Fluid Mechanics Through Problems R.J. Garde Pro Vice-chancellor Indira Gandhi National Open University New Delhi, India (Formerly, Professor of Hydraulic Engineering University of Roorkee Roorkee, India) JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore
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Fluid Mechanics Through Problems
R.J. Garde Pro Vice-chancellor
Indira Gandhi National Open University New Delhi, India
(Formerly, Professor of Hydraulic Engineering University of Roorkee
Roorkee, India)
JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore
Contents
Preface v
I. Properties of Fluids 1 1.1 Introduction / 1.2 Mass Density, Specific Weight, Specific Volume,
II. Kinematics of Fluid Flow 21 2.1 Velocity 21 2.2 Types of Flow 22 2.3 Stream Lines, Path Lines, Streak Lines 22 2.4 Continuity Equation 22 2.5 Acceleration 23 2.6 Rotation, Vorticity, Circulation 24 2.7 Velocity Potential and Stream Function 26 2.8 Flow-Net 27 2.9 Relaxation Method for Drawing Flow-net 28 Illustrative Examples 29 Problems 46 Descriptive Questions 53
III. Equations of Motion and Energy Theorem 57 3.1 Equations of Motion 57
viii Contents
3.2 Integration of Euler's Equation of Motion Along a Stream Line 58
3.3 Physical Meaning of Terms in Eq. (3.4. a) and Applications 59
3.4 Energy Equation with Heat Transfer 60 Illustrative Examples 60 Problems 78 Descriptive Questions 82
IV. Fluid Statics 85 4.1 Fluid Pressure 85 4.2 Pressure Variation in Static Compressible Fluid 85 4.3 Manometers 86 4.4 Forces on Immersed Plane Surfaces 87 4.5 Total Force on Immersed Curved Surfaces 88 4.6 Floating Bodies 89 4.7 Stability of Floating and Submerged Bodies 89 4.8 Fluid Mass Subjected to Uniform Acceleration 91 4.9 Stresses in Pipes Due to Internal Pressure 92 Illustrative Examples 92 Problems 118 Descriptive Questions 129
V. Applications of Bernoulli's Equation 131 5.1 Introduction 131 5.2 Pressure Distribution in Irrotational Flow 131 5.3 Hydraulic Grade Line and Total Energy Line 132 5.4 Cavitation 132 5.5 Flow Through Small and Large Orifices 132 5.6 Flow Through Mouthpieces 134 5.7 Two and Three Dimensional Orifices and Flow
Measuring Devices in Pipes 755 5.8 Weirs 137 5.9 Flow Under a Sluice Gate 141 Illustrative Examples 142 Problems 161 Descriptive Questions 167
VI. Momentum Equation and Its Applications 169 6.1 Linear Momentum Equation 169 6.2 Momentum Correction Factor ß 170 6.3 Applications 171 6.4 Angular Momentum 171 6.5 Applications of Energy and Momentum
XI. Problems in Pipe Flow 355 11.1 Introduction 355 11.2 Sudden Expansions and Diffusers 355 11.3 Contractions and Contracting Transitions 357 11.4 Flow in Pipe Bends 358 11.5 Loss Coefficients for Pipe Fittings 360 11.6 Equivalent Length of Pipe 361 11.7 Siphons 361 11.8 Pipe Flow Problems 362 11.9 Parallel Pipes 363 11.10 Branching Pipes 364 11.11 Pipe Net-Works 366 Illustrative Examples 367 Problems 394 Descriptive Questions 403
XII. Forces on Immersed Bodies 407 12.1 Introduction 407 12.2 Deformation Drag, Friction Drag, Form Drag 408 12.3 Variation of CD with Re 409 12.4 Effects of Free Surface and Compressibility on
XIII. Open Channel Flow 447 13.1 Some Definitions 447 13.2 Steady Uniform Flow 447 13.3 Most Efficient Channel Section 450 13.4 Specific Energy and Specific Force 450 13.5 Brink Depth, Broad Crested Weirs, Contracting
Transitions 451
Contents xi
13.6 Hydraulic Jump 455 13.7 Flow in a Bend 456 13.8 Gradually Varied Flow 457 13.9 Surges and Gravity Waves 459 Illustrative Examples 461 Problems 507 Descriptive Questions 5i7
XIV. Compressible Flow 520 14.1 Effects of Compressibility 520 14.2 Perfect Gas Relationships 520 14.3 Internal Energy, Entropy and Enthalpy 521 14.4 Propagation of Elastic Wave and Flow Classification 522 14.5 Equations of Motion for One Dimensional Steady
Compressible Flows 523 14.6 Normal Shock Waves 524 14.7 Stagnation Pressure in Compressible Fluids 525 14.8 Flow through Nozzles, Orifices, Venturimeters 525 Illustrative Examples 527 Problems 541 Descriptive Questions 544