z)≥ 2,under the map w=iz 8 JULY 2017

20 Under the transformation𝑤 = 1/ 𝑧 , find the image of |𝑧 − 2𝑖| = 2.

8 MAY 2019

21 Check whether the function f(z) = 𝑅𝑒 (𝑧2)

1−|𝑧| if z ≠ 0

= 0if z = 0 is continuous at z=0

7 SEPTEMBER 2020

22 Determine a so that u=𝑒−𝑎𝑥 cos ay is harmonic and find the harmonic conjugate

8 SEPTEMBER 2020

23 Show that 𝑓(𝑧) = 𝑒𝑧 is analytic for all z. 8 SEPTEMBER 2020

Module IV

1 Evaluate ∫𝑐

𝑅𝑒(𝑧) 𝑑𝑧 where is the straight line from 0 to 1+2i 7 DEC2016

2 Show that ∫∞

0

1

1+𝑥4 𝑑𝑥 =𝜋

2√2 8 DEC2016

3

Integrate 𝑧2

𝑧2−1 counter clockwise around the circle |𝑧_1_𝑖|=

𝜋

2 7 DEC2016

4

Evaluate ∫𝑐

|𝑧| dz

i)where c is the line segment joining i and –i

ii) where c is the unit circle in the left of the half plane

3+4 MARCH2017

5 Verify Cauchy’s integral theorem for z2 taken over the boundary of the rectangle with vertices -1,1,1+i,1-I in the counter clockwise sense.

8 MARCH2017

6 Evaluate ∫𝑐

𝐼𝑚(𝑧2) 𝑑𝑧 where c is the triangle with vertices 0,1,i

counter clockwise.

7 APRIL 2018

7 Use Cauchy’s Integral Formula, evaluate ∫𝑐

𝑧2

𝑧3−𝑧2−𝑧+1 𝑑𝑧 where c is

taken counter clockwise around the circle:

i)|𝑧 + 1| =3

2 ii)|𝑧 − 1 − 𝑖| =

𝜋

2

8 APRIL 2018

8 Find the Taylor series and Laurent series of 𝑓(𝑧) =−2𝑧+3

𝑧2−3𝑧+2 with centre 0

in

i)|𝑧| < 1 ii1 < |𝑧| < 2

8 APRIL 2018

9 Find the Laurent series expansion of 𝑓(𝑧) =1

1−𝑧2 which is convergent in

i)|𝑧 − 1| < 2 ii)|𝑧 − 1| > 2

8 MARCH2017

10 If (𝑧) =1

𝑧2 , find the Taylor series that converges in |𝑧 − 𝑖| < 𝑅 and the

Laurent series that converges in |𝑧 − 𝑖| > 𝑅

8 DEC 2016

11 Using Cauchy’s integral formula, evaluate ∫𝑒𝑧

(𝑧2+4)(𝑧−1)2𝑐dz

where 𝐶 is the circle |𝑧 − 1| = 2

7 MAY2019

12 Evaluate ∫2+𝑖

0 (�̅�)2 dzalong (i) the real axis to 2 and then

vertically to 2 + 𝑖 . ii) the line 2𝑦 = 𝑥 .

8 MAY2019

13. Evaluate ∫ 𝑧̅1+2𝑖

0dz along z=𝑡2 +it 7 SEPTEMBER2020

14 Evaluate∫2𝑧−1

𝑧2−𝑧

4+2𝑖

𝑐dz along the curve C:|𝑧|=3 using Cauchy’s

integral formula.

8 SEPTEMBER202

15.

Module V

1 Define three types of isolated singularities with an example for each 7 DEC2016

2 Determine the nature and type of singularities of i)

𝑒−𝑧2

𝑧2 ii)1

𝑧

7 MARCH 2017

3 Use Residue theorem to evaluate ∫𝑐

30𝑧2−23𝑧+5

(2𝑧−1)2 (3𝑧−1) 𝑑𝑧 where c is|𝑧| =

1

7 MARCH 2017

4 Evaluate ∫∞

0

1

(1+𝑥2)2 𝑑𝑥 using residue theorem 8 MARCH 2017

5 Determine and classify the singular points for the following functions

i)𝑓(𝑧) =𝑠𝑖𝑛𝑧

(𝑧−𝜋)2 ii) g(z) = (𝑧 + 𝑖)2𝑒1

𝑧+𝑖

7 APRIL 2018

6 Evaluate ∫∞

−∞

1

(1+𝑥2)3 𝑑𝑥 8 APRIL 2018

7 Evaluate ∫−𝑐

𝑡𝑎𝑛𝑧

𝑧2−1 𝑑𝑧 counter clockwise around c :|𝑧| =

3

2 using

Cauchy’s Residue theorem

7 APRIL 2018

8 Using contour integration evaluate ∫∞

−∞

𝑥2−𝑥+2

𝑥4+10𝑥2+9 𝑑𝑥

7 JULY 2017

9 Evaluate ∫ 𝑙𝑜𝑔𝑧𝑑𝑧 where 𝐶 is the circle |𝑧| =1 7 MAY2019

10 Evaluate∫ 1/( 5−3𝑠𝑖𝑛𝜃)𝑑𝜃 8 MAY2019

11 Find all singular points and residues of the functions

(a)f (𝑧) = (𝑧−𝑠𝑖nz)/𝑧2 (𝑏) f(z) =tanz

8 MAY2019

12 Evaluate ∫𝑥2

(𝑥2+1)(𝑥2+4)

∞

−∞𝑑x

8 MAY2019

13 Find the Laurent series expansion of f(z)=1

𝑧2+3𝑧+2 in the region 1< |𝑧 < 2| 8 SEPTEMBER2020

14 Find all singularities and corresponding residues 8

1+𝑧2 ,tanz 8 SEPTEMBER2020

15 Evaluate ∫𝑒𝑧

𝑐𝑜𝑠𝜋𝑧𝑐dz,where C is the unit circle |𝑧| =

1 𝑢𝑠𝑖𝑛𝑔 𝑅𝑒𝑠𝑖𝑑𝑢𝑒 𝑡ℎ𝑒𝑜𝑟𝑒𝑚

8 SEPTEMBER2020

16 Evaluate ∫𝑑𝜃

2+𝑐𝑜𝑠𝜃

2𝜋

0 8 SEPTEMBER2020

S3 CE QUESTION BANK

CET 201: MECHANICS OF SOLIDS

MODULE 1 1 (a)Draw and explain stress strain diagram of mild steel 7.5 KTU JAN

2017 , SEPT

2020

(b) derive the expression for elongation of a tapering circular

section subjected to axial load

7.5 KTU JAN

2017

2 (a) In an experiment , a bar of 30mm diameter is subjected to a

pull of 60kN .the measured extension of gauge length of

200 mm is 0.09 mm and the change in diameter is 0.0039

mm .calculate the poisson’s ratio and three modulus

10 KTU JULY

2017

(b) Define the terms stress and strain ? What are the different

types of stress and strains?

5 KTU JULY

2017, DEC

2017

3 State and Explain Hooke’s law 7 KTU DEC

2017

4 Prove that maximum value of poisson’s ratio is 0.5 5 KTU DEC

2017

5 A bar of 20 mm diamete5r is subjected to a pull of 50kN .The

measured extension on a gauge length of 250mm is 0.12 mm and

change in diameter is 0.00375 mm .calculate :

(i) Youngs Modulus (ii) Poisson’s ratio (iii) Bulk Modulus

6

KTU APR

2018

6 A Steel rod tapers uniformly from 20 cm at one end to 5cm

diameter at the other end in alength of 75 cm .how much will it

stretch under an axial pull of 5 kN . Given E = 2 X 10^5 N/mm2

4 KTU APR

2018

7 Write down the expression for elongation of tapering bars of (i)

circular cross section (ii) rectangular cross section

4 KTU DEC

2018,SEPT

2020

8 Define the following terms: (i) Modulus of Rigidity (ii) Proof

Resilience (iii) Factor of safety.

3 KTU DEC

2018

9 Derive the relation between Modulus of elasticity and Bulk

Modulus.

4 KTU DEC

2018

10 Define Bulk modulus. Calculate the change in volume of a

cubical block of side 120 mm subjected to a hydrostatic

pressure of 70 MPa. Take Poisson’s

ratio 0.28 and young’s modulus 200 GPa.

5 KTU MAY

2019

11 Differentiate between(i) Normal stress and shear stress (ii)

Young’s modulus and

Rigidity modulus (iii) Poisson’s ratio and volumetric strain

3 KTU DEC

2019

12 A circular steel bar having three segments is subjected to various

forces at different cross-sections as shown in figure. Determine

the necessary force to be applied at section C for the equilibrium

of the bar. Also find the total elongation of the bar. Take

E=2x105N/mm2

7 KTU SEPT

2020

S3 CE QUESTION BANK

13 Calculate the diameter of a circular bar of length 10m, if the

elongation of the bar due to an axial load of 100kN is 0.15mm.

E=200GN/m2

4 KTU SEPT

2020

MODULE II

1 (a)A copper rod 25 mm in diameter is encased in a steel tube 30

mm internal diameter and 35 mm external diameter. The ends are

rigidly attached. The composite bar is 500 mm long and is subjected

to an axial pull of 30 kN. Find the stresses induced in the rod and the

tube. Take E for steel as 2 x 10 5 N/mm2 and E for copper as l x 10

N/min2

10 KTU JAN

2017

(b)The rails of a railway line is laid so that there is no stress in the

rails at 10 ° C. Calculate the stress in the rails at 60 ° C if there is an

expansion allowance of 10 mm per rail.

5 KTU JAN

2017

2 (a)A compound bar consists of a circular rod of steel of diameter

20 mm rigidly fitted into a copper tube of internal diameter 20

mm and thickness 5 mm. If the bar is subjected to a load of 100

kN , Find the stresses developed in the two materials. Take Es =

2.x 10" N/mm' and Ec -l .2x105 N/mm2

10 KTU JULY

2017

(b)What is strain energy? Give the expression for strain energy

due to axial force

5 KTU JULY

2017, APR

2018 , DEC

2019

3 A steel bar is placed between two copper bars each having the same

area and length as the steel bar at 15°C. At this stage they are rigidly

connected together at both the ends. When the temperature is raised

to 315°C, the length of the bars increases by 1.50 mm. Determine

the original length and the final stresses in the bars. Take Es= 2.1 x

105 N/mm2, Ec = 1 x 105 N/mm2, αs = 0.000012 per °C, αc =

10 KTU APR

2018

S3 CE QUESTION BANK

0.0000175 per °C

4 A cylindrical bar with two sections of lengths 50cm and 25cm, and

diameters 20mm and 15mm respectively, is subjected to an axial pull

such that the maximum stress is 150MN/m2. Calculate the strain

energy stored in bar. E= 200 GN/m2.

10 KTU DEC

2017

5 A steel rod of 3 cm diameter and 5 m length is connected to two

grips and the rod is maintained at a temperature of 95oC. Determine

the stresses and pull exerted when the temperature falls to 30oC if

(i) the ends do not yield and (ii) the ends yield by 0.12 cm. Take E

= 2×105 N/mm2 and α = 12×10-6 /o C.

7 KTU DEC

2018

6 A compound tube consists of a steel tube 140 mm internal

diameter and 160mm external diameter and an outer brass tube

160 mm internal diameter and 180 mm external diameter. The

length of the compound tube is 150 mm and it carries an axial

load of 900 kN. Find the stresses and load carried by each tube

and the amount it shortens. Take E steel = 2×105 N/mm2 and E

brass = 1.1×105 N/mm2.

9 KTU DEC

2018

7 The composite bar shown in fig.2 is rigidly fixed at the ends A and

B. Determine the reaction developed at ends when the temperature

is raised by 250c. Given Ecu =140 kN/mm2 , Es =200 kN/mm2,

acu = 17.5×10-6/0C, as =

12×10-6/0C

10 KTU MAY

2019

8 A brass bar of 25 mm diameter is enclosed in a steel tube of 25

mm internal diameter and 50 mm external diameter. Both of them

are 1m long at room temperature and fastened rigidly to each other

10 KTU DEC

2019

S3 CE QUESTION BANK

at the ends. If the room temperature is 20oC, find to what

temperature the assembly should be heated so as to generate a

compressive stress of 48.7 MN/m2 in brass. What is the stress in

steel at this temperature? Assume Es=200 GN/m2; Eb=100

GN/m2; αs=11.6 x 10 -6/oC; αb

=18.7 ×10 -6/oC

9 A vertically suspended bar with collar at lower end has 30

mm diameter. If a

tensile load of 7500 N is applied gradually it produces an

extension of 0.3 mm. Determine the height from which this

load should be dropped to produce a maximum stress of 95

N/mm2. Assume E = 200GPa

9 KTU DEC

2019

10 A rod is 2 m long at a temperature of 10°C. Find the expansion of

the rod when the temperature is raised to 80°C. If this expansion is

prevented, find the stress induced in the material of the rod. Take

E=1x105N/mm2 and α=0.000012 per degree centigrade

5 KTU SEPT

2020

11 A mild steel rod of 20mm diameter and 300mm long is enclosed

centrally inside a hollow brass tube of external diameter 30mm and

internal diameter of 25 mm. The ends of the tube and rods are brazed

together and the composite bar is subjected to an axial pull of 40kN.

If E for steel and brass is 200 GN/mm2 and 100 GN/mm2

respectively, find the stresses developed in the rod and tube. Also,

find the extension of the rod.

10 KTU SEPT

2020

MODULE III

1 (a)Draw the BMD and SFD for a cantilever beam subjected to central

concentrated load.

7.5 KTU JAN

2017

(b) Draw the BMD and SFD for a simply supported beam with udl

over entire span

7.5 KTU JAN

2017

2 (a)Draw the shear force and bending moment diagram for the beam

given

10 KTU DEC

2017

S3 CE QUESTION BANK

(b) Derive the relation between intensity of loading, shear force and

bending moment

5 KTU DEC

2017, DEC

2019

3 (a)simply supported beam AB of 4 m span carries a uniform load of

30 k m over the right hand half of the span. Draw SFD and BMD.

10 KTU DEC

2017

4 (a) Name and explain the various types of beam supports,

indicating the reaction components diagrammatically.

(b) Derive a relationship between bending moment and shear

force.

(c) Draw the shear force and bending moment diagrams for a

cantilever of span 3m, with a UDL of 10Kn/m on the

entire span, and a point load of 100Kn at the free end.

15 KTU DEC

2017

5 Construct shear force diagram and bending moment diagrams for a

beam ABE, 3L/2 m long, which is supported at A and B, ‘L’ m long.

The beam carries a concentrated load of 2W at L/4 distance from

left support A, and point load W/2 at E. It also carries an upward

point load of W at a distance of L/4 from support B.

10 KTU APR

2018

6 Draw the shear force and bending moment diagram of the simply

supported beam AB shown below. Mark the salient values. Also find

maximum bending moment

10 KTU DEC

2018

S3 CE QUESTION BANK

7 A beam ABCD 12 m long carries a uniformly distributed load of

25Kn/m. It is simply supported at A and C 10 m apart with an

overhang CD of 2m. It also carries a clockwise couple of 100 kNm

at B, 3 m from A. State the position and amount of maximum BM.

Sketch the SFD and BMD

10 KTU DEC

2018

8 Explain the following:

i) Shear force and bending moment in a beam.

ii) Hogging and sagging moments.

iii) Point of contra flexure.

5 KTU JULY

2019

9 The intensity of loading on simply supported beam of 5 m span

increase gradually from 1 Kn/m at one end to 2 Kn/m at the other

end. Find the position and amount of maximum bending moment.

Also draw the SFD and BMD.

10 KTU DEC

2019

10 A simply supported beam of span L carries a clockwise moment

M at its centre. Draw the SFD and BMD

4 KTU DEC

2019

11 Draw the shear force and bending moment diagrams for a

cantilever beam of span 5 m subjected to a uniformly distributed

load of 5 kN/m over a length of 2m starting from the free end

7 KTU DEC

2019

12 A 10 m long simply supported beam carries two point loads of

l0kN and 6kN at 2m and 9m respectively from the left end. It

also carries a uniformly distributed load of 4kN/m run for the

length between 4m to 7m from the left end. Draw shears force

and bending moment diagrams. State the position and magnitude

of maximum bending moment

10 KTU SEPT

2020

MODULE IV

1 (a) A rectangular timber joist of 6 m span has to carry a load of

15 kN/m. Find the dimensions of the joist if the maximum

permissible stress is limited to 8 N/mm2. The depth of the joist has

to be twice the width.

7.5 KTU JAN

2017

(b) A 300 mm x 160 mm rolled steel joist of I section has flanges l

l mm thick and web 8 mm thick. Find the safe unikumly

distributed load that the section will carry over a span of 5 m if

the permissible stress is limited to 120 N/mm2.

7.5 KTU JAN

2017

S3 CE QUESTION BANK

2 Derive the expression for shearing stress in a beam section stating

the assumptions made

15 KTU JAN

2017, MAY

2019

3 A cast iron beam has an 1-section with top flange 80 mm x 40

mm. web 1 20 mm x 20 mm and bottom flange 160 mm x 4D mm.

If tensile stress is not to exceed 30 N/man' and compressive stress

90 N/mm', what is the maximum CODL the beam can carry. over

a simple supported span of 6 m if the larger flange is in tension?

10 KTU JULY

2017

4 Sketch the bcnding stress as well as shear stress distribution

diagram for a beam of rectangular cross section.

5 KTU JULY

2017

5 A cantilever beam with span 3m and cross section 200×300mm is to

carry a UDL on the entire span. If the tensile stress is limited to

3MPa, what is the maximum UDL that can be applied on the beam?

8 KTU DEC

2017

6 Derive the classic bending equation. 9 KTU DEC

2017, APR

2018

7 A simply supported rectangular wooden beam of span 2.5m has

cross section 150mm×250mm and carries a central point load of

100N. Find the shear stressat 50mm below the top edge of the middle

cross section

6 KTU DEC

2017

8 Determine and draw the shear stress variation along the depth of an

I section beam having a uniform thickness of 10 mm, for the web

and flanges. The total height of the section is 200 mm and overall

width of each flange is 100 mm. The shear force is 250 Kn.

15 KTU APR

2018

9 A cast iron beam of triangular section of 100 mm width and 100 mm

depth is placed with its base horizontal. The beam is simply

supported over a span of 6 m. If the allowable stress in tension and

compression are 50 MPa and 150 MPa respectively, find the safe

concentrated load at the centre of the beam. What are the extreme

fibre stresses

10 KTU 2018

DEC

10 A simply supported beam of length 3 m carries a point load of 12

kN at a distance of 2 m from left support. The cross section of the

beam is as shown in Fig.4 b

12 KTU MAY

2019

S3 CE QUESTION BANK

Determine the bending stresses at extreme fibres at section X-X.

Take moment of inertia about neutral axis of the section as 2.56×107

mm4.

11 Calculate the moment of resistance of a composite beam made of

wood and steel. The cross section is rectangular,with wood 150

mm wide and 300 mm deep, strengthened by fixing steel plates of

12 mm thickness and 300 mm deepth on either side.If the

maximum stress in wood is 8 N/mm2, what is the

corresponding maximum stress attained in steel?.Take Ew=10 GPa

and Es=200 GPa.

15 KTU MAY

2019

12 What is section modulus? Express the section modulus of (i)

rectangular section

(width=b, depth=d) , (ii) circular section (diameter=d) and (iii)

Hollow circular section (Internal diameter=d, External

diameter=D)

5 KTU DEC

2019

13 A beam of I section 200 mm wide and 300 mm deep with flange

and web thickness 20 mm is used as a simply supported beam over

a span of 7 m. The beam carries a distributed load of 5 kN/m over

the whole span and a concentrated load of 20 kN at mid span.

Determine the maximum bending stress set up and

sketch the stress distribution

10 KTU DEC

2019

14 A cast iron tee section having overall depth 150mm with flange

width and thickness as 100mm and 30mm respectively is used as

a cantilever bracket of length 300mm. Web thickness is 30mm. If

the tensile stress is restricted to 20N/mm2, calculate the point load

that can be placed at the free end of bracket. Also calculate the

compressive stress developed.

10 KTU SEPT

2020

S3 CE QUESTION BANK

15 State the governing relation to find the shear stress in beams. Sketch

the shear stress distribution across depth in a)rectangular section b)I

section

5 KTU SEPT

2020

MODULE V

1 Select a suitable diameter of a solid shaft of circular section to transmit

l 12.5 kW of power at 200 r.p.m., if the allowable shear stress is 75

N/mm2 and the allowable twist is l ° in a length of 3 m. Take G as 0.82

x 10 N/mm'.

20 KTU JAN

2017

2 A point is subjected to a tensile stress of 60 N/mm2 and a compressive

stress of 40 N/mm 2, acting on two mutually perpendicular planes. A

shear stress of 10 N/mm2 is also acting on these planes. Determine the

principal stresses and the maximum shear stress.

15 KTU JAN

2017

3 (a)What are the assumptions in Euler’s column theory

(b) Write the equations for Euler’s crippling load for cnlumns with both

ends hinged, both ends fixed, one end fixed and the other hinged, one

end fixed and the other free

©A hollow alloy tube 5 m long with diameters 40 mm and 25 mm

was found to extent 6.4 mm under a tensile load of 60 kN. Find the

buckling load for the tube when used as a strut with both ends pinned.

20 KTU JAN

2017, JULY

2017

3 A hollow metallic tube of 60 mm external diameter. 50 mm internal

diameter and S m long is fixed at one end and its upper end is free.

Calculate the maximum load that it can withstanf Crushing strength

of the material — 300 Pa. Rankine’s constant = 1/7500

12 KTU JULY

2017

4 A 2m long thin cylindrical shell (both ends closed), internal

diameter 90cm and thickness 12mm, is subjected to internal

pressure 2N/mm2. Find 1) hoop and longitudinal stresses, 2)

changes in diameter and length shell. Take E = 2×105 N/mm2 and

Poisson’s ratio = 0.3.

10 KTU DEC

2017

5 Draw Mohr’s circlefor the two-dimensional state of stress shown

in Fig. 2. Find the principal stresses and their planes.

14 KTU DEC

2017

S3 CE QUESTION BANK

6 Find the buckling load given by Rankine’s formula for a tubular

strut hinged at both ends, 6 m long having outer diameter 15 cm

and thickness 2 cm. Given, E= 2×105N/mm2, σc= 567N/mm2 and

Rankine’s constant, a= 1/1600. For what length of the column does

the Euler’s formula cease to apply?

10 KTU DEC

2017

7 A hollow shaft is to transmit 300 kW power at 80 rpm. If the shear

stress is not to exceed 60N/mm2 and the diameter ratio is 0.6, find

the external and internal diameters assuming the maximum torque

is 1.4 times the mean.

10 KTU MAY

2018

8 Define effective length of a column. Give the effective lengths for

various end conditions

6 KTU MAY

2018, DEC

2019 , SEPT

2020

9 Calculate the safe compressive load on a hollow cast iron column

with one end rigidly fixed and other hinged, of 15 cm external

diameter, 10 cm internal diameter and 10 m in length. Use Euler’s

formula with a factor of safety 5 and E= 95 kN/mm2.

8 KTU MAY

2018

10 Determine the maximum power transmitted at 280 rpm by a steel

shaft of 35 mm internal diameter and 4.5 mm thick, if the allowable

stress is 75 MPa and the angle of twist is not to exceed 1˚ in a length

of 1.5 m. Assume G= 80 GPa for the material

8 KTU DEC

2018 , MAY

2019

11 A steel column made of a 4 m long hollow circular section, having

300 mm internal diameter and 20 mm thick, is fixed at both the ends.

Determine the safe axial load the column can carry with a factor of

safety 3.5 using Euler’s formula. E=2.1×105 N/mm2

6 KTU DEC

2018

S3 CE QUESTION BANK

12 Define i) slenderness ratio ii) Kern of a circular section 5 KTU DEC

2018, MAY

2019

13 Derive the expression for normal stress on a plane inclined at an

angle θ to x axis and subjected to normal stresses in X and Y

directions.

6 KTU DEC

2018

14 A hollow rectangular cast iron column having outside width and

depth 250×500 mm and thickness 20 mm is fixed at one end and

hinged at the other end. Length of the column is 8 m. Calculate the

safe load that can be applied on the column assuming a factor of

safety of 4. Use Rankine’s theory. Take α =1/1600

and σc =600 N/mm2.Compare the value by Euler’s theory. Take E=

95 Kn/mm2

14 KTU MAY

2019

15 At a point in a strained material a direct tensile stress of 70 N/mm2

and a direct compressive stress of 50 N/mm2 are acting on planes

at right angles to each other. If the maximum principal stress is

limited to 75 N/mm2 tensile, determine the shear stress that may

be allowed on these planes. Also determine the i) minimum

principal stress ii) maximum shear stress and iii) direction of

principal planes.

15 KTU MAY

2019

16 Calculate minimum wall thickness of a thin cylinder 1 m in

diameter if it is to

withstand an internal pressure of 2 N/mm2 and hoop stress not

to exceed 40 N/mm2. Also find change in diameter. E = 210 GPa;

Poisson’s ratio = 0.3

10 KTU DEC

2019

17 Determine the ratio of buckling strength of two columns one

hollow and other solid, both are made of same material and have

equal length, cross sectional area and same end conditions.

Internal diameter of hollow column is half the external

diameter

6 KTU DEC

2019

18 An elemental cube is subjected to tensile stresses of 30N/mm2 and

15N/mm2 acting on two mutually perpendicular planes and a shear

stress of 25N/mm2 on these planes. Determine magnitude and

directions of principal stresses. Also calculate greatest shear stress

and its planes.

15 KTU SEPT

2020

19 A hollow cast iron column 10m long and 10cm internal diameter

and 15cm external diameter is having its one end hinged and other

rigidly fixed. Find the crippling load and safe load taking factor of

7 KTU SEPT

2020

S3 CE QUESTION BANK

safety as 5. Take E=95kN/mm2. Use Eulers formula

20 A solid steel shaft has to transmit 75kW at 200rpm. Determine the

suitable diameter of shaft if the maximum torque transmitted is not

to exceed the mean by 30% in each revolution. The shear stress is

not to exceed 70N/mm2. Also calculate the maximum angle of twist

in a length of 4m of the shaft. G=80Gpa

7 KTU SEPT

2020

CE 203 FLUID MECHANICS 1

Module 1

1. Two pipelines, one carrying oil of relative density 0.9 and other carrying

water are connected to a manometer as shown in Figure 1. By what amount,

the pressure in water pipeline should be increased so that mercury levels in

both the limbs of the manometer become equal?

(KTU DECEMBER 2017) – 8 marks

2. Obtain an expression for centre of pressure of a lamina paced in inclined

position. (KTU DECEMBER 2017) – 7 marks

3. A door in a tank retaining water is in the form of a quadrant of a cylinder of

1.5 m radius and 1.8 m wide as shown in Figure 2. Calculate the resultant

force on the gate.


4. The pressure difference between two points A and B in a pipe conveying oil

of specific gravity 0.9 is measured by an inverted U-tube and the column

connected to B stands 1.2 m higher than that of A. A pressure gauge

attached at A reads 9.81*105 N/m2 determine the pressure in the pipe at B.


5. A hollow equilateral triangular plate of side 4 m on the outside and 2m in the

hollow portion is immersed in water with its plane vertical, with its vertex

downwards and base upwards, base being parallel to the free surface at a

depth of 1m below the free surface. Determine the hydrostatic pressure force

on one side of the plate and the depth of centre of pressure.


6. Calculate the pressure due to a column of 0.4 m of (i) water, (ii) an oil of

specific gravity 0.9 and (iii) mercury of sp. gr. 13.6. Take density of water as

1000kg/m3. (KTU APRIL 2018) – 5 marks

7. A circular plate 5 m diameter is immersed in water in such a way that its

greatest and least depth below the free surface are 4 m and 1.5 m

respectively. Determine the total pressure on one face of the plate and

position of centre of pressure.

(KTU APRIL 2018) – 5 marks

8. A cubical tank has sides of 1.5 m. It contains water in the lower 0.6 m

depth. The upper remaining portion is filled with oil of relative density 0.9.

Calculate for one vertical side of the tank (i) the pressure force and (ii)

position of the centre of pressure.


9. Define the terms gauge pressure, vacuum pressure and absolute pressure.

Indicate their relative positions on a chart.


10. An annular ring cut in a sheet metal has 1.5 m outer diameter and 1.0 m

inner diameter. It is inserted vertically in a liquid of relative density 0.90

with its centre 1.75 m below the surface. Calculate the total force on one

side of this ring and the location of the centre of pressure.

(KTU MAY 2019) – 10 marks

11. A cylinder contains a fluid at a gauge pressure of 350 kN/m2 Express the

pressure in terms of head of (a) water, (b) mercury. What would be the

absolute pressure in the cylinder if the atmospheric pressure is 101.3 kN/m2


12. A U-tube differential gauge is attached to the two sections A and B in a

horizontal pipe in which oil of specific gravity 0.8 is flowing. The deflection

of the mercury in the gauge is 60 cm, the level nearer to A being the lower

one. Calculate the difference in pressure between sections A and B.

(KTU OCTOBER 2020) – 6 marks

13. Show that a cylindrical body of 1.25m diameter and 3.25m high weighing

11127 N will not float vertically in sea water weighing 10055N/m3 . Find

the tension necessary. In a vertical chain attached to the centre of the base of

the buoy that will just keep the cylinder vertical.

(KTU JANUARY 2017) – 13 marks

14. A single column vertical manometer with a reservoir to is

connected to a pipe containing oil of specific gravity 0.9. The area

of reservoir is 100 times the area of the manometric tube. The

reservoir contains mercury of specific gravity 13.6. The level of

mercury in the reservoir is at a depth 30cm below the centre of

pipe. If the difference of mercury levels in the reservoir and the

right limb is 50cm, calculate the pressure in the pipe.

(KTU JULY 2017) – 13 marks

Module 2

1. A ship 60 m long and 10 m wide displaces 15000 kN of water. A weight of

200kN is displaced across the deck through a distance of 5 m and the ship is

tilted through 4.50. The moment of inertia of the ship about the fore - and -

aft axis is 80 % of the circumscribing rectangle. The centre of buoyancy is 2

m below the water surface. Determine the metacentric height and the

position of the centre of gravity of the ship. Take specific gravity of water as

1.03. (KTU MAY 2019) – 10 marks

2. A wooden block of 1m side cube of relative density 0.7 floats in water.

Determine the volume of concrete of relative density 2.5 that needs to be

placed on it so that the block is just immersed in water.


3. The velocity vector in an incompressible flow is given by V=(6xt+yz2)i

+(3t+xy2)j+ (xy-2xyz-6tz)k Verify

(i)whether continuity equation is satisfied

(ii) Determine the acceleration and velocity at a point A (1,1,1) at t=1


4. What are the different mathematical conditions for irrational flow

(KTU JANUARY 2017) – 5 marks

5. A solid cylinder of diameter 30 cm and height 15 cm is to float in in water

with its axis vertical in sea water (specific gravity 1.03). If the relative

density of the cylinder material is 0.9, examine the stability of cylinder.


6. A velocity field is given by u = t2 + 3y and v = 4t + 5x. Calculate the

acceleration at the point (5, 3) at time t = 2 units.


7. Show that the streamlines and equipotential lines form a net of mutually

perpendicular lines.


8. Derive continuity equation in three-dimensions.


9. A solid cylinder of diameter 3m has a height of 2 m. Find the metacentric

height of the cylinder when it is floating in water with its axis vertical. The

specific gravity of the cylinder is 0.6. State whether the body is stable or not.


10. Derive the continuity equation for a three dimensional flow in Cartesian co-

ordinates


11. A rectangular barge 16 m x 5 m has a depth of immersion of 1.6 m when

floating horizontally. The centre of gravity of the barge is 1.9 m above the

bottom. Determine the angle of tilt if a 50 kN weight is moved across the

deck by 3.5 m.


12. Explain convective and local acceleration.


13. How is the metacentric height of a body determined experimentally?


Module 3

1. Name the minor and major losses during the flow of liquid through a

pipeline. (KTU MAY 2019) – 5 marks

2. Derive Euler’s equation of motion and then obtain Bernoulli’s equation by

integrating it along a streamline. What are the assumptions made in deriving

the equation?


3. What is an orifice? How are the orifices classified?


4. Derive Dupuit’s equation for pipes in series.


5. Derive the Darcy-Weisbach equation for head loss in pipes due to friction.


6. A city water supply main is 1000 m long and delivers a flow of 100 l/s

between two reservoirs with a head difference of 15 m. It is proposed to

increase the flow by 30 % by adding another pipe from the upstream

reservoir in parallel and joining to the main pipe at a suitable location.

Assume all pipes are of same diameter and same friction factor (f=0.02).

Determine length of the additional pipe.


7. Determine the rate of flow of water through a pipe of diameter 20 cm and

length 50 m when one end of the pipe is connected to a tank and other end of

the pipe is open to the atmosphere. The pipe is horizontal and the height of

water in the tank is 4 m above the centre of the pipe. Consider all losses and

take f=0.036


8. A pipe line carrying oil of specific gravity 0.8, changes in diameter from 300

mm at a position A to 500 mm diameter at a position B, which is 5m at a

higher level. If the pressure at A and B are 19.62 N/cm2 and 14.91 N/cm2

respectively and the discharge is 150 litres/sec, determine the loss of head

and direction of flow.


9. A venturimeter is used for measuring the flow of petrol in a pipeline inclined

at 35° to the horizontal. The specific gravity of petrol is 0.81 and throat area

ratio is 4. If the difference in mercury levels in the gauge is 50 mm, calculate

the flow in litres/hour if the pipe diameter is 0.3 m. Take coefficient of

discharge of veturimeter as 0.975.


10. An orifice in the side of a large tank is rectangular in shape 1.2 m wide and

0.7 m deep. The water level on one side of the orifice is 1.2 m above the top

edge and the water level on the other side of the orifice is 0.25 m below the

top edge. Compute the discharge if Cd=O.62.


11. Differentiate between hydraulic gradient line and total energy line.


12. Explain the methods of experimental determination of orifice coefficients


13. What is an orifice? How are the orifices classified


14. A venturimeter 30 cm x 10 cm is provided in a vertical pipeline to measure

the flow of oil of relative density 0.85. The difference in elevations of the

throat section and entrance section is 40 cm, the direction of flow of oil

being vertically upwards. The oil-mercury differential U tube manometer

shows a gauge deflection of 20 cm. Calculate the discharge of oil and the

pressure difference between the entrance section and throat section. Take the

coefficient of discharge as 0.97 and specific gravity of mercury as 13.6.


15. Define coefficient of velocity, coefficient of contraction and coefficient of

discharge. Find out the relation among the three.


Module 4

1. What is a Cipoletti weir. Show how the effect of end contraction is

compensated in a Cippoletti weir


2. Water flows over a rectangular weir 2 m wide at a depth of 200 mm and

afterwards passes through a triangular right angled weir. Taking Cd for the

rectangular and triangular weir as 0.61 and 0.58 respectively, find the depth

over the triangular weir.


3. A 40 metres long weir is divided into 12 equal bays by vertical posts, each

0.6m wide. Taking Cd = 0.623, calculate the discharge over the weir if the

head over the crest is 1.20 m and velocity of approach is 2 m/s.


4. Differentiate between hydraulic radius and hydraulic depth.

(KTU SEPTEMBER 2020) – 5 marks

5. A triangular channel has a side slope of 1.5 horizontal to 1 vertical and is

laid on a longitudinal slope of 1 in 1650. Assuming Manning’s coefficient as

0.013, estimate the normal depth required to pass a discharge of 0.3 m3/s.


6. A trapezoidal section has side slopes of 1 vertical to 1 horizontal and has to

carry a discharge of 14 m3/s. The bed slope of the channel is 1 in 1000.

Chezy’s constant is 45 if the channel is unlined and is 70 if the channel is

lined with concrete. The cost per cubic meter of excavation is 3 times the

cost per square metre of lining. The channel is to be the most efficient one.

Find whether the lined canal or unlined canal will be cheaper.


7. For maximum discharge in a circular channel section, prove that the depth of

flow is 0.95 times the diameter of the channel.


8. A rectangular channel 10 m wide carries a discharge of 10 m3/s. It is laid at

a slope of 0.0001. If the depth of flow at a section is 1.6 m, how far

(upstream or downstream) will be the depth be 2 m? Manning’s coefficient

N = 0.015.


9. Find the slope of free water surface in a rectangular channel of width 3 m

and depth of flow 0.75 m. The discharge through the channel is 0.84 m 3/s.

The bed of the channel is having a slope of 0.15 m per km. Assume Chezy’s

constant, C as 55.


10. Derive Chezy’s equation for uniform flow in open channel


11. It is required to convey 10 m3/s of water at a mean velocity of 1.25 m/s.

Calculate the dimensions of the most efficient section of the channel whose

shape is a) rectangular and b) trapezoidal channel of side slope 1/√3


12. A trapezoidal channel with side slopes of 2 horizontal : 1 vertical has to be

designed to carry 15 m3/s at a slope of 1/5000. Determine the dimensions of

the efficient section. Manning’s coefficient is 0.014.


13. A rectangular channel 3.5m wide is laid on a slope of 0.0005. Calculate the

normal depth of flow for a discharge of 5m3/s in this channel. The

Manning’s coefficient can be taken as 0.02.


14. On what slope should one construct a 3m wide rectangular channel

(Manning’s coefficient is 0.014) so that critical flow will occur at a normal

depth of 1.2m?


15. A circular drainage pipe 0.8m in diameter conveys a discharge at a depth of

0.3m. If the pipe is laid on a slope of 1 in 1000, estimate the discharge.

N=0.02.


Module 5

1. List out any three practical cases in which a hydraulic jump may occur


2. Explain specific force curve.


3. A discharge of 18m3/s flows through a rectangular channel 6m wide at a

depth of 1.6m. Find the specific energy and critical depth. State whether the

flow is subcritical or supercritical.


4. With a neat sketch explain the characteristics of water surface profile in

critical sloped channels.


5. Draw and explain the specific energy curve.


6. In a hydraulic jump occurring in a rectangular horizontal channel the

discharge per unit width is 2.5 m2/s and the depth before the jump is 0.25 m.

Estimate the sequent depth and the energy loss


7. Define the terms: i) alternate depths, ii) Normal Slope and iii) Hydraulic

mean depth. (KTU DECEMBER 2019) – 5 marks

8. A rectangular channel 2.5 m wide has a specific energy of 1.50 m when

carrying a discharge of 6.48 m3/s. Calculate the alternate depths and

corresponding Froude numbers.


9. Sketch the water surface profiles that can occur in a mild slope channel


10. State the assumptions made in the derivation of the dynamic equation for

gradually varied flow


11. Derive the condition for maximum discharge for a given value of specific

energy.


12. In a hydraulic jump on a horizontal rectangular channel the Froude number

before the jump is 10 and energy loss during the jump is 4 m. Find i) depths

before and after the jump, ii) the discharge per unit width and iii) Froude no

after the jump.


13. Sketch the water surface profiles that can occur in a steep slope channel


14. Differentiate between alternate depths and conjugate depths.


15. In a hydraulic jump on a horizontal rectangular channel the depth and

Froude number before the jump are 0.2 m and 9 respectively. Estimate the

energy loss and specific energy head at the end of the jump.


SURVEYING VAST TC

CET205 SURVEY AND GEOMATICS -

MODULE -1

1. Explain with sketch, ranging a line if the end stations are not intervisible.

5 marks – KTU Sept 2020

2. Define local attraction. Which are the different methods of eliminating local attraction in a

closed traverse? 8 marks KTU Dec 2018, May 2019

3. The following consecutive readings were taken with a level and 5m leveling staff on a continuously

slopping ground at a common interval of 20 m, :0.385,

1.030,1.925,2.825,3.730,4.685,0.625,2.005,3.110,4.485. Prepare a page of field book and calculate

the reduced level of points if first reading was taken on a bench mark of RL 208.125 m.

10 marks KTU DEC 2018

4. .Define bearing.Which are the different systems of designating bearings?

4 marks KTU may 2018, 2019

5. Distinguish between dip and declination, isogonic and agonic lines. 5 marks KTU May 2018

6. The magnetic bearing of a line AB is S 2800 30’E. Find the true bearing if

declination is 70030’ W. 5 marks KTU DEC 2018

7. Explain the different methods of orientation in plane table survey. 6 marks KTU Dec 2018

8. What are the principles of surveying ?

9. Discuss survey stations and survey lines 8 marks KTUMay 2018

11. Write short notes on Dip, Declination, Latitude and Departure 12 marks KTU may 2018

12. What is meant by ranging out a survey line. Explain in detail direct and indirect ranging of

survey lines with neat sketches ? 12 marks KTU Dec 2018

13. What is orientation? Which are the methods of orientation? 4 marks KTU SEPT 2020

14. Explain with neat sketches? What type of orientation will you prefer and why?

10 marks KTU may 2018, 2019

15. What do you mean by bearing of a survey line? Explain the difference between whole circle

SURVEYING VAST TC

bearing and quadrantal bearing? Also discuss fore bearing and back bearing?

10 marks KTU Dec 2018

16. The following bearings were observed in running a closed traverse. At what stations do you

suspect the local attraction? Correct the bearings and also find the interior angles.

Line F.B B.B

AB 75o 5’ 254o 20’

BC 115o 20’ 296o 35’

CD 165o 35’ 345o 35’

DE 224o 50’ 44o 5’

EA 304o 50’ 125o 5’

11 marks KTU may 2018

17. Explain the term Ranging of a line. Describe how you would range a chain line between two

points which are not intervisible. 10 marks KTU Dec 2017

18. A level is set up at O on a line AB 50m from A and 1400m from B. The staff reading on A is

0.585 m and that on B is 3.695 m. Find the true level difference between A and B.


19. The following consecutive readings were taken with a dumpy level at 20 m intervals.

1.535, 2.020, 2.720, 2.965, 3.015, 2.625, 1.620, 1.895, 2.320, 2.710, 1.960, 2.34. The

instrument was shifted after the 4th, 7th and 9th readings. Reduced level of first point was

120 m. Calculate the reduced level of all stations and Find the gradient of the line connecting

first and last points. 12 marks KTU may 2019

20. The following consecutive readings were taken with a level and a 4m leveling staff on a

continuously sloping ground at common intervals of 30m. 8.855 (on A), 1.545, 2.335, 3.115,

3.825, 0.455, 1.380, 2.055, 2.855, 3.455, 0.585, 1.015, 1.850, 2.755, 3.845 (on B). The RL of

A was 380.500m. Make entries in a level field book and apply the usual checks. Determine the

gradient? 12 marks KTU may 2018, May 2019

21. Write short notes on simple levelling & differential levelling with neat sketches


22. Differentiate between profile levelling & cross sectioning?

SURVEYING VAST TC

23. Explain reciprocal leveling 15 marks KTU may 2018

24. What are the temporary adjustments of a dumpy level ? 10 marks KTU may 2018

MODULE - 2 1. Define contour. Which are the different methods of locating contour? 9 marks KTU May

2019

2. What are the characterestics of contours? 12 marks KTU may 2018

3. Explain the steps in ascertaining the intervisibility between triangulation stations.

8 marks KTU May 2018

4. What is Mass Haul diagram? What are the characteristics and discuss its uses?


5. What are the uses of contours?

6. Define i) Contour ii) contour Interval iii) Contour Gradient iv) Horizontal Equivalent.


7. Explain the factors affecting the choice of contour interval. 10 marks KTU Dec 2018

8. Explain repetition method of measurement of horizontal angle. 5 marks KTU may 201

9. Two triangulation stations A and B are 60 km apart and have elevation 240 m and 280 m

respectively. Find minimum height of signal required at B so that line of sight may not pass near

the ground than 2 m. The intervening ground has an elevation of 200 m.


10. Briefly explain any two methods for computation of area 6 marks KTU may 2018

11. A series of offsets were taken from a chain line to a curved boundary at 15 m intervals in the

following order. 0, 2.65 , 3.80, 3.75, 4.65, 3.60, 4.95, 5.85 m. Compute the area enclosed between

the ordinates using

(1) average ordinate rule

(2) trapezoidal rule

(3) Simpson’s one third rule 12 marks KTU Dec 2018

SURVEYING VAST TC

12. A road embankment is 8 m wide and 200 m in length, at the formation level, with a side

slope of 1.5:1. The embankment has a rising gradient of 1 in 100. The ground levels are

given below. The formation level of zero chainage is 166 m. Calculate the volume of

earthwork using end area formula and prismoidal formula. 12 marks KTU may 2018

Distance m) 0 50 100 150 200

R.L (m) 164.5 165.2 166.8 167 167.2

13. a) Define mass diagram. What are its uses? 5 marks KTU Dec 2018

b) Explain the different steps in triangulation survey. 10 marks KTU may 2018

14. a) Explain prismoidal rule for calculating volume of a plot. 5 marks KTU may 2019

b) A railway embankment is 10 m wide with side slope 1.5 (H) : 1 (V). Assuming

the ground to be levelled in a direction transverse to centre line, calculate the volume contained in a

length of 120 m, the centre height at 20 m interval being in metres 2.2, 3.7, 3.8, 4.0, 3.8, 2.8, 2.5 using

trapezoidal and prismoidal formulae. 12 marks KTU may 2019

15. Volume of earth work is to be calculated for a railway embankment 12m wide with side slope

1.5:1. Assuming the ground to be level in a direction transverse to the centre line, calculate the

volume contained in a 180m length, the centre heights at 30m intervals in meters as

0.70,1.20,1.75,1.45,1.20,0.95,0.65 using a) prismoidal rule and b) trapezoidal rule.

10 arks KTU Dec 2018

16. List the temporary adjustments of a theodolite. 5 marks KTU may 2018

17. Explain the horizontal angle measurement procedure. 6 marks KTU may 2018

SURVEYING VAST TC

18. Two triangulation stations A and B are 60 km apart and have elevation 240 m and 280 m

respectively. Find minimum height of signal required at B so that line of sight may not pass

near the ground than 2 m. The intervening ground has an elevation of 200 m.


19. The elevation of two triangulation stations A and B, 100 km apart, are 180 m and 450 m

respectively. The intervening obstruction situated at C, 75 km from A, has an elevation of 259

m. Ascertain if A and B are intervisible. If not, by how much B should be raised so that the line

of sight must nowhere be less than 3 m above the surface of the ground, assuming A as the

ground station. 10 marks KTU May 2018

20. Discuss the classification of triangulation figures? 5 marks KTU may 2018

21. Explain the term strength of figure? 10 marks KTU may 2018

22. Write short notes on intervisibility of triangulation stations?

23. What are the factors to be considered while selecting triangulation stations?


24. What are satellite stations and Reduction to centre? 10 marks KTU Dec 2019

25. What are well conditioned and ill conditioned triangles? 8 marks KTU Dec 2017

MODULE 3

1. Write short note on weight of an observation 5 marks KTU Dec 2018

2. Explain the principle of least squares 5 marks KTU Sep 2020

3. The following are the mean values observed in the measurement of three angles A, B, C at one

station, Calculate the most probable value.

SURVEYING VAST TC


4. Form the normal equation for x, y, z in the following equation


5. State the laws of weights with examples. 6 marks KTU Dec 2018

7. Determine the most probable values of A, B and C of a triangle ABC from the following

measurements.

A=63º 54_ 40_ weight 1

B=75º 34_ 29_ weight 2

C= 40º 30_ 56_ weight 1 8 marks KTU Dec 2018

8. What is a true value? What is most probable value?` 8 marks KTU Dec 2018

9. Find the most probable values of the angles A, B and C from the following observations at a

station P using method of differences.

A = 38o 25' 20” wt.1

B = 32o 36‟ 12” wt.1

A +B = 71o 01‟ 29” wt .2

A + B+ C = 119 o 10‟ 43” wt.1

B + C = 80o 45‟ 28 wt.2 12 marks KTU May 2019

SURVEYING VAST TC

10. Form the normal equation for x, y, z in the following

equations a. 3x+3y+z-4 = 0,

b. x+2y+z-2 = 0

i.5x+y+4z-21 = 0 10 marks KTU May 2018

Also form the normal equation, if weights of the equations are 2, 3 and 1 respectively.

MODULE 4

1. Explain the principle of EDM measurement 5 marks KTU May 2018

2. Explain the operation of total station. 10 marks KTU May 2018

3. Explain different types of EDM instruments.

3. Which are the different types of modulation of electromagnetic waves?


4. What is EDM? Discuss the principles of EDM? 4 marks KTU May 2019

5. What is electromagnetic wave? 4 marks KTU May 2019

6. Define “Geodimeter” 4 marks KTU May 2019

7. Define Total Station . 4 marks KTU Dec 2019

8. What are the basic principles of Total Station? 5 marks KTU Dec 2019

9. List out the total station Instruments 6 marks KTU Dec 2018

SURVEYING VAST TC

10. a) Write the parts of the Total Station?

(b) Explain in detail about Electromagnetic Spectrum and its applications

(c) Explain in detail about the different types of EDM 12 marks KTU Dec 2017

11.Why phase comparison and modulation is preferred over time measurement in EDM

(b) Explain in detail about the sources of errors in Total station and EDM.


12. a) Explain in detail about the fundamental measurements of the Total Station.

b) Explain the working principle of “Tellurometer” 10 marks KTU Dec 2018

13. a) Explain the working principle of “Geodimeter '”

(b) Explain the working principle of “Wild Distomats” 10 marks KTU Dec 2017

14. a). Explain in detail about the properties of electromagnetic waves. How are they useful in

measuring distances

b) What are the advantages of using Total station survey 15 marks KTU May 2018

15. a) Briefly explain the field procedure of Total station survey for co ordinate determination

b) Explain the steps to be followed for the set up of a total station over a point during field

work. 20 marks KTU Dec 2018

16. ) What are the three classes of circular curves? 10 marks KTU July 2019

17. What are the elements of a simple Circular curve? 8 marks (KTU dec 2019)

18. What are the difficulties in setting out simple curves? Describe briefly the methods

employed in overcoming them. 20 marks ( KTU dec 2018)

19. What are the functions of a transition curve? What are the types of transition curve?

15 marks ( KTU Sep 2020)

20. Explain Rankine’s method for setting out simple circular curve. 10 marks ( KTU Dec

2019)

SURVEYING VAST TC

21. Explain the elements of a compound circular curve 10 marks ( KTU July 2019)

MODULE 5

1. Briefly explain about Global Navigation System and its types? 20 marks KTU July

2. What you mean by Global Positioning System, 10 marks KTU July 2019)

3. Explain errors in GPS ranging, Explain any two in detail 10 marks KTU dec 2019

4. Briefly explain about the various applications of GPS 10 marks KTU sep 2020

Explain the principle of position determination by satellite ranging

20 marksKTU Dec 2019

5. Explain about the principles of GPS? 15 marks( KTU sep 2019)

6. List the advantages and disadvantages of GPS surveying methods

7. Explain static and rapid static methods of GPS surveying 20 marks ( KTU sep 2019)

8. What you mean by visibility diagram? Illustrate with sketch 20marks( KTU Dec19)

9. What is meant by DGPS? Explain code based and carrier based DGPS system

20 marks( KTU July 2019)

10. Explain briefly about various phases of GPS survey? 20marks( KTU sep 2019)

11. Enumerate the applications of GPS. 10 marks( KTU Dec 2020)

12. What is meant by multi spectral scanning? 8marks( KTU sep 2020)

13. Explain along track and across track scanning? 10 marks( KTU sep 2020)

14. What is meant by remote sensing? 5 marks( KTU sep 2019)

15. Describe the principles of remote sensing? 5 mark( KTU sep 2019)

16. Explain passive and active remote sensing? 15 marks( KTU July 2019)

17. What is meant by spectral reflectance? Explain the reflectance characteristics of soil,

vegetation and water with the help of spectral reflectance curve?

20 marks( KTU Dec 2018)

EST 200 DESIGN AND ENGINEERING

MODULE 1

Sl.No.

Questions Marks KTU, Year

1 Write about the basic design process. 4

Model

2 Describe how to finalize the design objectives. 4 Model

3 List the constraints and objectives of designing a lunch

box for the school students

5 KTU- May,2019

4 Design a length adjustable mop to clean ceiling fan 5 KTU- May,2019

5 what are the objectives and constraints of above design 5 KTU- May,2019

6 Prepare the objective tree for the product coconut peeling

machine given below

5 KTU- May,2019

7 Give the main objectives and constraints for the design

a)Main entrance door of a house b)The door of a room

with in the house c)The door to a bathroom within the

house

MODULE 2

1 State the role of divergent-convergent questioning in

design thinking

3 Model

2 Discuss how to perform design thinking in a team

managing the conflicts.

3 Model

3 Construct a number of possible designs and then refine

them to narrow down to the best design for a drug trolley

used in hospitals. Show how the divergent-convergent

thinking helps in the process. Provide your rationale for

each step by using hand

sketches only.

14 Model

4 Illustrate the design thinking approach for designing a bag

for college students within a limited budget. Describe each

stage of the process and the iterative procedure

involved. Use hand sketches to support your arguments.

14 Model

5 Design a manual mango plucker (with height adjusting

mechanism)which can be used by a common man to pluck

and collect safely the mangoes from the mango tree n his

yard.

• Prepare a detailed design highlighting the benefits

of our design

• Draw a neatly labeled sketches showing your

design

10 KTU- july,2018

MODULE 3

1 Show how engineering sketches and drawings convey

designs.

4 Model

2 Explain the role of mathematics and physics in design

engineering process.

3 Model

3 Graphically communicate the design of a thermo flask

used to keep hot coffee. Draw the detailed 2D drawings of

the same with design detailing, material selection, scale

drawings, dimensions, tolerances, etc. Use only hand

sketches.

14 Model

4 Describe the role of mathematical modelling in design

engineering. Show how mathematics and physics play a

role in designing a lifting mechanism to raise 100 kg of

weight to a floor at a height of 10 meters in a construction

site

14 Model

5 A round glass of 600 mm diameter and 6mm thick is

available .This is to be designed as a table supported at

three points by a steel tube bent in a convenient way .The

height of the table is to be 300 mm and the total legth of

10 KTU- Sep,2020

the tube used should not exceed 1.8 m,The tubeshould not

be out or joined .Design the bent tube for supporting the

table

MODULE 4

1 What is meant by modular design? 5 KTU- May,2019

2 Apply the modular design concept for a product bicycle 5 KTU- May,2019

3 How modular design is realized in i) Umbrella and ii) Ink

Pen ? Draw the different modules involved in each of

these products.

4 KTU- May,2019

4 Apply the principles of value engineering,design a school

bag for the students residing in poor home.Neatly sketch

the design and prepare a descrption for the same

5 KTU- July,2018

5 Show the development of a nature inspired design for a

solar powered bus waiting shed beside a highway. Relate

between natural and man-made designs. Use hand

sketches

14 Model

6 Show the design of a simple sofa and then depict how the

design changes when considering 1) aesthetics and 2)

ergonomics into consideration. Give hand sketches and

explanations to justify the changes in designs.

14 Model

7 Distinguish between project-based learning and problem-

based learning in design engineering.

3 Model

8 Describe how concepts like value engineering , concurrent

engineering and reverse engineering influence engineering

designs?

3 Model

9 Considering the principle of value engineering. Design a

suitable product for easy cleaning of dust from

windows,fans and lamp shades.

5 KTU- june ,2017

10 Draw the figure of a smart phone which is both aesthetic

and ergonomic

5 KTU- june ,2017

MODULE 5

1 Examine the changes in the design of a foot wear with constraints of 1) production methods, 2) life span requirement, 3) reliability issues and 4) environmental factors. Use hand sketches and give proper rationalization for the changes in design.

14 Model

2 Show how designs are varied based on the aspects of

production methods, life span, reliability and

environment?

3 Model

3 Explain how economics influence the engineering

designs?

3 Model

4 Describe the how to estimate the cost of a particular design using ANY of the following: i) a website, ii) the layout of a plant, iii) the elevation of a building, iv) an electrical or electronic system or device and v) a car. Show how economics will influence the engineering designs. Use hand sketches to support your arguments.

14 Model

MCN 201 SUSTAINABLE ENGINEERING

Module 1

Sl.

No Questions Marks

KU/KTU

(Month/Year)

1 Define sustainable development. 5 KTU APRIL 2018

2 Write a short note on Millennium Development

Goals. 10 KTU APRIL 2018

3 Discuss the evolution of the concept of sustainability.

Comment on its relevance in the modern world. 10 KTU DEC 2019

4 Explain Clean Development Mechanism 5 KTU DEC 2017

5 Explain with an example a technology that has

contributed positively to sustainable development. 5

KTU DEC 2017

KTU MAY 2019

KTU SEP 2020

6 Illustrate the nexus between agricultural technology

and sustainability. 5 KTU DEC 2017

7

Comment on the challenges for sustainable

development in our country and suggest a way to

overcome the same

5 KTU DEC 2018

8 Technology may affect sustainability in positive and

negative ways. Give one example each for both cases. 5 KTU APRIL 2018

Question Bank

Module 2

Sl.

No Questions Marks

KU/KTU

(Month/Year)

1 Describe carbon credit. 5 KTU APRIL 2018

2 Give an account of climate change and its effect on

environment. 5 KTU APRIL 2018

3 Explain the common sources of water pollution and

its harmful effects. 5 KTU APRIL 2018

4 Give an account of solid waste management in cities

10 KTU DEC 2019

5 Explain the 3R concept in solid waste management?

10 KTU DEC 2017

6 Write a note on any one environmental pollution

problem and suggest a sustainable solution.

5 KTU DEC 2018

7

In the absence of green house effect the surface

temperature of earth would not have been suitable for

survival

of life on earth. Comment on this statement.

10 KTU DEC 2018

8

Write short note on the need of environmental

sustainability? Also explain the concept of zero

waste?

5 KTU DEC 2018

9.

What is Environmental Impact Assessment

(EIA)?What are the standard procedures of EIA in

India?

10 KTU SEPT2020

Module 3

Sl.

No Questions Marks

KU/KTU

(Month/Year)

1 Describe biomimicry? Give two examples.

5 KTU APRIL 2018

2 Explain the basic concept of Life Cycle Assessment.

10 KTU APRIL 2018,SEPT2020

3 Explain the different steps involved in the conduct of

Environmental Impact Assessment

5 KTU APRIL 2018

4 Suggest some methods to create public awareness on

environmental issues. 5 KTU DEC 2017

5 “Nature is the most successful designer and the most

brilliant engineer that has ever evolved”. Discuss.

10 KTU DEC 2017

6

Match the items in the following sets:

SetA: {ISO 14006; ISO 14041; ISO 14048;ISO

14012}

Set B: {LCA Data Documentation Format;

Environmental Auditing qualifying criteria; Eco

design guidelines; LCA inventory analysis}

5 KTU DEC 2017

7 Write short notes on ISO 14000 series

5 KTU DEC 2018,SEPT2020

8

Suppose you are required to do the Life Cycle

Assessment of an Electric Vehicle. In the utilisation

stage, the assessment must be made for the energy

used to drive the vehicle. List any three possible

impacts of the Electric Vehicle during the usage

stage? Suggest a possible way to reduce the impact

during utilisation of the vehicle?

5 KTU DEC 2018

Module 4

Sl.

No Questions Marks

KU/KTU

(Month/Year)

1 Name three renewable energy sources. 5 KTU APRIL 2018

2 Mention some of the disadvantages of wind energy. 5 KTU APRIL 2018

3 Comment on the statement, “Almost all energy that

man uses comes from the Sun”. 10 KTU APRIL 2018

4 Write notes on:

a. Land degradation due to water logging.

b. Over exploitation of water.

5 KTU DEC 2017

5 Enumerate the impacts of biomass energy on the

environment 10 KTU DEC 2017

6 Explain the working of a photovoltaic cell with a neat

sketch? What are the steps involved in bio fuel

production?

5 KTU DEC 2018

7 How can energy be derived from oceans?

5 KTU DEC 2018

8 Explain in detail any one methodogy to extract

geothermal energy 5 KTU DEC 2018

9 What are the prospects of using Biofuel as a 5 KTU SEPT 2020

renewable energy source?

Module 5

Sl.

No Questions Marks

KU/KTU

(Month/Year)

1 Enlist some of the features of sustainable habitat

5 KTU APRIL 2018

2 Explain green engineering.

5 KTU APRIL 2018

3 Discuss the elements related to sustainable

urbanisation.

5 KTU APRIL 2018

4

4 Discuss any three methods by which you can increase

energy efficiency in buildings 5 KTU DEC 2017

5 How a green building differs from a conventional

building? Compare any five aspects? 5 KTU DEC 2017, 2019

6 Explain the criteria for the material selection of

sustainable builings? 10 KTU DEC 2017

7 Write short note on the green building certification in

india 5 KTU DEC 2018

8 Write short note on sustainable transportation? What

are all the characterestics? 10 KTU DEC 2019

9

Explain the concept of smart city with an

example.How a smart city helps in sustainable

development?

5 KTU SEP 2020

Documents

MAT201 PARTIAL DIFFERENTIAL EQUATIONS &COMPLEX …