PREPARED BY :
A.NALAYINI DEVI M.SC., M.PHIL.,
LECTURER, DEPARTMENT OF MATHEMATICS,
N.P.R.COLLEGE OF ENGINEERING AND TECHNOLOGY,
NATHAM624 401
A discipline that aims at producing fault free software that is delivered on time within budget which meets the end user’s requirements. Furthermore, it aims in producing easily modifiable software when the user needs change. (Schach)
• 1967, a NATO group coined the term “Software Engineering”
• 1968 NATO Software Engineering Conference concurred that “Software production should be an engineeringlike activity”.
• Using philosophies and paradigms of established engineering disciplines to solve “Software Crisis: that the quality of software was generally unacceptably low and that deadlines and cost limits were not being met”.
Economic Aspects
• Software Engineering v.s. Computer Science
• The computer scientist investigates several ways
to produce software, some good and some bad.
• But the software engineer is interested in only those techniques that make sound economic sense.
For example: A coding technique that can execute very efficiently but with higher maintenance cost may not be a good choice.
Maintenance Aspects
• Software Life Cycle / Software Process
• Requirements Phase
• Specification (Analysis) Phase
• Planning Phase
• Design Phase
• Implementation Phase
• Integration Phase
• Maintenance Phase (highest cost among all these phases)
• Corrective, Perfective, and Adaptive Maintenance
• Retirement
Scope of Software Engineering
Maintenance is so important, a major aspect of software engineering consists of techniques, tools, and practices that lead to a reduction in maintenance cost.
Approximate relative costs of the phases of the software life cycle.
• Software professionals are humans, and humans can make error.
• The fact that so many faults are introduced early in the software life cycle, highlights another important aspects of software engineering, namely, techniques that yield better specifications and designs.
• For example, reducing specification and design faults by 10% will reduce the overall number of faults by 67%. Scope of Software Engineering
• Most software being developed and maintained by a team of software engineers
• Scope of software engineering must also include techniques for ensuring that teams are properly organized and managed.
• For example, team programming leads to interface problems among code components and communication problems among team members.
~19751985: Structured Paradigm
• Structured Systems Analysis, Composite/Structured Design, Structured Programming, Structured Testing
• Lead to major improvements for software industry.
• But only good for small programs (say, 5,00050,000 lines of codes)
• Not scale well with today larger programs (say, 500.0005,000,000 LOC)
• Not so good in software maintenance aspects, (for instance, because of the separation of actionoriented and dataoriented in structured paradigm).
ObjectOriented Paradigm
• An object is a unified software component that incorporates both data and actions that operate of those data.
How can you systematically develop software?
How do you make this process costeffective?
• Project Cycle time
• Cost
• Quality of the software
For a project that is already delayed, employing more number of people further delays the process
Does not wear out
• However it becomes obsolete
Needs to be custom built
• Software ICs – reality?
Maintenance costs are high
Software productivity
• Average to expert programmer 25:1
In mathematics a transform is an operator applied to a function so that under the transform certain operations are simplified. In higher mathematics this idea is applied to functions in order to solve certain types of differential equations, for example, the Laplace transform.
Another type of transform used to simply the process of solving differential equations is called the Fourier transform. Jean Baptiste Joseph Fourier (March 21, 1768  May 16, 1830) was a French mathematician and physicist who is best known for initiating the investigation of Fourier series and their application to problems of heat flow. The Fourier transform is also named in his honor.
Fourier analysis has many scientific applications — in physics, number theory, combinatorics, signal processing, imaging, probability theory, statistics, option pricing, cryptography, numerical analysis, acoustics, oceanography, optics and diffraction, geometry, and other areas. When processing signals, such as audio, radio waves, light waves, seismic waves, and even images, Fourier analysis can isolate individual components of a compound waveform, concentrating them for easier detection and/or removal. For example, Telephone dialing; the touchtone signals for each telephone key, when pressed, are each a sum of two separate tones (frequencies). Fourier analysis can be used to separate (or analyze) the telephone signal, to reveal the two component tones and therefore which button was pressed.
INTEGRAL TRANSFORM
FOURIER INTEGRAL THEOREM
FOURIER SINE AND COSINE INTEGRALS
FOURIER TRANSFORMS COMPLEX FOURIER TRANSFORMS
INVERSION FORMULA FOR THE COMPLEX FOURIER TRANSFORM
FOURIER SINE TRANSFORMS
FOURIER COSINE TRANSFORMS
PROPERTIES
FINITE FOURIER TRANSFORMS
Problems
Question Bank
B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2011.
PG COURSES :  UG COURSES : 
MCA  Master of Computer Applications MBA  Master of Business Administration  BE  Marine Engineering BE  Aeronautical Engineering BE  Mechanical Engineering BE  Electronics and Communication Engineering BE  Computer Science Engineering B.TECH  Information Technology 
SCET is very particular about the placement of their wards. The Placement should not only be immediate but also fruitful with future prospects and growth. In this endeavor, the College is training their wards continuously to face the Recruitment Board for positive results.
The college is equipped with an effective Placement Cell. The college is only 4 years old and hence the role of Placement Cell commences from this Academic year. Leading MNCs and Corporate Majors will participate in the campus Selection Programme conducted by the College to facilitate the Placement of students. 
1. Determine whether the following systems are linear,time invariant,causal ,stable.
2. Determine whether the following systems are linear or not
dy(t) / dt + 3ty(t) = t^{2}x(t) & y(n)=2x(n)+ 1 / x(n1)
3. Explain the classification of signals with examples
4. Determine whether the following systems are TimeInvarient or not
Y(t) = t x(t) & y(n) = x(2n)
5. (a) Find whether the signal x(t) = 2 cos (10 t+1) – sin(4t1) is periodic or not.
(b) Evaluate Σ n_{=( ∞ to ∞) }e^{2n} δ (n2)
(c) Find the fundamental period of the Continuous time signal
1. Find the inverse laplace transform of X(S) = S / S^{2}+5S+6
2. Find the fourier transform of a rectangular pulse of duration T and amplitude A
3. Obtain the cosine fourier series representation of x(t)
4. Find the trigonometric fourier series of the figure shown below
5. Find the laplace transform of the signal x (t) = e^{at} u(t) + e ^{bt} u(t)
1. Find the convolution of the two signals x(t)= e ^{2t} u(t) h(t)= u(t+2)
2. State and prove the convolution property of ZTransform
3. Determine the Z=Transform of x_{1}(n)=a^{n }and x_{2}(n) =nu(n)
4. Find the convolution of x(t) = u(t+1) and h(t) = u(t2)
5. Find the Fourier transform of x(t) = t cos ωt
1. Find the Unilateral Ztransform and R.O.C of x(n) = sin ω_{0 }n u(n)
2. Discuss the block diagram representation of an LTIDT system
3. Consider a causal LTI system as in the fig
Determine the differential equation relating x(n) and y(n).
4. State and prove the Parseval’s relation.
5. Explain any 4 properties of DTFT.
1. Develop the Direct form I & II realization of the differential equation
dy(t) / dt + 5 x(t) = 3 x(t)
2. Prove any 2 properties of Ztransform
3. Obtain the cascade form realization of the system described by the differential Equation
y(n) – ¼ y (n1) – 1/8 y (n2) = x(n) + 3 x(n1) +2 x(n2)
4. Find the state variable matrices A,B,C,D for the equation
y(n)  3y(n1)  2y(n2) = x(n) + 5 x(n1) + 6 x(n2)
5. Discuss the block diagram representation of an LTIDT system
Thanks to :
Adhiparasakthi Engineering College,
Melmaruvathur,Tamil Nadu.
B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2010
Third Semester
Civil Engineering
CE2202 — MECHANICS OF FLUIDS (Regulation 2008)
Time: Three hours
Maximum: 100 Marks
Answer ALL Questions
PART A — (10 * 2 = 20 Marks)
1. Define the term continuum.
2. What is the difference between an ideal and a real fluid?
3. Distinguish between path lines, stream lines and streak lines.
4. To what type of flow is the concept of velocity potential and stream function applicable?
5. What are the assumptions made in the derivation of Euler's equation?
6. Sketch the velocity and shear stress distribution for laminar flow of an incompressible fluid through a circular pipe.
7. Give four examples in every day life where formation of boundary layer is important.
8. What are the characteristics of laminar flow?
9. What are the applications of model testing?
10. Enumerate the applications of dimensional homogeneity.
PART B — (5 * 16 = 80 Marks)
11. (a) (i) An open reservoir contains a liquid having density of 1.23 g/cc. At a certain point the gauge pressure is 0.31 atmosphere. At what height above the given point is the liquid level? (8)
(ii) Define Viscosity. Explain the effect of temperature and pressure on viscosity of liquids and gases. (8)
Or
(b) (i) Explain the characteristics of non Newtonian fluids in detail. (8) (ii) The velocity distribution for flow over a plate is given by u = 2 y – y^{2 }where u is the velocity in m/s at a distance y meters above the plate. Determine the velocity gradient and shear stress at the boundary and 0.15 m from it. (8)
12. (a) Derive an expression for the depth of centre of pressure from free surface of liquid of an inclined plane surface submerged in the liquid. (16)
Or
(b) (i) Derive the differential equation of continuity. (8)
(ii) In a two dimensional incompressible flow, the fluid velocity
components are given by
u = x  4 y and
v =  y  4x .
Show that velocity potential exists and determine its form as well as stream function. (8)
13. (a) A drainage pump has tapered suction pipe. The pipe is running full of water. The pipe diameter at the inlet and at the upper end is 1 m and 0.5 m respectively. The free water surface is 2 m above the centre of the inlet and centre of upper end is 3 m above the top of free water surface. The pressure at the top end of the pipe is 25 cm of Hg and it is known that loss of head by friction between top and bottom section is one tenth of the velocity head at the top section. Compute the discharge in litre/sec. Neglect loss of head at the entrance of the tapered pipe. (16)
Or
(b) Show that the momentum correction factor and kinetic energy correction factor for laminar flow through a circular pipe are 4/3 and 2 respectively.
(16)
14. (a) Explain what you understand by boundary layer thickness and displacement thickness. Determine the relationship between the two for a boundary layer which is
(i) laminar throughout and
(ii) turbulent throughout.
Assume :
(1) in the laminar boundary layer, the flow obeys the law, shear
where m is the viscosity, which leads to velocity profile
velocity, u is the velocity at a distance y above the plate and k is a constant.
(2) the velocity distribution in the turbulent boundary layer is
(16)Or
(b) Derive an expression for the calculation of loss of head due to
(i) sudden enlargement
(ii) sudden contraction. (16)
15. (a) Describe Buckingham’s p – theorem to formulate a dimensionally homogeneous equation between the various physical quantities effecting a certain phenomenon. (16)
Or
(b) By dimensional analysis, show that the power P developed by a hydraulic turbine is given by
where p – mass density of liquid, N – rotational speed, D – diameter of runner, H – working head and g – acceleration due to gravity. (16)
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S.No.

Description
of Equipment

Quantity required


D.C motor – Generator set
D.C motor – Shunt Generator
D.C motor – Compound Generator

2 set
2 set


D.C. Shunt Motor

2 Nos.


D.C. Series Motor

1 No.


D.C. Compound Motor

1 No.


Single phase transformers

7 Nos.


Three phase transformers

2 Nos.


D.C. Motor – Alternator set

4 sets


Three phase Induction Motor (Squirrel cage)

3 Nos.


Three phase slip ring Induction Motor

1 No.


Single phase Induction Motor

2 Nos.


Resistive load
3 phase – 2 , single phase  3

5 Nos.


Inductive load

1 No.


Single phase Auto transformer

5 Nos.


Three phase Auto transformer

3 Nos.


Moving Coil Ammeter of different ranges

20 Nos.


Moving Coil Voltmeter of different ranges

20 Nos.


Moving Iron Ammeter of different ranges

20 Nos.


Moving Iron voltmeter of different ranges

20 Nos.


Wire wound Rheostats of different ratings

30 Nos.


Tachometers

10 Nos.


Single element wattmeters of different
ranges
UPF /
LPF

20 Nos.


Double element wattmeters of different ranges

4 Nos.


Power factor meter

2 Nos.


Digital multimeter

5 Nos.


Three point starter, four point starter,DOL
starter, manual star / delta starter, semi automatic and fully automatic star
/ delta starter

1 No each for study experiment
