## Wednesday, 18 March 2015

### Electrical Engineering Important Questions Unit Wise

Important Questions in Electrical Engineering
Electrical Engineering Important Questions Unit Wise

UNIT I
1. Draw the experimental set up to predetermine the efficiency of the given DC machine and give the necessary relations to find the efficiency of the machine while it is running as a motor as well as a generator. Also list the advantages and disadvantages of the test.
2. Determine the torque developed and the shaft torque of a 220 v. 4-pole series motor with 800 conductors wave connected supplying a load of 8.2kW by taking 45 amps from the mains.The flux per pole is 25 mWb. And its armature circuit resistance is 0.6 ohm

3. Derive the emf equation of the DC generator when the winding is lap and wave connected

4. Derive the torque equation of a DC motor.

5.. Explain and draw the N-T, N-Ia and T-Ia characteristics of a series, shunt and compound motor.

UNIT II

1. Obtain the equivalent circuit of a 200/400 V, 50 Hz, 1f transformer from the following test data.
OC test: 200 V, 0.7 a, 70 W on LV Side, SC Test: 15 V, 10 A, 85 W on .V side.

2. The primary and secondary windings of a 40 KVA, 6600/250V, 1f transformer has resistances of 10 Ω and 0.02Ω respectively. The leakage reactance of the transformer referred to the primary is 35 Ω. Calculate the full – load regulation at upf and 0.8 lagging pf. Neglect the no-load current.
3. Explain the operation of the 1f transformer under load condition with necessary phasor diagram. \
4. Give the classification of transformer based on primary-secondary combination, rating and application.

UNIT III
1. Draw the slip – torque of 3finduction motor and explain the significance of it.
2. Find the % tapping required on an autotransformer required for a squired – cage motor to start the motor to start the motor against 25 % of full – load torque. The short – circuit current on normal voltage is 4 times the full – load current and full – load slip is 3%.
3. Explain the emf injection method of speed control with a neat diagram.
4. Discuss in detail the principle of three phase induction motor, starting from the production of rotating magnetic field.

UNIT IV
1. Explain in detail the MMF method of obtaining regulation of an alternator.
2. Write detailed notes on (i) reluctance motor (ii) stepper motor
3. Explain any one type of stepper motor in detail with connection diagram and different operating modes.
4. An alternator has 18 slots / Pole and the first coil lies in slots 1 and 16. Calculate the pitch factor for fundamental and third harmonics.

UNIT V

1. Draw the single line diagram showing the structure of electric power system and explain each component in detail.
2. Describe the types of DC links.
3. Explain various types of cables with neat diagrams.
4. Derive an expression for string efficiency.

## Sunday, 15 March 2015

### ELECTRICAL MACHINES – II IMPORTANT QUESTIONS For Exams

ELECTRICAL MACHINES – II  IMPORTANT QUESTIONS For Exams

1. Write the causes of harmonics in the voltage and current waves of electrical
machinery?
2. What are conditions for parallel operation of alternators?
3. List the inherent disadvantages of synchronous motor?
4. When is a synchronous motor said to receive 100% excitation?
5. Under what condition, the slip in an induction motor is
(a) Negative
(b) Greater than one.
6. What are the two fundamental characteristics of a rotating magnetic field?
7. State two advantages of speed control of induction motor by injecting an e.m.f
in the rotor circuit.
8. What is the effect of change in input voltage on starting torque of induction
motor?
9. What are the drawbacks of the presence of backward rotating magnetic field in
a single phase induction motor?
10. What are the demerits of repulsion motor?

PART B — (5 × 16 = 80 Marks)

11. (a) (i) Derive the e.m.f. equation of an alternator. Explain pitch factor and
distribution factor. (12)
(ii) A 3 phase, 6 pole, star-connected alternator revolves at 1000 r.p.m.
The stator has 90 slots and 8 conductors per slot. The flux per pole
is 0.05 wb (sinusoidally distributed). Calculate the voltage
generated by the machine if the winding factor is 0.96. (4)
Or
(b) (i) Elaborate the discussion on capability curve with its boundaries of
synchronous machine. (8)
(ii) Discuss the parallel operation of two alternators with identical
12. (a) (i) Draw the equivalent circuit and phasor diagram of a synchronous
motor. (8)
(ii) Explain the significance of V and inverted V curves. (8)
Or
(b) (i) Discuss the methods of starting and procedure for starting
synchronous motor. (10)
(ii) A 3000 V, 3 phase synchronous motor running at 1500 r.p.m, has its
excitation kept constant corresponding to no-load terminal voltage
of 3000 V. Determine the power input, power factor and torque
developed for all armature current of 250 A if the synchronous
reactance is 5 per phase and armature resistance is neglected. (6)
13. (a) (i) Discuss the different power stages of an induction motor with
losses. (8)
(ii) An 18.65 KW, 4 pole, 50 Hz, 3 phase induction motor has friction
and windage losses of 2.5% of the output. Full load slip is 4%. Find
(1) rotor copper loss,
(2) rotor input
(3) shaft torque
(4) the gross electromagnetic torque. (8)
Or
(b) (i) Write a brief note on induction generator. (8)
(ii) Write a brief note on double cage rotor induction motors. (8)
14. (a) (i) Explain the speed control of three phase induction motor by pole
changing. (8)
(ii) Explain the rotor rheostat control of 3 phase slip ring induction
motor. (8)
Or
(b) Discuss the various starting methods of squirrel cage induction motors.
(16)
15. (a) (i) Explain the operation of a single phase induction motor using
double field revolving theory. (8)
(ii) Explain the operation of shaded pole induction motor with neat
diagram. (8)
Or
(b) (i) Explain the principle and operation of AC series motor. (8)
(ii) Explain the principle and operation of reluctance motor and state
its applications. (8)

### Electrical Machines II

EE2302 Electrical Machines II Part B Expected Questions |
EE 2302 EM -2 Part B (16 Marks) Expected Important Questions for EEE -5th Machines

Unit-1

1. Derive EMF equation of Alternator and derive expression for pitch factor & distribution Factor. (16) -Expected.
2.Explain the voltage regulation of alternator by EMF and MMF method. -expected. (16)
3.(i) Elaborate the discussion on capability curve with its boundaries of

synchronous machine. (8)
(ii) Discuss the parallel operation of two alternators with identical
4. PROBLEMS for EMF or MMF method -Expected *** (8)
5.. What is the effect of armature reaction at different power factors on synchronous machine? (16)
6.. Explain two reaction theory of synchronous machine. How can Xd and Xq be determined? -expected .

Unit -2

1. Explain the working of synchronous motor with different excitations? - expected
2. Explain the significance of V curve and inverted V curve -16 marks -expected
4. (i)describe the construction and principer of synchronous motor(ii)Discuss various methods starting synchronous motor -Expected
5. explain a)hunting b) synchronous condensor

Unit -3

1. Problems expected (8)

2.Explain about (i)Double cage induction motor (ii)Induction generator (10)
3. (i)Derive the torque equation of 3phase induction motor and deduce condition for maximum torque (8)
(ii) Explain Torque – Slip characteristics of 3phase induction motor (8)
4. Draw the equivalent circuit of induction motor and deduce the approximate equivalent circuit
5. Discuss different power stages of 3phase induction motor and derive the relation between P2,Pcu & Pm

Unit -4

1.Explain various methods of speed control from rotor side of an induction motor? (16)
2. Explain various methods of speed control from stator side of an induction motor? (16)

3. explain v/f control - expected
4. describe a)star – delta starter b) Auto transformer starter

******from above study 1st and 2nd questions all methods.*****

Unit -5

1. Explain the Double field revolving theory of operation of single phase induction motor (8)
2. Explain shaded pole induction motor with diagrams (8)
3. (i) Explain the principle and operation of AC series motor. (8)
(ii) Explain the principle and operation of reluctance motor and state
its applications. (8)

### Data Communication & Networking

Data Communication & Networking

1.        What is data communication and identify the 5 components of data communication. (6 marks)

2.        What are the three main functions of data link layer? (3 marks)

3.        What is the difference between Simplex, Half Duplex and Full Duplex Transmission? (6 marks)

4.        Define what is Internetworking. (2 marks)

5.        Name two major categories of transmission media. (2 marks)

6.        List 5 various types of network topologies. (5 marks)

7.        Contrast an analog signal with a digital signal. (4 marks)

8.        What are the four types of line encoding which fall under bipolar types? (4 marks)

9.        Define and explain 3 various types of categories of network types. (6 marks)

10.    Difference between packet switching and circuit switching. (6 marks)

11.    List 5 types of protocols. (5 marks)

12.    What is the difference between connection-oriented and connectionless? (5 marks)

13.    What are the 3 types of frames in HDLC and their functions? (6 marks)

14.    What are the 3 types of line encoding? (3 marks)

15.    List down 7 layers in Open Systems Interconnection (OSI) Model. (7 marks)

### Basic Electrical and Electronic Engineering Very Important Questions For External Exams

Basic Electrical and Electronic Engineering Very Important Questions For External Exams

Question Bank
Define electric current
Define electric resistance
Define electric conductance
Define specific resistance
Differentiate electric power and energy
Define electromotive force
State ohms law
State kirchoff’s law
What is an alternating quantity?
Define cycle
Define time period
Define frequency
Define amplitude
Define RMS value
Define average value
Define the expression for form factor and peak factor
Define power factor
What do you understand by balanced system?
What is an indicating instrument?
Write two essential requirements of indicating instruments
List the three different torques employed in the measuring instruments for the satisfactory operation
Write any four methods by which the deflecting torque can be obtained
Mention the two methods of obtaining controlling torque
What is meant by damping torque?
Write any two features of moving coil instrument
Write any two features of moving iron instrument
What is meant by creeping?
Convert (100001110.010)2 to decimal.
Give that (79)10 = (142)b determine the value of b.
Perform the arithmetic operations 35+40 and (-3.5)+(-40) with binary number in signed 2’s complement representation.
Convert (342.45)10 to binary and Octal.
Perform the following arithmetic operation using 1’s complement scheme. (4-8) ,(8-4) ,(-2-3)
Convert the following: (369)10 =( )8 =( )16 =( )2.
How many bits are required to represent the decimal numbers in the ranges from 0 to 999 using straight binary code? Using BCD codes?
Explain how addition and subtraction can be performed with 1’s complement and 2’s complement representations with suitable examples.
State de-Morgan’s Law.
Why NAND gate is called as an universal gates?
Write the dual of AB+ĀC+BC
Realize XOR function using only NAND gates.
How do you implement y=A+B using a 3 input OR gate?
Define distributive law.
What is mean by duality in Boolean Algebra?
Simplify the following function using algebraic method.

a) F=C(B+C)(A+B+C)
Implement AND and OR using NAND and NOR gates.
Give the truth table for JK flip-flop?
Name the problem associated with the asynchronous counter.
What is an universal shift register?
Draw MOD-8 Ripple counter using JK flip-flop and give the timing diagram
Give the excitation table for JK flip-lop.
Draw a MOD-6 counter using feedback counter.
Draw the timing diagram for a 3 stage ring counter.
How do you construct D flip-flop and T Flip-lop using JK flip-flop.
Distinguish between Synchronous and asynchronous counter.
Draw the circuit of serial n and serial out shift register and explain its operation.
Name the two problems that may arise in the ripple counter.
Draw the circuit of up-down counter and explain its working.
What is mean by the term edge triggered?
Describe the operation of BCD counter.
Draw the logic for 4-stage ring counter using JK flip-flo0p?
Define the hold time requirement of a clocked FF?
Show the T flip-flop implementation from S-R flip-flop?
Give the logical expression for sum and carry for a Half adder.
Obtain the expression for SUM and CARRY outputs of a full adder and implement the same.
Draw the block diagram of a communication system and explain its operation.
Explain briefly some of the telecommunication services.
Distinguish between telegraphy and telephony.
What is facsimile? how does it work?
What are the different transmission paths for communication?
What is the difference between analog and digital signals?
What is modulation?
Explain briefly the need for modulation.
What are the types of analog modulation ?
Write down a general expression for AM wave.
Write the expression for modulation index in AM .
Write down the mathematical expression for a FM wave.
What is advantage of a FM over AM?
Compare FM and PM.
State sampling theorem.
Define the following terms:

a) Pulse Width Modulation(PWM)

b) Pulse Amplitude Modulation(PAM)

c) Pulse Time Modulation (PTM)

d) Pulse Code Modulation (PCM)
Compare PAM and PWM.
Describe briefly some digital modulation schemes.
Define and describe pulse – position modulation.
What is pulse width modulation ?What other names does it have?
What is meant by Frequency-Shift Keying?
Differentiate FSK from PSK
What is back emf?
Why a dc series motor cannot be started on no load?
What are the various types of dc motors?
What is the necessity of a starter for a dc motor?
What is torque?
What is speed regulation?
What is called armature torque?
What is called shaft torque?
Draw the characteristics curve of a dc shunt motor?
What is the difference between three point and four point starters?
What is the method available for testing dc series motor?
Name the protective devices used in a 3point starter?
Mention the methods of speed control for a dc motor?
What are the losses that occur in a dc motor?
What are the various types of dc generators?
Draw the internal and external characteristic curves of dc shunt generator?
Draw the internal and external characteristic curves of dc series generator?
Draw the characteristics curves of dc compound generator?
DC series generators are suitable for ?
What is the function of commutator in DC generator?
What is the function of carbon brushes in DC generator?
What is called voltage regulation?
Write short notes on efficiency of a DC motor?
How the voltage builds up in Dc generator?
Why the armature core is made by laminated sheets?
Explain the construction and working principle of D.C. generator with neat diagram. (16)
Explain the different types of D.C. generators. (16)
Draw and explain the characteristics of different types of d.c.generators. (16)

a). Derive the emf equation of D.C. Generator. (8)
Sketch and explain the speed-current, speed-torque and torque-current characteristics of a shunt motor, series motor and compound motor. (16)
Draw the characteristic curves of D.C. shunt, series and compound motors. Use these curves to explain the applications for which these motors are used. (16)
a) List all the important parts of a D.C. Motor and explain the importance of each..a)Calculate the emf generated by 4 pole wave wound generator having 65 slots with 12 conductors per slot when driven at 1200 rpm. The flux per pole is 0.02 wb. (8)
A 4 pole lap wound dc shunt generator has a useful flux per pole of 0.07wb. The armature winding consists of 220 turns, each of 0.004 ohm resistance. Calculate the terminal voltage when running at 900 rpm if the armature current is 50A. (16)
Explain the principle of working a 1f transformer?
Discuss the difference between core type and shell type construction?
What is KVA rating of a transformer?
Draw the no load phasor diagram of a transformer?
Draw the phasor diagram of a transformer under load condition?
Explain voltage regulation?
Derive the emf equation of a transformer?
What is meant transformation ratio?
How the transformers are classified?
Write short notes on autotransformer.
Derive the condition for maximum efficiency?
What are the various losses that must be present in a transformer?
Explain the construction and working principle of single-phase transformer.(16)
Enumerate the various types of transformer. (4)
Derive an expression for the emf of an ideal transformer winding. (6)
Draw and explain the no load phasor diagram for a single-phase transformer. (6)
What is KVA rating of a transformer? (8)
Explain various features of an ideal transformer. (8)
b)The no load current of a transformer is 10A at a power factor of 0.25 lagging, when connected to 400v,50Hz supply, calculate(i)magnetizing component of no load current(ii) iron loss and(iii) maximum value of the flux in the core. Assume primary winding turns as 500. (8)
What is the frequency of induced emf of an induction motor?
Why squirrel cage induction motors are common in the domestic pump sets?
Distinguish between squirrel cage & slip ring induction motor?
What are the applications of induction motors?
Name the speed control methods of a 3 induction motors?
Define a slip of an induction motor?
What is called synchronous speed?
Define electron volt?
State the relationship between electric field intensity, and potential?
An electron beam from rest is accelerated by a potential of 200V. Find the final velocity of the electron?
List out the common diode applications?
Define zener breakdown?
Differentiate photodiode and light emitting diode.
Explain the forward and reverse bias operation and VI characteristics of a PN Junction diode. (16)
a)Derive the diode current equation? . (8)
b)Discuss the current components of PN junction diode? (8)
a)Explain any two applications of diode with neat diagram . (8)
Define pinch - off voltage?
Derive the relation between pinch - off voltage & drain current?
What is a MOSFET?
What is a MESFET?
Explain the operation of PNP & NPN transistor? (12)
b). What is transistor? State its types
Compare CE – CB – CC Configuration? (8)
a). Explain the input & output characteristics of CE configuration of a transistor?
State FET& its types? (4)
a)Explain the input & output Characteristic of CB configuration of a transistor?
Explain the construction & characteristics of JFET
What is a rectifier?
Explain the operation & characteristics of TRIAC?
Explain the operation & characteristics of UJT?

### Signals and Systems Important Questions

Signals and Systems Important Questions

UNIT I
REPRESENTATION OF SIGNALS
PART-A (2 Marks)
1. Define Signal.
2. Define system.
3. What are the major classifications of the signal?
4. Define discrete time signals and classify them.
5. Define continuous time signals and classify them.
6. Define discrete time unit step &unit impulse.
7. Define continuous time unit step and unit impulse.
8. Define unit ramp signal.
9. Define periodic signal and non-periodic signal.
10. Define even and odd signal ?
11. Define Energy and power signal.
12. Define unit pulse function.
13. Define continuous time complex exponential signal.
14. What is continuous time real exponential signal.
15. What is continuous time growing exponential signal?
16. State the BIBO criterion for stability.
17. Find whether the signal given by x (n) = 5cos (6 _n) is periodic
18. Write down the exponential form of the Fourier series representation of a
Periodic signal?
19. Write down the trigonometric form of the fourier series representation of a
periodic signal?
20. Write short notes on dirichlets conditions for fourier series.
21. State Time Shifting property in relation to fourier series.
22. State parseval’s theorem for continuous time periodic signals.

PART – B
1. (a) For the systems represented by the following functions. Determine whether
every system is (1) stable (2) Causal (3) linear (4) Shift invariant (4)
(i) T[x(n)]= ex(n)
(ii) T[x(n)]=ax(n)+6
2. Determine whether the following systems are static or Dynamic, Linear or Nonlinear,Shift variant or Invarient, Causal or Non-causal, Stable or unstable. (4)
(i) y(t) = x(t+10) + x2(t)
(ii) dy(t)/dt + 10 y(t) = x(t)
3. Explain about the properties of continuous time fourier series. (8)
4. Find the fourier coefficients of the given signal. (4)
x(t) = 1+ sin 2_ot + 2 cos 2_ot + cos (3_ot + _/3)
5. Determine the Fourier series coefficient of exponential representation of x(t)
x(t) = 1, ItI (8)
0, T1< ItI < T/ 2

6. Find the exponential series of the following signal. (8)

7. Find which of the following signal are energy or power signals. (8)

a) x(t)=e-3t u(t) b) x(t) = ej(2t+_/4) c) x(n)= cos(_/4n)

8. Explain the properties of Discrete time fourier serier (8)

9. Find the cosine fourier series of an half wave rectified sine function. (8)

10. Explain the classification of signals with examples. (8)

UNIT II ANALYSIS OF CONTINUOUS TIME SIGNALS AND SYSTEMS

PART-A (2 Marks)

1. Define continuous time system.

2. Define Fourier transform pair.

3. Write short notes on dirichlets conditions for fourier transform.

4. Explain how aperiodic signals can be represented by fourier transform.

5. State convolution property in relation to fourier transform.

6. State parseval’s relation for continuous time fourier transform.

7. What is the use of Laplace transform?

8. What are the types of laplace transform?

9. Define Bilateral and unilateral laplace transform.

10. Define inverse laplace transform.

11. State the linearity property for laplace transform.

12. State the time shifting property for laplace transform.

13. Region of convergence of the laplace transform.

14. What is pole zero plot.

15. State initial value theorem and final value theorem for laplace transform.

16. State Convolution property.

17. Define a causal system.

18. What is meant by linear system?

19. Define time invariant system.

20. Define stable system?

21. Define memory and memoryless system.

22. Define invertible system.

23. What is superposition property?

24. Find the fourier transform of x(t)=cos(_0t)

PART – B

1. Determine the inverse laplace of the following functions. (6)

1) 1/s(s+1) 2) 3s2 +8s+6 (s+2)(s2+2s+1)

2. Explain about the classifications of continuous time system. (8)

3. A system is described by the differential equation. (10) d2y(t)/dt2+3dy(t)/dt+2y(t)=dx(t)/dt if y(0) =2;dy(0)/dt = 1 and x(t)=e-t u(t) Use laplace transform to determine the response of the system to a unit step input applied at t=0.

4. Obtain the transfer function of the system when y(t) = e-t-2 e-2t+ e-3t and x(t)= e-0.5t (8) 5. a) Discuss the condition on stability of an LTI system based on Laplace domain representation. (3)

b) Bring the equivalence between Laplace transform and Fourier transform.(5)

6. Explain the properties of laplace transform (8)

7. Find the impulse and step response of the following systems H(s) = 10/s2+6s+10 (6)

8.For the transfer function H(s) = s+10/ s2+3s+2 find the response due to input x(t) = sin2(t) u(t) (6)

9. Find the fourier transform of triangular pulse (10) x(t) = _(t/m) ={1-2|t|/m |t| 0 otherwise

10. The input and output of a causal LTI system are related by the differential equation. (10)

d2y(t)/dt2+6dy(t)/dt+8y(t)=2x(t) i) Find the impulse response of the system. ii) What is the

response of this system if x(t) = t e-2t u(t) 11. Consider a causal LTI system with frequency

response. (10) H(j_) = 1/ j_ +2 For a particular input x(t) this system is y(t)= e-2t u(t) – e-3t u(t)

UNIT III SAMPLING THEOREM AND Z – TRANSFORMS

PART-A (2 Marks)

1. Why CT signals are represented by samples.

2. What is meant by sampling.

3. State Sampling theorem.

4. What is meant by aliasing.

5. What are the effects aliasing.

6. How the aliasing process is eliminated.

7. Define Nyquist rate.and Nyquist interval.

8. Define sampling of band pass signals.

9. Define Z transform.

10. What are the two types of Z transform?

11. Define unilateral Z transform.

13. What is region of Convergence.

14. What are the Properties of ROC.

15. What is the time shifting property of Z transform.

16. What is the differentiation property in Z domain.

17. State convolution property of Z transform.

18. State the methods to find inverse Z transform.

19. State multiplication property in relation to Z transform.

20. State parseval’s relation for Z transform.

21. What is the relationship between Z transform and fourier transform.

22. What is meant by step response of the DT system.

PART – B

1.State and prove the sampling theorem. Also explain how reconstruction of original signal is done from sampled signal (16)

2. Find the Z – transform of the signal (8) (i)x(n)= nan u(n) (ii)x(n)= an cos(_0) u(n)

3. Determine the inverse z transform of the following function x(z)=1/(1+z-1) (1-z-1 )2 ROC : |Z>1|
4. Explain the properties of z-transform (8)
5. Find the z-transform of x(z)= 1+2z-1 / 1- 2z-1 + z-2 if x(n) is anticausal using long
division method. (8)
6. find the inverse z-transform of x(z)= 1+3z-1 / 1+ 3z-1 + 2z-2 using residue method(8)
7. Give the relationship between z-transform and fourier transform. (8)

UNIT IV DISCRETE TIME SYSTEMS

PART-A (2 Marks)
1. Define Transfer function of the DT system.
2. Define impulse response of a DT system.
3. State the significance of difference equations.
4. Write the differece equation for Discrete time system.
5. Define frequency response of the DT system.
6. What is the condition for stable system.
7. What are the blocks used for block diagram representation.
8. State the significance of block diagram representation.
9. What are the properties of convolution?
10. State theCommutative properties of convolution?
11. State the Associative properties of convolution
12. State Distributive properties of convolution
13. Define causal system.
14. What is the impulse response of the system y(t)=x(t-t0).
15. What is the condition for causality if H(z) is given.
16. What is the condition for stability if H(z) is given.
17. Check whether the system is causal or not ,the H(z) is given by (z3 + z)/(z+1).
18. Check whether the system is stable or not ,the H(z) is given by (z/z-a).,|a|<1.
19. Determine the transfer function for the sys tem described by the difference
equation y(n)- y(n-1) = x(n)- x(n-2).
20. How the discrete time system is represented.

PART – B
1. Give the properties of convolution (6)
2. Determine the step response of the difference equation, y(n)-(1/9)y(n-2)=x(n-1)
with y(-1)=1 and y(-2)=0 (8)
3. Find the impulse response and step response.
Y(n)-3/4y(n-1) +1/8 y(n-2) = x(n) (8)
4. Find the output y(n) of a linear time invariant discrete time system specified by the
equation. (16)
Y(n)-3/2y(n-1) +1/2 y(n-2) = 2x(n) +3/2 x(n-1) when initial conditions are y(-1)
=0,y(-2) = 1 and input x(n)=(1/4)n u(n)
5. Determine the Nyquist sampling rate and Nyquist sampling intervals for
sinc(200_t) + 3sinc2(120_t) (6)
6. Find the frequency response of the following causal system.
Y(n)=1/2x(n)+x(n-1)+1/2 x(n-2) (4)
7. Determine inverse Discrete Time Fourier Transform of
X(k)={1,0,1,0} (8)
8. Give the summary of elementary blocks used to represent discrete (4)
time systems.

UNIT V SYSTEM WITH FINITE AND INFINITE DURATION IMPULSE RESPONSE

PART-A (2 Marks)
1. What is meant by FIR system.
2. What is meant by IIR system.
3. What is recursive system?
4. What is Non recursive system?
5. What is the difference between recursive and non recursive system
6. Define realization structure.
7. What are the different types of structure realization.
8. What is natural response?
9. What is zero input Response?
10. What is forced response?
11. What is complete response?
12. Give the direct form I structure.
13. Give the direct form II structure..
14. How the Cascade realization structure obtained.
15. Give the parallel for Realization structure.
16. What is transformed structure representation?

PART – B
1..a) Determine the transposed structure for the system given by difference equation
y(n)=(1/2)y(n-1)-(1/4)y(n-2)+x(n)+x(n-1) (16)
b) Realize H(s)=s(s+2)/(s+1)(s+3)(s+4) in cascade form
2. A difference equation of a discrete time system is given below:
y(n)-3/4 y(n-1) +1/8 y(n-1) = x(n) +1/2 x(n-1)
draw direct form I and direct form II. (6)
3. Realize the following structure in direct form II and direct form I
H(s) = s+1/s2 + 3s+5 (10)
4. Determine the recursive and nonrecursive system (16)
5. Determine the parallel form realization of the discrete time system is
y(n) -1/4y(n-1) -1/8 y(n-2) = x(n) +3x(n-1)+2x(n-2) (10)

### Signals and systems - Part B – Important Questions

Signals and systems - Part B – Important Questions
UNIT I

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) = t2x(t) & y(n)=2x(n)+ 1 / x(n-1)

3. Explain the classification of signals with examples

4. Determine whether the following systems are Time-Invarient 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(4t-1) is periodic or not.

(b) Evaluate Σ n=( -∞ to ∞) e2n δ (n-2)

(c) Find the fundamental period of the Continuous time signal

UNIT II

1. Find the inverse laplace transform of X(S) = S / S2+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) = eat u(t) + e bt u(t)

UNIT III

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 Z-Transform

3. Determine the Z=Transform of x1(n)=an and x2(n) =nu(n)

4. Find the convolution of x(t) = u(t+1) and h(t) = u(t-2)

5. Find the Fourier transform of x(t) = t cos ωt

UNIT IV

1. Find the Unilateral Z-transform and R.O.C of x(n) = sin ω0 n u(n)

2. Discuss the block diagram representation of an LTI-DT 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.

UNIT V

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 Z-transform

3. Obtain the cascade form realization of the system described by the differential Equation

y(n) – ¼ y (n-1) – 1/8 y (n-2) = x(n) + 3 x(n-1) +2 x(n-2)

4. Find the state variable matrices A,B,C,D for the equation

y(n) - 3y(n-1) - 2y(n-2) = x(n) + 5 x(n-1) + 6 x(n-2)

5. Discuss the block diagram representation of an LTI-DT system

### Signals and systems Important Questions

Signals and systems Important Questions

UNIT I

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) = t2x(t) & y(n)=2x(n)+ 1 / x(n-1)

3. Explain the classification of signals with examples

4. Determine whether the following systems are Time-Invarient 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(4t-1) is periodic or not.

(b) Evaluate Σ n=( -∞ to ∞) e2n δ (n-2)

(c) Find the fundamental period of the Continuous time signal

UNIT II

1. Find the inverse laplace transform of X(S) = S / S2+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) = eat u(t) + e bt u(t)

UNIT III

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 Z-Transform

3. Determine the Z=Transform of x1(n)=an and x2(n) =nu(n)

4. Find the convolution of x(t) = u(t+1) and h(t) = u(t-2)

5. Find the Fourier transform of x(t) = t cos ωt

UNIT IV

1. Find the Unilateral Z-transform and R.O.C of x(n) = sin ω0 n u(n)

2. Discuss the block diagram representation of an LTI-DT 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.

UNIT V

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 Z-transform

3. Obtain the cascade form realization of the system described by the differential Equation

y(n) – ¼ y (n-1) – 1/8 y (n-2) = x(n) + 3 x(n-1) +2 x(n-2)

4. Find the state variable matrices A,B,C,D for the equation

y(n) - 3y(n-1) - 2y(n-2) = x(n) + 5 x(n-1) + 6 x(n-2)

5. Discuss the block diagram representation of an LTI-DT system

### DIGITAL LOGIC CIRCUITS IMPORTANT QUESTIONS FOR MAY/JUNE 2012 ANNA UNIVERSITY EXAMINATIONS

DIGITAL LOGIC CIRCUITS IMPORTANT QUESTIONS FOR MAY/JUNE 2012 ANNA UNIVERSITY EXAMINATIONS

Anna University Examination May/June 2012
Important Questions

Common To

EE46:Digital Logic Circuits
EC1261A Digital Logic Circuits
080280029:Digital Logic Circuits
131405:Digital Logic Circuits
10133EE406A:Digital Logic Circuits

Note: These are only Important questions , These Question May Or May Not be Asked for University Examination

Unit I
1. Obtain the minimum SOP using Quine McCluskey’s method and verify using K – Map.
F = m0 + m2 + m4 + m8 + m9 + m10 + m11+ m12 + m13

2. Determine the prime implicants of the following function using tabulation method and verify using K –Map. F = (A,B,C,D) = ∑ (3,4,5,7,9,13,14,15)
3. Design a Binary to BCD code converter and BCD to Excess -3 code converter.
4. Reduce the given expressions using Boolean algebra:
(1) x’y’z’ + x’y’z + x’yz + xy’z + xyz
(2) p’q’r + p’qr’ + p’qr + pqr’ + pq’r’

Unit II

1. Design a asynchronous decade counter using JK flipflop.
2. Design a 8 X1 Mux using 2 X1 multiplexers.
3. Design a synchronous counter using JK flipflop in the sequence 7,4,3,1,5,0,7….
4. Draw and explain the block diagram of Mealy circuit
5. Design a MOD -5 synchronous counter using JK flip-flops .Draw a timing diagram.
6. Design a 2 bit Magnitude Comparator.
Unit III

1. Describe the steps involved in design of asynchronous sequential circuit in detail with an example.
2. Explain the working of a 3 – input TTL totem-pole NAND gate.
3. Explain the concept and implementation of ECL logic family.
4. Explain In detail about FPGA.
5. A combinational circuit is defined by the functions .
F1 (A,B,C ) =∑ (3,5,6,7)
F2 (A,B,C ) =∑ (0,2,4,7).Implement the circuit with PLA

Unit IV
1. Design an asynchronous sequential circuit that has two inputs X2 and X1 and one output Z. When
X1 = 0, that output Z is 0. The first change in X2 that occurs while X1 is 1 will cause output Z to be 1. The output Z will remain 1 until X1 returns to 0.

2. An asynchronous sequential circuit has two internal states and one output. The excitation and
output functions describing the circuit are
Y1 = x1x2 + x1 y’2 + x’2y1
Y2 = x2 + x1 y’1y2 + x’1y1
Z = x2 + y1

a) Draw the logic diagram of the circuit.
b) Derive the transition table and output map.
c) Obtain a flow table for the circuit.

3. The Circuit has two inputs T (toggle) and C (clock) and one output Q. The output state is complemented if T=1 and clock C changes from 1 to 0 otherwise, under any other input condition, the output Q remains unchanged. Derive the primitive flow table and implication table and the logic diagram.

4. Draw the State diagram and obtain the primitive flow table for a circuit with two inputs X1 and X2 and two outputs Z1 and Z2 that satisfies the following conditions.

1) When X1 X2 =00, output Z1 Z2 =00.
2) When X1 = 1 and X2 change from 0 to 1, the output Z1 Z2 =01.
3) When X2 = 1 and X1 change from 0 to 1, output Z1 Z2 =10.
4) Otherwise output does not change.

5. Implement the following Boolean functions with a PLA.
F1 (A, B, C) = ∑ (0, 1, 2, 4)
F2 (A, B, C) = ∑ (0, 5, 6, 7)
F3 (A, B, C) = ∑ (0, 3, 5, 7)

Unit V

1. Write VHDL program for 4x1 multiplexer.
2. Explain in detail the design procedure for register transfer language.
3. Write an HDL behavioral description of JK flip-flop using if-else statement based on the value of present state.
4. Write VHDL program for 4-bit ripple counter.
5. Explain the design procedure of RTL using VHDL

### Digital Logic Circuits Very Important Questions

Digital Logic Circuits Very Important Questions

IMPORTANT QUESTIONS FROM PART B :

UNIT -1

1. Problem from Quine Mc-Cluskey method (16)

2. Problem from Code converters (16)

3. Design (or) implementation of multiplexer ,de-multiplexer circuits (each 8)

4. Problem from designing the combinational circuits. (16)

5. problem from simplification and implementation of SOP and POS functions using gates (8)

unit -2

1. problems from realisation of SR,D,T,JK flip flops (8)

2. problems from analysis of synchronous sequential circuits (16)

3. problems from design of synchronous sequential circuits using flip flop(16)

4. design of counters (12)

unit -3

1. problems of analysis of asynchronous sequential circuits (16)

2. problems of design of asynchronous sequential circuits (16)

unit-4

1. draw the TTL inverter circuits (12)

2. explain the working of 2 input and 3 input TTL totem pole NAND gate .(16)

3. explain the concept of concept ,operation and characteristics of CMOS family. Draw the circuit of CMOS two input NAND gate and explain its operation (16)

4. draw the circuit of CMOS using NAND and NOR gates (6)

5. write a note on ROM and its type (16)

6. problem from designing a ROM circuits (8)

7. problem from implementing the Boolean function with the PLA (12)

unit -5

1. explain the design procedure of RTL design using VHDL (16)

2. write the note on test benches and its types (8)

3. program using VHDL code can be asked (16)

(example : mod 16, full adder, half adder, counters, multiplexers, de-multiplexer etc.)

Tips :

· be knowledgeable with all gates and flip flop truth tables.

· Especially be knowledgeable in excitation table of all flip flop so that u can attend part A and B question of unit 2 and 3.

· Be knowledgeable in steps of design and analysis of both synchronous and asynchronous sequential circuits... sometimes it can be asked as a 16 mark question.

· Be knowledgeable in Boolean function i.e expression for half adder, full adder, parity generator, code convertor etc.......

## Thursday, 5 March 2015

### Electromagnetic Fields Most Important Questions External Exams

Electromagnetic Fields Most Important Questions External Exams

Unit-1

1. State gauss law for the electric and magnetic fields. Derive its integral and differential forms. Make at least two conclusions

2. A positive charge Qv c/m3 occupies the volume of a sphere. At a point in the interior at a distance of r from the centre, a small probe of charge of +q is inserted. What is the force acting on the probe charge?

3. State ampere’s force law. How it is different from coulombs law?

4. Explain the tracing of a charged particle motion in x-y plane, in the region of crossed electric field B=B0 az.Assume that the charge q having mass m start at t=0 at that point with initial velocity v= vx ax + vyoay.What is the result for B0 = 0?

5. Prove that divergence of a curl of avector is zero,using stokes theorem

6. A magnetic field H= 3 cosx ax+z cosx ay,A/m for z0

= 0 for z<0

is applied to a perfectly conducting surface in xy plane. Find the current density on the conductor surface

7. Let A=5 ax and B= 4 ax+ By. Find by such that, angle between A and B is 45. If B also has a term Bz az, what relationship must exist between by By and Bz

8. A uniform line charge =25 nc/m lies on the line, x=-3m and y=4m, in free space. Find the electric field intensity at a point(2,3,15)m

9. Two small identical conducting sphere have charges of 2nc and -1nc respectively. When they are separated by 4cm apart, find the magnitude of the force between them. If they are brought into contacts and then again separated by 4cm, find the force between them

10. Obtain the expressions for D and E using gauss’s law

Unit-2

1. Derive the expression for coefficient of coupling in terms of mutual and self inductances

2. An iron ring with a cross sectioned of 3 cm2 and a mean circumference of 15 cm is wound with 250 turns wire carrying a current of 0.3A. The relative permeability of the ring is 1500. Calculate the flux established in the ring

3. Obtain the expressions for D and E using Gauss’s law

4. Write short notes on faradays laws of electromagnetic induction

5. Derive the electrostatic boundary conditions at the interface of two dielectric media. If one of the medium is conductor, discuss the field pattern

6. Discuss electric field in free space, dielectric and in conductors

7. Derive the expression for curl H=J

8. Explain the concepts of scalar magnetic potential and vector magnetic potential

Unit-3

1. Using the concept of magnetic vector potential, derive Biot Savart’s law and amperes law

2. Find the magnetic flux density at the centre of a square of sides equal to 5 cm and carrying 10A of current

3. List the properties of dielectric materials

4. Derive the expression for coefficient of coupling in terms of mutual and self inductances

5. Derive the expression for the capacitance of a parallel plate capacitor with two dielectric media

6. Derive an expression for inductance of a solenoid with N turns and l meter length carrying a current of I amperes

7. Explain in detail the principle of operation of a motor

8. Derive H due to a circular current loop and extend the same to compute H due to a long solenoid?

9. Derive the boundary relation at the boundary between a conductor and dielectric

Unit-4

1. Derive general field relations for time varying electric and magnetic fields using Maxwell’s equation

2. On the basis of the analysis of the transmission line compare circuit theory and field theory

3. With necessary explanation, derive the Maxwell’s equation in differential and integral forms

4. What do you mean by displacement current? Write down the expression for the total current density

5. Derive the expression for total power flow in coaxial cable

6. Derive Maxwell’s equations derived from amperes law in integral and point forms

7. Explain briefly about the motional emf and derive an expression for it

8. Discuss the pointing sector and pointing theorem

9. Define faradays laws. What are the different ways of emf generation? Explain with governing equation and suitable example for each

Unit-5

1. Derive wave equations in phasor form and also derive for

2. Explain about the propagation of EM waves in good conductor

3. Derive the transmission and reflection coefficients for the electromagnetic waves. Discuss the above for an open line and a short circuited line

4. Derive the electromagnetic wave equations

5. State pointing vector and establish its usage in EM wave analysis

6. Discuss the wave motion in good conductors

7. Explain the reflection of plane waves by a perfect dielectric

8. Derive the expression for input impedance and standing wave ratio of transmission lines

9. Define Brewster angle and derive its expression

10. Derive the relationship between electric and magnetic fields

### Fluid Mechanics & Machineries Very Important Questions

Fluid Mechanics & Machineries Very Important Questions

Fluid Mechanics & Machineries :
Module –I (Introduction) :
1. Define fluid? :
A fluid is a substance having a property to flow easily.

Example : liquid, vapour, gas.

2. Define fluid mechanics? :
Fluid mechanics is a branch of science which deals with property and behaviour of fluids at rest and in motion.

3.Define fluid statics? :
The study of fluids at rest is called fluid statics .

4.Define fluid kinematics? :
The study of fluids in motion where pressure forces are not considered is called fluid kinematics.

5.What is the SI unit of density ? :
The SI unit of density is kg/m3.

Example : Density of water is 1000 kg/m3.

6.Define specific volume? :
It is the ratio of volume to the mass of a fluid. It is denoted by .Its unit is m3/kg.
= volume of fluid/Mass of fluid
=V/m m3/kg

7. Define specific gravity with respect to density? :
It is the ratio of density of a fluid to density of a standard fluid. It is denoted by s.

i.e, s = density of liquid/density of water
s = density of gas/density of air

8.Define viscosity? :
It is defined as the resisting property of liquid to its flow corresponding to its adjacent layers.

9. Which one of the following has high viscosity, (i) water or (ii) lubricating oil? :
Lubricating oil has high viscosity.

10. Define poise ? :
Poise is the other name of unit of viscosity in CGS system which equals dyne-sec/cm2.

11.Give the classification of fluids? :
Classification of fluids are,
(i) Ideal fluid
(ii) Real fluid
(iii) Newtonian fluid
(iv) Non Newtonian fluid
(v) Ideal plastic fluid.

12. What is real fluid? :
A fluid which has viscosity is a real fluid. All fluid in practice are real fluids.

13.What is non Newtonian fluid? :
A real fluid in which shear stress is not proportional to rate of shear strain.

14.What is compressibility? :
Compressibility is the property of fluid which undergoes change in volume under various pressure conditions.

15. Define compressible fluid? :
A liquid is considered to a compressible fluid only when there is a change in volume of liquid that occurs under large pressure variation .

16. Define compressibility? :
It is also defined of reciprocal of bulk modulus of elasticity (k).

i.e,
compressibility = 1/k .
k= compressive stress / volumetric strain

17.Define capillarity? :
It is the phenomenon of rise or fall of liquid surface relative to out side liquid surface

18.Give the types of gas laws? :
The types of gas laws are,
(i) Boyles law
(ii) Charles law

19. Give some properties of fluid? :
Some properties of fluids are density, specific weight, viscosity, surface tension and capillarity

20. Define fluid dynamics? :
The study of fluid in motion where pressure forces are considered is called as fluid dynamics.

### Fluid Mechanics & Machineries Very Important Questions

Fluid Mechanics & Machineries Very Important Questions

Unit – 1
Explain the terms :
(i) dynamic viscosity (ii) Kinematic Viscosity. Give their dimensions
A 15cm diameter vertical cylinder rotates concentrically inside
What is the difference between U-tube differential manometers
Where are they used-
What are the gauge pressure and absolute pressure

Unit – 2
Obtain an expression for continuity equation for a three-dimensional
The velocity potential function is given by F = 5(x2 – y2 )
calculate the velocity components at the point (4,5)
A stream function is given by – = 5x-6y.
Calculate the velocity components and also magnitude

Unit – 3
From the principle of Euler’s equation of motion derive Bernoulli’s
Water if flowing upto a pipe of 5 cm diameter
Find the total head or total energy per unit weight of the water
What is a minor energy loss (head losses)-
Derive an expression for determining loss of head due to sudden
At a sudden enlargement of a water main from 240 mm to 480 mm
diameter the hydraulic gradient rises by 10mm. Estimate the rate of flow.

Unit – 4
What are the methods of preventing the separation of boundary layer-
Oil with a free stream velocity of 2 m/s flows over a thin plate 2 m
Calculate the boundary layer thickness and the shear stress a
determine the total surface resistance of the plate.
What is the relation between pressure and density of a compressive
i. Isothermal process and ii. Adiabatic process.a
A gas with a velocity of 300 m/sec is flowing through a horizontal pipe
Define Mach number.
What is the significance of Mach number in compressible fluid flows-
Find the sonic velocity for the following fluids :
i. Crude oil of specific gravity 0.8 bulk modulus 153036 N/cm2.
ii. Mercury having a bulk modulus of 2648700N/cm2.

### Fluid Mechanics and Hydraulic Machines Very Important Questions

Fluid Mechanics and Hydraulic Machines Very Important Questions

Fluid Mechanics And Hydraulic Machines is a very important topic of Engineering comes under the Mechanical and Civil streams.This section will provide you with the Important questions which are asked in exams under the Fluid Mechanics and Hydraulic Machines with the combination of all objective type questions, subjective type questions and a section with numerical problems.

Hydraulic machine

What is a fluid?
Three common states of matter are solid, liquid, and gas.
What is mechanics?
The dictionary says mechanics is the application of the laws of force and motion.There are two branches, statics and dynamics.

So, putting it all together, fluid mechanics is the application of the laws of force and motion to fluids i.e. liquids and gases.

Questions with their Answers on Fluid Mechanics And Hydraulic Machines

1. A fluid is a substance that
(a) Always expands until it fills any container
(b) Has the same shear stress at a point
regardless of its motion
(c) Cannot remain at rest under action of any
shear force
(d) Cannot be subjected to shear forces

2. Length of mercury column at a place at analtitude will vary with respect to that at ground in a

(a) Linear relation
(b) hyperbolic relation
(c) Parabolic relation.
(d) Manner first slowly and then steeply

3. When power is transmitted through a considerable distance by means of water under
pressure, the maximum power is transmitted when frictional loss of head is
(a) One third of the total head supplied
(b) Half of the total head supplied
(c) 10% of the total head
(d) 17.7% 0f the total head.

4. A rotameter is a device used to measure
(a) Velocity of fluid in pipes
(b) Velocity of gauges
(c) Votex flow
(d) Flow of fluids

5. The continuity equation
(a) Expresses relationship between hydraulic
parameters of flow
(b) Expresses the relationship, between work and
energy
(c) Is based on Bernoulli’s theorem
(d) Relates the mass rate of flow along a stream
line.

6. Of the following, dimensionless parameter is
(a) Pressure coefficient
(b) Froude number
(c) Darcy Weisbach friction factor
(d) All of the above

7. One dimensional flow
(a) Restricted to flow in a straight line
(b) Neglects changes in a transverse direction
(d) A uniform flow

(a) Pressure does not change along the flow
(b) Velocity does not change
(c) Conditions change gradually with time
(d) Conditions do not change with time at any point.

9. Equation Continuity of fluids is applicable only when the flow is
(b) One dimensional
(c) Compressive
(d) All of the above

10. If the particles of a fluid attain such velocities that vary from point to point in magnitude and
direction as well as from instant, the flow is
(a) Uniform flow
(c) Turbulent flow
(d) Laminar flow

Short Type Questions On Fluid Mechanics & Hydraulic Machines

1. Why the Centrifugal Pump is called High Discharge pump?

Centrifugal Pump

Ans. Centrifugal pump is a kinetic device. The centrifugal pump uses the centrifugal force to push out the fluid. So the liquid entering the pump receives kinetic energy from the rotating impeller. The centrifugal action of the impeller accelerates the liquid to a high velocity, transferring

mechanical (rotational) energy to the liquid. So it discharges the liquid in high rate. It is given in the following formulae:

Centrifugal force F= (M*V2)/R.

Where,

M-Mass

V-Velocity

2. How Cavitation can be eliminated by Pump?

Ans. Cavitation means bubbles are forming in the liquid.To avoid Cavitation, we have to increase the Pump size to One or Two Inch;To increase the pressure of the Suction Head, or Decrease the Pump Speed.

3. Why Cavitation will occur in Centrifugal Pump and not in Displacement Pump?

Ans. The formation of cavities (or bubbles) is induced by flow separation, or non-uniform flow velocities, inside a pump casing. In centrifugal pumps the eye of the pump impeller is smaller than the flow area of pipe. This decrease in flow area of pump results in increase in flow rate. So pressure drop happened between pump suction and the vanes of the impeller. Here air bubbles or cavities are formed because of liquid vapour due to increase in temperature in impeller. This air bubbles are transmitted to pump which forms cavitation.

4. Which Pump is more Efficient Centrifugal Pump or Reciprocating Pump?

Ans. Centrifugal pump. Because flow rate is higher compared to reciprocating pump. Flow is smooth and it requires less space to install. Lower initial cost and lower maintenance cost.

Centrifugal Pump

5. Why Centrifugal Pump is not called as a Positive Displacement Type of Pump?

Ans. The centrifugal has varying flow depending on pressure or head, whereas the Positive Displacement pump has more or less constant flow regardless of pressure.

Likewise viscosity is constant for positive displacement pump where centrifugal pump have up and down value because the higher viscosity liquids fill the clearances of the pump causing a higher volumetric efficiency. When there is a viscosity change in supply there is also greater loss in the system. This means change in pump flow affected by the pressure change.

One more example is, positive displacement pump has more or less constant efficiency, where centrifugal pump has varying efficiency rate

Long Type Questions On Fluid Mechanics & Hydraulic Machines

Problem 1

Consider a fluid (of density ρ) in incompressible, laminar flow in a plane narrow slit of length L and width W formed by two flat parallel walls that are a distance 2B apart. End effects may be neglected because B << W << L. The fluid flows under the influence of both a pressure difference Δp and gravity.

Fig 1

Figure.

Fluid flow in plane narrow slit.a) Using a differential shell momentum balance, determine expressions for the steady-state shear stress distribution and the velocity profile for a Newtonian fluid (of viscosity μ).

b) Obtain expressions for the maximum velocity, average velocity and the mass flow rate for slit flow.

(a) For a plane narrow slit, the natural choice is rectangular Cartesian coordinates. Since the fluid flow is in the z-direction, vx = 0,vy = 0, and only vz exists. Further, vz is independent of z and it is meaningful to postulate that velocity vz = vz(x) and pressure p= p(z). The only nonvanishing components of the stress tensor are τxz = τzx, which depend only on x.

Consider now a thin rectangular slab (shell) perpendicular to the x-direction extending a distance W in the y-direction and a distance L in the z-direction. A ‘rate of z-momentum’ balance over this thin shell of thickness Δx in the fluid is of the form:

Rate of z-momentum In − Out + Generation = AccumulationAt steady-state, the accumulation term is zero. Momentum can go ‘in’ and ‘out’ of the shell by both the convective and molecular mechanisms. Since vz(x) is the same at both ends of the slit, the convective terms cancel out because (ρ vz vz WΔx)|z = 0 = (ρ vz vz W Δx)|z = L. Only the molecular term (L W τxz ) remains to be considered. Generation of z-momentum occurs by the pressure force (p W Δx) and gravity force (ρ g W L Δx). On substituting these contributions into the z-momentum balance, we get

(L W τxz ) | x − (L W τxz ) | x+Δx+ ( p 0 − p L ) W Δx + ρ g W L Δx = 0

Dividing the above equation by L W Δx yields

( τxz | x+Δx- τxz | x ) / Δx = ( p 0 − p L + ρ g L) /L (2)

On taking the limit as Δx → 0, the left-hand side of the above equation is the definition of the derivative. The right-hand side may be compactly and conveniently written by introducing the modified pressure P, which is the sum of the pressure and gravitational terms. The general definition of the modified pressure is P = p + ρ g h , where h is the distance upward (in the direction opposed to gravity) from a reference plane of choice. Since the z-axis points downward in this problem, h = − z and therefore P = p − ρ g z . Thus, P0 = p0 at z = 0 and PL = pL − ρ g L at z = L giving p0 − pL + ρ g L = P0 − PL ≡ ΔP. Thus, equation (2) gives

(dτxz ) /dx=( ΔP)/L (3)

Equation (3) on integration leads to the following expression for the shear stress distribution:

τxz = X(ΔP)/L+ C1 (4)

The constant of integration C1 is determined later using boundary conditions.

It is worth noting that equations (3) and (4) apply to both Newtonian and non-Newtonian fluids, and provide starting points for many fluid flow problems in rectangular Cartesian coordinates.

Substituting Newton’s law of viscosity for τxz in equation (4) gives

− μ(dvz)/dx =x(ΔP)/L+ C1 (5)

The above first-order differential equation is simply integrated to obtain the following velocity profile: vz =x2(ΔP)/2 μ L–x( C1)/ μ+ C2 (6)

The no-slip boundary conditions at the two fixed walls are BC 1: at x = B, vz = 0 (7)

BC 2: at x = −B, vz = 0 (8)

Using these, the integration constants may be evaluated as C1 = 0 and C2 = ΔP B2 / (2 μ L). On substituting C1 = 0 in equation (4), the final expression for the shear stress (or momentum flux) distribution is found to be linear as given by

τxz =x( ΔP)/L (9)

Further, substitution of the integration constants into equation (6) gives the final expression for the velocity profile as

vz= (ΔP B 2)/( 2 μ L)(1-((x)/B)2 ) (10)

It is observed that the velocity distribution for laminar, incompressible flow of a Newtonian fluid in a plane narrow slit is parabolic.

b) From the velocity profile, various useful quantities may be derived.

(i) The maximum velocity occurs at x = 0 (where dvz/dx = 0). Therefore,

vz,max= vz, | x = 0 =( ΔP B2)/ 2 μ L (11)

(ii) The average velocity is obtained by dividing the volumetric flow rate by the cross-sectional area as shown below.

vz,avg = ( − B∫ B vz W dx)/( B∫ B W dx )=(1/2B) -B∫ B vz dx=( ΔP B2)/( 3 μ L)=2/3 vz,max (12)

Thus, the ratio of the average velocity to the maximum velocity for Newtonian fluid flow in a narrow slit is 2/3.

(iii) The mass rate of flow is obtained by integrating the velocity profile over the cross section of the slit as follows.

W= B∫ B ρ vz W dx = ρ W (2 B) vz,avg (13)

Thus, the mass flow rate is the product of the density ρ, the cross-sectional area (2 B W) and the average velocity vz,avg. On substituting vz,avg from equation (12), the final expression for the mass rate of flow is

w =(2 ΔP B3 W ρ)/ 3 μ L (14)

The flow rate vs. pressure drop (w vs. ΔP) expression above is the slit analog of the Hagen-Poiseuille equation (originally for circular tubes). It is a result worth noting because it provides the starting point for creeping flow in many systems (e.g., radial flow between two parallel circular disks; and flow between two stationary concentric spheres).

Finally, it may be noted that the above analysis is valid when B << W. If the slit thickness B is of the same order of magnitude as the slit width W, then vz = vz (x, y), i.e., vz is not a function of only x. If W = 2B, then a solution can be obtained for flow in a square duct.

PROBLEM 2

Consider a Newtonian liquid (of viscosity μ and density ρ) in laminar flow down an inclined flat plate of length L and width W. The liquid flows as a falling film with negligible rippling under the influence of gravity. End effects may be neglected because Land W are large compared to the film thickness δ.

Fig 2

Figure. Newtonian liquid flow in a falling film.a) Determine the steady-state velocity distribution.

b) Obtain the mass rate of flow and average velocity in the falling film.

c) What is the force exerted by the liquid on the plate in the flow direction?

d) Derive the velocity distribution and average velocity for the case where x is replaced by a coordinate x‘ measured away from the plate (i.e., x‘ = 0 at the plate and x‘ = δ at the liquid-gas interface).

Ans (a)

For axial flow in rectangular Cartesian coordinates, the differential equation for the momentum flux is

(dτxz)/( dx)=( ΔP)/(L) (1)

where P is a modified pressure, which is the sum of both the pressure and gravity terms, that is, ΔP = Δp + ρ g L cos β. Here,β is the angle of inclination of the z-axis with the vertical. Since the flow is solely under the influence of gravity, Δp = 0 and therefore ΔP/L = ρ g cos β. On integration,

τxz = ρ g x cos β + C1 (2)

On using the boundary condition at the liquid-gas interface (τxz = 0 at x = 0), the constant of integration C1 is found to be zero. This gives the expression for the shear stress τxz for laminar flow in a falling film as

τxz = ρ g x cos β (3)

It must be noted that the above momentum flux expression holds for both Newtonian and non-Newtonian fluids (and does not depend on the type of fluid).

The shear stress for a Newtonian fluid (as per Newton’s law of viscosity) is given by

(τxz)/( dx)=- μdvz (4)

To obtain the velocity distribution, there are two possible approaches.

In the first approach, equations (3) and (4) are combined to eliminate τxz and get a first-order differential equation for the velocity as given below.

(dvz)(dx)=-(( ρ g cos β)/( μ ))(x) (5)

On integrating, vz = − ρ g x2 cos β/(2μ) + C2. On using the no-slip boundary condition at the solid surface (vz = 0 at x = δ ), C2= ρ g δ2 cos β/(2μ). Thus, the final expression for the velocity distribution is parabolic as given below.