Power Plant Engin EE ring
R. K. Hegde Professor
Department of Mechanical Engineering
Srinivas Institute of Technology
Mangalore, Karnataka, India
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Dedicated to my father, N. R. Hegde, a humble teacher, who during his life time strived very hard to cherish the dreams of budding young kids and helped them to grow as responsible citizens.
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Preface xxiii
About the Author xxv
1. Introduction to Power Plants
1.1 Introduction to the sources of energy: conventional and non-conventional principle of power generation—1
1.1.1 Conventional energy sources—2
1.1.2 Non-conventional energy sources—5
1.2 Factors affecting selection of site—14
1.2.1 The factors to be considered for site selection of steam power plants—14
1.2.2 Factors affecting selection of site for hydro-electric power plant—16
1.2.3 Factors affecting selection of site for a nuclear power plant—18
1.3 Principal types of power plants—18
1.4 Present status and future trends—19
1.5 Layout of steam, hydel, diesel, nuclear and gas turbine power plants—20
1.5.1 Layout of steam turbine plant—20
1.5.2 Layout of hydro-electric plant—22
1.5.3 Plant layout of diesel engine plant—23
1.5.4 Layout of a nuclear plant—23
1.5.5 Layout of gas turbine plant—24
1.6 Combined power cycles – comparison and selection—25
1.7 Merits of steam, gas, diesel, hydro and nuclear power plants—26
1.7.1 Advantages and disadvantages of the gas turbine plant—26
1.7.2 Advantages and disadvantages of the nuclear plant—30
1.7.3 Advantages and disadvantages of diesel plants—30
1.7.4 Advantages of hydro-electric power plants—32
1.8 Resources and development of power in India—33
1.8.1 Coal and lignite—33
1.9 Petroleum and natural gas—34
1.10 Present status of power generation in India—38
1.11 Role of private and government organization—39
1.12 State-level scenario, load shedding—41
1.13 Carbon credits—42
1.14 Questions—44
1.14.1 Objective questions—44
1.14.2 Review questions—45
1.14.3 References—45
2. Fuels and Combustion
2.1 Introduction—46
2.2 Classification of fuels and different types of fuels used for steam generation—46
2.2.1 Solid fuels—47
2.2.2 Liquid fuels—49
2.2.3 Gaseous fuels—50
2.2.4 Nuclear fuels—51
2.3 Calorific values of fuels—52
2.3.1 Higher calorific value and lower calorific value of fuels—52
2.3.2 Experimental procedure for determining Cv of fuels—54
2.4 Combustion of fuels—60
2.4.1 Minimum air required per kilogram of liquid fuel for complete combustion—61
2.4.2 Minimum air required per cubic metre of gaseous fuel for complete combustion—62
2.4.3 Combustion equation for a hydrocarbon fuel—63
2.4.4 Flue gas analysis—64
2.4.5 Conversion of gravimetric analysis to volumetric analysis and vice versa—65
2.4.6 Mass of air supplied per kilogram of fuel—66
2.4.7 Carbon burnt to CO2 and CO—69
2.4.8 Excess air supplied—70
2.5 Properties of coal, Indian coals—86
2.5.1 Analysis of coal—87
2.5.2 Indian coals—89
2.6 Selection of coal in thermal power station—90
2.6.1 Geological resources of coal in India—91
2.6.2 Status of coal resources in India during the past five years—92
2.7 Questions—93
2.7.1 Objective questions—93
2.7.2 Review questions—94
3. Fuel-Handling Systems 96
3.1 Coal handling—96
3.1.1 Outplant handling of coal—96
3.1.2 Storage of coal—97
3.1.3 Inplant handling of coal—97
3.1.4 Inplant handling system—98
3.1.5 Stages of coal handling—99
3.2 Choice of handling equipment—100
3.3 Fuel burning—103
3.3.1 Overfeed and underfeed fuel bed stokers—103
3.4 Equipment for burning coal in lump form—106
3.4.1 Chain grate stoker—107
3.4.2 Travelling grate stoker—107
3.4.3 Spreader stoker—108
3.4.4 Retort stoker—110
3.5 Advantages and disadvantages of stoker firing over pulverized system of firing—112
3.6 Preparation and burning of pulverized coal—113
3.6.1 Unit or direct system—113
3.6.2 Bin or central system—113
3.6.3 Advantages and disadvantages of pulverized coal burning—114
3.7 Pulverized fuel furnaces (burners)—116
3.8 Pulverized mills—116
3.8.1 Causes for mill fires—121
3.9 Fuel-burning equipments—122
3.9.1 Coal burners—122
3.9.2 Oil burners—125
3.9.3 Gas burners—126
3.10 Flue gas analysis—126
3.10.1 Procedure—126
3.11 Ash handling system—128
3.11.1 Advantages and disadvantages of wet and dry ash-handling systems—132
3.12 Dust collection—132
3.12.1 Mechanical dust collectors—133
3.12.2 Electrical dust collector (electrostatic precipitators)—135
3.12.3 Soot blowers—137
3.13 Questions—139
3.13.1 Objective questions—139
3.13.2 Review questions—140
4. Steam Power Plant 141
4.1 Introduction—141
4.2 General layout of modern thermal power plant—142
4.3 Rankine and modified rankine cycles—147
4.3.1 Carnot cycle—147
4.3.2 Rankine cycle—148
4.3.3 Modified rankine cycle—159
4.3.4 Reheat cycle—160
4.3.5 Regenerative cycle—167
4.4 Working of different circuits—176
4.5 Selection of site for steam power plants—178
4.6 Questions—180
4.6.1 Objective questions—180
4.6.2 Review questions—182
5. Steam Generator 183
5.1 Fossil fuel steam generators—183
5.2 Classification of boilers—183
5.2.1 Fire tube boilers and water tube boilers—183
5.2.2 Stationary and mobile boilers—185
5.2.3 Internally fired and externally fired boilers—185
5.2.4 Horizontal, vertical and inclined tube boilers—185
5.2.5 Based on heat sources—185
5.2.6 Natural circulation and forced circulation boilers—185
5.2.7 Comparison of water tube boilers and fire tube boilers—186
5.3 Circulation in water tube boilers—187
5.4 Modern high-pressure water tube boilers—187
5.4.1 Generation of steam using forced circulation, high and supercritical pressures—188
5.4.2 A brief account of modern steam generators—190
5.5 Boiler performance calculations—196
5.5.1 Turbine efficiency—197
5.5.2 Rankine cycle efficiency (hc )—198
5.5.3 Generator efficiency (hg )—198
5.5.4 Overall turbo-alternator efficiency (hota )—198
5.5.5 Heat rate—199
5.5.6 Boiler performance—199
5.6 Accessories for the steam generator—200
5.6.1 Superheaters arrangement—202
5.6.2 Control of superheaters—203
5.6.3 Reheaters—207
5.6.4 Economizers—208
5.6.5 Air preheaters—210
5.7 Boiler mountings—212
5.7.1 Water-level indicator—212
5.7.2 Pressure gauge—213
5.7.3 Steam stop valve or junction valve—213
5.7.4 Feed check valve—213
5.7.5 Blow-down valve or blow-off-cock—214
5.7.6 Fusible plug—215
5.7.7 Safety valves—215
5.8 Questions—216
5.8.1 Objective questions—216
5.8.2 Review questions—220
6. Fluidized Bed Combustion 221
6.1 Introduction to fluidized bed combustion—221
6.2 Regimes of combustion—221
6.3 Fluidized bed boilers – classification—223
6.3.1 Atmospheric FBC system or bubbling FBC—223
6.3.2 Circulating FBC—226
6.3.3 Pressurized FBC system—227
6.4 Advantages of FBC system—228
6.5 Control of oxides of nitrogen—228
6.6 Desulphurization technology—229
6.7 Questions—229
6.7.1 Objective questions—229
6.7.2 Review questions—230
6.7.3 References—231
7. Draught System 232
7.1 Introduction to draught system—232
7.2 Air and supply systems (natural mechanical draught systems)—232
7.3 Chimneys—235
7.4 Calculations involving height of chimney to produce a given draught—236
7.4.1 Chimney height and diameter—237
7.4.2 Condition for maximum discharge through a chimney—239
7.4.3 Chimney efficiency—242
7.5 Questions—247
7.5.1 Objective questions—247
7.5.2 Review questions—247
8. Feed Water Treatment 249
8.1 Feed water system – necessity—249
8.1.1 Feed water impurities—249
8.2 Feed water treatment—250
8.2.1 Mechanical methods—251
8.2.2 Thermal methods—252
8.2.3 Chemical methods—253
8.3 Questions—256
8.3.1 Objective questions—256
8.3.2 Review questions—257
9. Flow Through Nozzles 258
9.1 Introduction—258
9.2 Types of steam nozzles—258
9.3 Flow of steam through nozzle—259
9.4 Discharge through nozzle and critical pressure ratio—261
9.5 Effect of friction and nozzle efficiency—265
9.6 Supersaturated flow—266
9.7 Relation between area, velocity and pressure in nozzle flow—267
9.8 Characteristics of converging–diverging nozzle—270
9.9 Steam injector—272
9.10 Questions—276
9.10.1 Objective questions—276
9.10.2 Review questions—280
10. Steam Turbines 281
10.1 Introduction to steam turbines—281
10.2 Turbine types—281
10.2.1 Impulse turbine working principle—281
10.2.2 Reaction turbine—282
10.3 Simple impulse turbines—283
10.3.1 Flow through turbine blades and velocity diagram—283
10.3.2 Compounding of steam turbines—283
10.3.3 Impulse turbine power and related calculations—287
10.3.4 Multistage impulse turbine—291
10.4 Reaction turbines—293
10.4.1 Flow through blades and velocity diagram—293
10.4.2 Degree of reaction—294
10.4.3 Parson’s reaction turbine—296
10.4.4 Power and related calculations—297
10.4.5 Blade height calculations—302
10.4.6 Bleeding in steam turbines—315
10.5 Losses in steam turbines—316
10.6 Reheat factor and condition line—317
10.6.1 Stage efficiency per stage—317
10.6.2 Reheat factor—318
10.6.3 Internal turbine efficiency—318
10.7 Governing of turbines—318
10.8 Questions—321
10.8.1 Objective questions—321
10.8.2 Review questions—326
11. Steam Condenser and Circulating Water Systems 328
11.1 Introduction to condenser and its necessity—328
11.1.1 Function of a condenser—329
11.1.2 Elements of a condensing plant—329
11.2 Classification and types of condensers—330
11.2.1 Direct-contact condensers—330
11.2.2 Surface condensers—333
11.2.3 Evaporative condenser—335
11.3 Surface condenser performance—336
11.3.3 vacuum and vacuum efficiency—336
11.4 Cooling tower—341
11.4.1 Types—342
11.4.2 Principle of operation and performance—343
11.4.3 Location of cooling tower—348
11.5 Cooling ponds—349
11.5.1 Cooling pond—349
11.5.2 Types of cooling ponds—350
11.6 Corrosion in condensers and boilers—352
11.7 Corrosion in boilers—352
11.7.1 Acidic corrosion—352
11.7.2 Galvanic corrosion—353
11.7.3 Steam blanketing—353
11.7.4 Oxygen attack—353
11.7.5 Carbon dioxide attack—354
11.8 Questions—354
11.8.1 Objective questions—354
11.8.2 Review questions—356
12. Gas Turbine Power Plant
12.1 Introduction—358
12.1.1 Joule or brayton cycle—359
12.2 Classification of gas turbines—371
12.2.1 Principle of working of open- and closed-cycle gas turbines—371
12.2.2 Comparison of open and closed-cycle turbines—374
12.3 Construction and plant layout with auxiliaries—375
12.3.1 Components of a gas turbine—375
12.3.2 Centrifugal compressor—376
12.3.3 Main parts of a centrifugal compressor—377
12.3.4 Impeller and diffuser—377
12.3.5 Diffuser—379
12.3.6 Axial centrifugal compressor—380
358
12.3.7 Stage velocity triangles—382
12.3.8 Work input to compressor—382
12.3.9 Work done factor—383
12.3.10 Degree of reaction—383
12.4 Fuel and fuel systems—384
12.4.1 Natural gas—385
12.4.2 Liquefied natural gas—385
12.4.3 Liquid fuels—385
12.5 Gas turbine material—386
12.6 Advantages and disadvantages of the gas turbine plant—388
12.6.1 Advantages and disadvantages of gas turbine plant—390
12.7 Method of improving output and performance—391
12.7.1 Reheating—391
12.7.2 Regeneration—393
12.7.3 Intercooling—396
12.8 Free-piston engine plant – limitation, application and advantages—414
12.9 Combined cycle power plants and comparison—418
12.9.1 Combined cycle principles of operation—418
12.9.2 Coupled cycle – GT–ST plant operation—419
12.9.3 Thermodynamic analysis of a simple combined cycle GT – ST plant—423
12.10 Layout of gas turbine plant—426
12.11 Questions—426
12.11.1 Objective questions —426
12.11.2 Review questions—428
12.11.3 References—429
13. Diesel Engine Power Plant
13.1 Introduction to diesel engine plant—430
13.1.1 IC engine nomenclature—430
13.1.2 Standard terminology—432
13.1.3 Four-stroke diesel engine—433
13.1.4 Two-stroke diesel engine—435
13.2 Types of diesel plants and components—436
13.3 Selection of engine type and engine size—437
13.4 Plant layout with auxiliaries—438
13.5 Fuel supply system—439
13.5.1 Fuel injection system—442
13.5.2 Types of fuel injection systems—443
430
13.6 Super charging—445
13.7 Method of starting diesel engines—446
13.8 Cooling and lubrication system for the diesel engine—449
13.8.1 Engine cooling system—449
13.8.2 Lubrication system—451
13.8.3 Filters, centrifuges and oil heaters—454
13.9 Intake and exhaust systems—456
13.9.1 Intake system—456
13.9.2 Exhaust system—457
13.10 Application of diesel power plant, advantages and disadvantages—458
13.10.1 Comparison with stream power plants—460
13.11 Layout of diesel plant—460
13.12 Diesel engine performance and operation—462
13.13 Questions—485
13.13.1 Review questions—485
14. Power from Non-Conventional Sources 487
14.1 Recent developments in methods of power generation—487
14.1.1 Conventional energy sources—487
14.1.2 Non-conventional energy sources—489
14.2 Utilization of solar energy—493
14.2.1 Solar radiation—493
14.2.2 Solar radiation at earth’s surface—494
14.2.3 Basic definitions of solar angles—495
14.2.4 Solar constant and intensity of solar radiation—499
14.2.5 Average solar radiation or monthly average daily global radiation—500
14.2.6 Solar radiation on tilted surfaces—504
14.2.7 Solar energy collectors—507
14.2.8 Photovoltaic power system—512
14.2.9 Solar central receiver system—515
14.3 Wind energy—518
14.3.1 Generation of wind energy—519
14.3.2 Wind turbine operation—521
14.3.3 Components of a wind generator—522
14.3.4 velocity and power from wind—525
14.3.5 Wind turbine operation—532
14.3.6 Horizontal and vertical axis (HAWT, vAWT) wind mills—533
14.3.7 Aerodynamic considerations of wind mill design—540
14.3.8 Coefficient of performance of wind mill rotor—545
14.3.9 Availability of wind energy in India—547
14.3.10 Wind power by country—549
14.4 Tidal energy—551
14.4.1 The simple single pool tidal system—552
14.4.2 The modulated single pool tidal system—555
14.4.3 The two-pool tidal system—555
14.5 Ocean thermal energy conversion—556
14.5.1 Principle of working—556
14.5.2 Ocean temperature differences—556
14.5.3 The open or claude cycle—557
14.5.4 The closed or anderson OTEC cycle—559
14.6 Wave energy—560
14.6.1 Energy and power from waves—560
14.6.2 Wave energy conversion by floats—562
14.6.3 High-pressure accumulator wave machines—563
14.7 Fuel cells—564
14.7.1 Working principle—564
14.7.2 Types of fuel cells—566
14.8 Thermoelectric and thermionic power—570
14.8.1 Thermoelectric power—570
14.8.2 Thermionic converter—572
14.9 MhD generation—573
14.10 Geothermal energy—574
14.10.1 A typical geothermal field—574
14.10.2 Hydrothermal systems—574
14.10.3 Petro thermal systems—578
14.10.4 Hybrid geothermal fossil systems—579
14.10.5 Problems associated with geothermal conversion—581
14.11 Electricity from city refuge—581
14.12 Questions—583
14.12.1 Objective questions—583
14.12.2 Review questions—586
15. Hydroelectric Power Plant 588
15.1 Introduction to water power—588
15.2 hydrological cycle—589
15.3 Rainfall and its measurement—590
15.3.1 Intensity of rainfall—591
15.3.2 Measurement of rainfall—592
15.3.3 Location of rain gauge—593
15.3.4 Average or mean depth of rainfall—593
15.3.5 Run-off and its measurement—597
15.4 h ydrographs—601
15.4.1 The unit hydrograph—603
15.5 Flow duration and mass duration curves—605
15.5.1 Flow duration curve—605
15.5.2 Mass curve and storage—609
15.6 h ydro electric plant – introduction—654
15.6.1 Site selection for hydel power plants—656
15.6.2 General arrangement of hydroelectric power plant—657
15.6.3 Plant layout—659
15.6.4 Penstock and water hammer—659
15.6.5 Specific speed and capacity calculations—660
15.7 Classification of hydro-plant—663
15.7.1 Low-, medium- and high-head plants—663
15.7.2 Pumped storage plant—665
15.7.3 Run-off river power plant—666
15.8 Surge tanks—666
15.9 Control gates and valves—667
15.9.1 Control gates—667
15.9.2 Interior gate valves—670
15.10 Classification of dams and spillways—671
15.11 Brief description of some of the important hydel installations in India—675
15.12 Water turbines—679
15.12.1 Selection of turbines—679
15.12.2 Classification and types of water turbines—680
15.12.3 Governing of turbines—700
15.13 Micro hydel developments—702
15.14 Project cost of hydroelectric plant—704
15.15 Advantages of hydro-power plant—709
15.16 Questions—711
15.16.1 Review questions—711
16. Nuclear Power Plants
16.1 Introduction to nuclear engineering—714
16.1.1 Atomic structure—715
16.1.2 Some definitions—716
16.2 Radioactive decay, half life—717
16.2.1 Radioactive decay—717
16.2.2 Half-life—719
16.3 Principles of release of nuclear energy—721
16.3.1 Fusion and fission reactions—721
16.3.2 Breeding and fertile materials—724
16.3.3 Nuclear fuels used in the reactors—724
16.3.4 Multiplication and thermal utilization factors—725
16.3.5 Life cycle of a neutron—727
16.4 Nuclear reactor components—728
16.5 Classification of nuclear reactors—730
714
16.6 Thermal fission reactors and power plant and their location—733
16.6.1 Pressurized water reactor—734
16.6.2 Boiling water reactor (BWR)—736
16.6.3 CANDU heavy water reactor—739
16.6.4 Gas-cooled reactor—742
16.6.5 Fast breeder reactors—743
16.6.6 Organic substance cooled reactor—747
16.7 Reactor control—750
16.8 Radiation hazards—751
16.8.1 Handling of nuclear waste and safety measures—751
16.8.2 Radioactive waste disposal—753
16.9 Nuclear power generation in India—758
16.10 Questions—760
16.10.1 Objective questions—760
16.10.2 Review questions—765
16.10.3 Reference—766
17. Power Plant Economics 767
17.1 Introduction and basic definitions—767
17.2 Types of loads—768
17.2.1 Load curves—769
17.2.2 Drawing load duration curve—774
17.2.3 Effect of variable load on power plant design and operation—775
17.2.4 Methods to meet variable load—776
17.2.5 Prediction of future loads—777
17.3 Terminology used in power supply—777
17.4 Cost of electrical energy—801
17.4.1 Depreciation—801
17.5 Energy rates (tariffs) for electrical energy—804
17.5.1 Different types of tariffs—804
17.6 Selection of types of generation and generating equipment—810
17.6.1 Steam power plants—810
17.6.2 Diesel engine plants—810
17.6.3 Gas turbine power plant—810
17.6.4 Hydro-electric power plant—810
17.7 Selection of the number and size of units—811
17.8 Factors affecting economics of generation and distribution of power—812
17.9 Planning for power generation in India (source: k PMG India)—813
17.10 Power achievement, target v/s achieved—813
17.11 Questions—814
17.11.1 Objective questions—814
17.11.2 Review questions—816
18. Environmental Aspects of Power Station 818
18.1 Environmental aspects—818
18.1.1 Constituents of the atmosphere—818
18.1.2 Different pollutants due to thermal power plant and their effect on human health—819
18.1.3 Environmental control of different pollutants such as particulate matter PM—820
18.1.4 Oxides of sulphur—820
18.1.5 Oxides of nitrogen—821
18.1.6 Oxides of carbon—821
18.2 Global warming and green house effect—821
18.3 Thermal pollution of water and its control—822
18.4 Acid precipitation – acid rain and acid snow—823
18.5 Effluents from power plants and impact on environment—824
18.5.1 Radiation from nuclear power plant effluents—824
18.5.2 Pollution standards—827
18.5.3 Methods of pollution control—829
18.6 Environmental impact of power plant: social and economical issues of the power plants—833
18.6.1 Land and air space—834
18.6.2 Water—834
18.6.3 Solid waste—834
18.6.4 Construction and operation—834
18.6.5 Noise—834
18.6.6 Economical aspects—835
18.7 Questions—835
18.7.1 Objective questions—835
18.7.2 Review questions—836
18.7.3 References—836
19. Instrumentation and Equipments in Power Station
19.1 Elements of instrumentation—837
19.1.1 Process control system—837
19.1.2 Operational monitoring system—838
19.1.3 Automatic generation control system—838
19.1.4 Load frequency control system—838
19.1.5 Power plant maintenance—838
19.1.6 Plant monitoring system—838
19.2 Important instruments on steam generator and turbine—838
19.2.1 Drum water-level control—838
19.3 Combustion control—840
19.3.1 Super heat temperature control—840
19.4 Introduction to generator and exciters—841
19.4.1 The elementary AC generator—842
19.4.2 Development of the sine wave—843
19.4.3 Types of generators—845
19.4.4 Generator parts and function—846
19.4.5 The exciter—846
19.5 Earthing of power system—848
19.6 Power and unit transformer—849
19.7 Circuit breakers—850
19.8 Protective equipments—850
19.9 Control board equipment—851
19.9.1 Control room instrumentation—851
19.10 Switch gear for power station auxiliaries—852
19.11 Testing of power plants and heat balance—852
19.11.1 British standards, BS845: 1987—853
19.11.2 ASME standard: PTC-4-1 power test code for steam generating units—853
19.11.3 IS 8753: Indian standard for boiler efficiency testing—854
19.11.4 The indirect method testing—855
19.11.5 Energy balance sheet—856
19.12 Questions—856
19.12.1 Objective questions—856
19.12.2 Review questions—857
19.12.3 References—858
Preface
Energy, or power as it is often referred to, is critical, directly or indirectly, in the entire process of evolution, growth and survival of all living beings. It plays a vital role in the socio-economic development and human welfare of a country.
Power is a ‘strategic commodity’. Any uncertainty about its supply can threaten the functioning of an economy, particularly in developing countries. Since the demand for power is growing consistently, an emphasis is given to generate power by utilizing various sources of environment-friendly energy. In this context, acquiring the fundamental aspects of power generation is a must for everyone.
The book discusses about the intricacies of power generation using both renewable and non-renewable resources throughout its nineteen chapters. Conventional method of power generation and the system details have been covered in the first fourteen chapters while the non-conventional methods of power generation have been explained in chapters 15 and 16.
The chapters cover issues like thermal power plant, steam power plant, diesel engine power plant, gas turbine plant, hydro-electric plant, and nuclear power plant, power from non-conventional sources and power plant economics and Instrumentation. All chapters are supplemented by neat sketches and illustrations while SI units have also been used throughout the book which makes it a good reference for engineering students and teachers alike.
Key Features
Salient features of the book are:
1. Thermal, hydro and nuclear power generations
2. Solar and wind energy conversion systems
3. Ocean, geothermal and biomass energy systems
4. Fluidized bed combustion technology
5. Power from non-conventional sources
6. Illustrations, sketches and supplementary photographs
7. Environmental aspect of power generation
8. Power plant economics
Acknowledgements
I would like to dedicate this book to my father late N. R. Hegde, who was a humble teacher and had been a role model for me. I thank my mother Savitri Hegde, who is a constant source of guidance and encouragement for me. My thanks are due to the publishing team of Pearson,
Preface
in particular Dheepika, for her timely response and utmost care taken during the manuscript preparation stage. I would also like to thank Sandhya Jayadev for her inputs. I would like to thank my family members, namely, my wife Sathyabhama and lovely daughters Divya and Disha for their support and sacrifice while writing this book.
My special thanks to CA. Raghavendra Rao, President, Srinivas Group of Institutions, Mangalore and Srinivas Rao, Vice-President, Srinivas Group of Institutions, Mangalore for their whole hearted support in bringing out this book.
My heartfelt thanks to Shrinivasa Mayya, Principal, Srinivas Institute of Technology for his encouragement and motivation. Finally, I would like to thank one and all who have been directly or indirectly involved during the process of writing this book.
R. K. Hegde
