P. Balachandran

ENGINEERINGFLUID MECHANICS

P. BALACHANDRANScientist

Indian Space Research Organisation (ISRO)Trivandrum, Kerala

Formerly, Assistant ProfessorTKM College of Engineering

Kollam, Kerala

ENGINEERINGFLUID MECHANICS

New Delhi-1100012011

ENGINEERING FLUID MECHANICSP. Balachandran

© 2011 by PHI Learning Private Limited, New Delhi. All rights reserved. No part of this book maybe reproduced in any form, by mimeograph or any other means, without permission in writing fromthe publisher.

ISBN-978-81-203-4072-5

The export rights of this book are vested solely with the publisher.

Published by Asoke K. Ghosh, PHI Learning Private Limited, M-97, Connaught Circus,New Delhi-110001 and Printed by Mohan Makhijani at Rekha Printers Private Limited,New Delhi-110020.

ToMy Parents and Teachers

v

Contents

Preface xix

1. Fundamental Concepts and Fluid Properties 1–301.1 Introduction 1

1.1.1 Fluid 11.1.2 Liquids, Gases and Vapours 2

1.2 Fluid Statics, Kinematics and Dynamics 21.3 Fluid Properties 3

1.3.1 Mass Density 31.3.2 Specific Weight 41.3.3 Specific Gravity 41.3.4 Specific Volume 51.3.5 Viscosity 51.3.6 Compressibility and Elasticity 91.3.7 Surface Tension and Capillarity 111.3.8 Vapour Pressure 14

1.4 Compressible Fluids 151.4.1 Equation of State 161.4.2 Thermodynamic Process 161.4.3 Isothermal and Isentropic Bulk Modulus 16

Illustrative Examples 17Review Questions 26Numerical Problems 27

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2. Analysis of Fluid at Rest 31–1112.1 Introduction 312.2 Fluid Pressure 32

2.2.1 Intensity of Pressure 322.2.2 Pascal’s Law 322.2.3 Hydrostatic Law 332.2.4 Pressure Head 342.2.5 Atmospheric Pressure 362.2.6 Absolute and Gauge Pressure 362.2.7 Pressure Variation in a Compressible Fluid 372.2.8 Manometers 402.2.9 Differential Manometers 44

Illustrative Examples 472.3 Hydrostatic Force Analysis 56

2.3.1 Total Pressure and Centre of Pressure 572.3.2 Force on Immersed Planar Aligned (Vertical/ Horizontal)

Surface 572.3.3 Force on Immersed Planar Non-aligned (Inclined) Surface 592.3.4 Force on Immersed Curved Surface 612.3.5 Pressure Diagram 622.3.6 Engineering Applications of Hydrostatic Force Analysis 62

Illustrative Examples 662.4 Analysis of Floating and Submerged Bodies 80

2.4.1 Forces on Immersed Bodies 802.4.2 Buoyant Force and Centre of Buoyancy 802.4.3 Archimedes Principle 802.4.4 Principle of Floatation 822.4.5 Metacentre and Metacentric Height 822.4.6 Evaluation of Metacentric Height 832.4.7 Experimental Method for Metacentric Height 852.4.8 Period of Oscillation 862.4.9 Stability of Floating and Submerged Bodies 87

Illustrative Examples 892.5 Liquid in Relative Rest 95

2.5.1 Liquid Subjected to Uniform Horizontal Acceleration 952.5.2 Liquid Subjected to Uniform Vertical Acceleration 972.5.3 Liquid Subjected to Uniform Acceleration along

Inclined Plane 982.5.4 Liquid Subjected to Uniform Rotation 99

Illustrative Examples 101Review Questions 104Numerical Problems 107

Contents vii

3. Kinematic Analysis of Fluid Flow 112–1693.1 Introduction 1123.2 Types of Flow 112

3.2.1 Lagrangian and Eulerian Approaches 1123.2.2 One, Two and Three-dimensional Flows 1133.2.3 States of Flow 1143.2.4 Steady and Unsteady Motion 1143.2.5 Uniform and Non-uniform Flow 115

3.3 Description of Fluid Flow 1153.3.1 Velocity and Acceleration of Fluid Particles 1163.3.2 Streamlines and Stream Tube 117

3.4 Flow Rate and Continuity Equation 1203.4.1 Principle of Conservation of Mass 1203.4.2 Continuity Equation for One-Dimensional Steady

Incompressible Flow 1203.4.3 General Continuity Equation in Differential Form 1213.4.4 Continuity Equation for Two-dimensional Flow 123

Illustrative Examples 1243.5 Rotational and Irrotational Flows 128

3.5.1 Circulation and Vorticity 1283.5.2 Possible Motions of a Fluid Element 1313.5.3 Component of Rotation 132

3.6 Velocity Potential and Stream Function 1333.6.1 Velocity Potential Function 1333.6.2 Stream Function 1343.6.3 Cauchy-Riemann Equations 1363.6.4 Equi-potential Lines and Streamlines 137

Illustrative Examples 1373.7 Flow of an Ideal Fluid (Potential Flow) 144

3.7.1 Flow Net 1453.7.2 Potential Flow Patterns 1463.7.3 Uniform Rectilinear Flow (Free Stream Flow) 1463.7.4 Flow from a Source 1483.7.5 Flow to a Sink 1493.7.6 Free Vortex Flow 1493.7.7 Source Flow with Uniform Rectilinear Flow

(Flow Around Rankine Half Body) 1503.7.8 Source and Sink of Equal Strength 1523.7.9 Source and Sink with Uniform Rectilinear Flow

(Flow Past Rankine Body) 1543.7.10 Doublet (Dipole) 1563.7.11 Doublet with Uniform Rectilinear Flow (Flow Past Cylinder) 156

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3.7.12 Doublet with Uniform Flow and Vortex (Flow Past Cylinderwith Circulation) 158

Illustrative Examples 160Review Questions 165Numerical Problems 166

4. Dynamic Analysis of Flow 170–2294.1 Introduction 1704.2 Energy Equation 170

4.2.1 Energy of a Flowing Fluid 1704.2.2 Bernoulli’s Theorem 1724.2.3 Bernoulli’s Equation in Terms of Energy Head 1734.2.4 Assumptions in Bernoulli’s Equation 1754.2.5 Proof of Bernoulli’s Equation 1754.2.6 Kinetic Energy Correction Factor 177

4.3 Equations of Motion 1784.3.1 Forces Influencing Fluid Motion 1794.3.2 Simplified Forms of Equations of Motion 1794.3.3 Euler’s Equations of Motion 1804.3.4 Euler’s Equation along a Streamline 1824.3.5 Bernoulli’s Equation Derived from Euler’s Equation 1844.3.6 Hydrostatic Equation from Euler’s Equation 1844.3.7 Bernoulli’s Equation for a Compressible Fluid 185

4.4 Practical Use of Bernoulli’s Theorem 1864.4.1 Venturimeter 1864.4.2 Nozzlemeter or Flow Nozzle 1904.4.3 Orificemeter or Pipe Orifice 1914.4.4 Pitot Tube 1934.4.5 Free Liquid Jet 194

Illustrative Examples 1964.5 Impulse Momentum Theorem 205

4.5.1 Impulse–Momentum Principle 2054.5.2 Impulse–Momentum Equations for Steady Flow 2054.5.3 Momentum Correction Factor 2074.5.4 Force Exerted on Pipe Bend 2084.5.5 Force Exerted on Nozzle 2094.5.6 Force Exerted by a Jet on Plane Surface 209

Illustrative Examples 2104.6 Angular Momentum Principle 2144.7 Vortex Motion 216

4.7.1 Types of Vortex Motion 2164.7.2 Fundamental Equation for Vortex Flow 2164.7.3 Forced Vortex 2184.7.4 Free Vortex 221

Contents ix

Illustrative Examples 222Review Questions 225Numerical Problems 226

5. Analysis of Incompressible Flow 230–3265.1 Introduction 230

5.1.1 Ideal and Real Flows 2305.1.2 Laminar and Turbulent Flows 231

5.2 Flow Regimes and Reynolds Number 2325.2.1 Reynolds Experiment 2325.2.2 Determination of Critical Reynolds Number 2335.2.3 Reynolds Number 234

5.3 Laminar Flow 2355.3.1 Navier–Stokes’ Equations of Motion 2355.3.2 Pressure Gradient in Laminar Flow 2395.3.3 Flow with Very Small and Very Large Reynolds Number 2405.3.4 Steady Laminar Flow in a Circular Pipe

(Hagen–Poiseuille Flow) 2405.3.5 Laminar Flow in Inclined Pipe 2465.3.6 Laminar Flow between Parallel Plates (Couette Flow) 2475.3.7 Laminar Flow around Sphere (Stokes’ Law) 250

Illustrative Examples 2515.4 Turbulent Flow 259

5.4.1 Characteristics of Turbulent Flow 2595.4.2 Intensity and Scale of Turbulence 2605.4.3 Reynolds Equations of Motion 2645.4.4 Turbulence Modelling 2645.4.5 Boussinesq Eddy Viscosity Concept 2655.4.6 Prandtl’s Mixing-length Concept 2655.4.7 Von–Karman Similarity Concept 2665.4.8 Prandtl Universal Velocity Distribution for Turbulent

Pipe Flow 2665.4.9 Karman–Prandtl Velocity Distribution in Turbulent

Pipe Flow 2685.4.10 Power Law for Velocity in Smooth Pipes 2725.4.11 Friction Factor for Smooth and Rough Pipes 2725.4.12 Charts for Friction Factor in Pipe Flow 273

Illustrative Examples 2755.5 Flow in Boundary Layer 278

5.5.1 Description of Boundary Layer—Growth of Boundary Layerover Flat Plate 278

5.5.2 Thickness of Boundary Layer 2815.5.3 Pandtl’s Boundary Layer Equations 2845.5.4 Von–Karman Momentum Integral Equation 285

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5.5.5 Shear Stress and Drag Force 2885.5.6 Laminar Boundary Layer 2885.5.7 Turbulent Boundary Layer 2925.5.8 Pressure Distribution in the Boundary Layer 2945.5.9 Boundary Layer Separation 295

Illustrative Examples 2955.6 Flow around Submerged Bodies 301

5.6.1 Drag and Lift Force 3025.6.2 Drag and Lift Coefficients 3025.6.3 Drag on a Cylinder 3065.6.4 Drag on an Airfoil 3095.6.5 Lift on Cylinder 309

Illustrative Examples 315Review Questions 319Numerical Problems 323

6. Analysis of Flow in Pipes, Ducts, Orifices and Mouthpieces 327–3986.1 Introduction 3276.2 Loss of Energy in Pipes and Ducts 328

6.2.1 Major Loss—Loss of Energy due to Friction 3296.2.2 Minor Losses 333

6.3 Graphical Reprsentation of Energy 3376.3.1 Total Energy Line 3386.3.2 Hydraulic Gradient Line 3386.3.3 Hydraulic Gradient and Energy Gradient 339

Illustrative Examples 3396.4 Fluid Circuit 345

6.4.1 Reservoirs Connected by Long Pipes 3456.4.2 Pipe Discharging to Atmosphere 3476.4.3 Pipe Connected in Series 3476.4.4 Dupuits Equation for Equivalent Pipe 3486.4.5 Pipes Connected Parallel 3486.4.6 Siphon Pipe 3496.4.7 Branching Pipe System 3506.4.8 Analysis of Pipe Networks 351

6.5 Hydraulic Transmission of Power 3526.5.1 Power Transmission Through Pipe 3526.5.2 Pipe with Nozzle at Exit 353

Illustrative Examples 3556.6 Hammer Blow (Water Hammer) 364

6.6.1 Pressure Rise due to Gradual Closure of Valve 3656.6.2 Pressure Rise due to Rapid Closure of Valve 366

Illustrative Examples 3686.7 Flow Through Orifice 370

6.7.1 Vena Contracta 370

Engineering Fluid Mechanics

Publisher : PHI Learning ISBN : 9788120340725Author : BALACHANDRAN,P.

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