1000 Solved Problems in Fluid Mechanics (Includes Hydraulic Machines) About the Author K Subramanya retired as Professor of Civil Engineering from the Indian Institute of Technology, Kanpur. He obtained his Bachelor's degree in Civil Engineering from Mysore University and Master's degree from the University of Madras. He obtained another Master's degree and Ph. D degree from the University of Alberta, Edmonton, Canada. He has over 35 years of teaching experience and has made significant contributions in the area of Water Resources Engineering. He is the author of several successful books which include Flow in Open Channels, 2e (TMH 1992) and Engineering Hydrology, 2e (TMH 1994). Dr. Subramanya has published over eighty technical papers in various national and international journals and conferences. He is a fellow of the Institution of Engineers (India); and Member of the Indian Society of Technical Education, Indian Society for Hydraulics and Indian Water Resources Association. Currently, he is a practicing consultant in Water Resources Engineering at Bangalore. 1000 Solved Problems in Fluid Mechanics (Includes Hydraulic Machines) K Subramanya Formerly Professor Department of Civil Engineering Indian Institute of Technology Kanpur IV \ A Tata McGraw-Hill Publishing Company Limited NEW DELHI McGraw-Hill Offices New Delhi New York St Louis San Francisco Auckland Bogota Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal San Juan Santiago Singapore Sydney Tokyo Toronto Tata McGraw-Hill Copyright © 2005, by Tata McGraw-Hill Publishing Company Limited. No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission of the publishers. The program listings (if any) may be entered, stored and executed in a computer system, but they may not be reproduced for publication. This edition can be exported from India only by the publishers, Tata McGraw-Hill Publishing Company Limited. ISBN 0-07-058386-2 Published by the Tata McGraw-Hill Publishing Company Limited, 7 West Patel Nagar, New Delhi 110 008, typeset in Times New Roman at Tej Composers, WZ-391, Madipur Village, New Delhi 110 063 and printed at Rashtriya Printers, M-135, Panchsheel Garden, Naveen Shandara, Delhi 110 032 Cover Printer: Rashtriya Printers RCXCRDLIDRYLA The McGraw•Hill Companies Contents Preface xi Chapter 1 Properties of Fluids 1 1.1 Introduction 1 1.2 Density and Specific Weight 1 1.3 Pressure 2 1.4 Shear Stress and Viscosity 2 1.5 Surface Tension 3 1.6 Compressibility 4 1.7 Vapour Pressure 5 Worked Examples 5 Objective Questions 12 Problems 15 Chapter 2 Fluid Statics 17 2.1 Measurement of Pressure 17 2.2 Forces on Plane Surfaces 19 2.3 Forces on Curved Surfaces 20 2.4 Buoyancy 20 2.5 Rigid Body Motion 21 Worked Examples 22 Objective Questions 53 Problems 59 Chapter 3 Fluid Flow Kinematics 69 3.1 Introduction 69 3.2 Classification of Row 69 3.3 Streamline 69 3.4 Acceleration 69 3.5 Continuity Equation 70 3.6 Rotational and Irrotational Motion 71 vi Contents 3.7 Stream Function 71 3.8 Potential Function 72 3.9 Relation Between yr and 0 for 2-Dimensional Flow 72 3.10 Some Common Formulae in Cylindrical Co-ordinates 72 3.11 Elementary Inviscid Plane Flows 73 Worked Examples 74 Objective Questions 85 Problems 89 Chapter 4 Energy Equation and Its Applications 93 4.1 Bernoulli Equation 93 4.2 Practical Applications of Bernoulli Equation 93 4.3 Energy Equation 94 4.4 Power 95 Worked Examples 95 Objective Questions 109 Problems 112 Chapter 5 Momentum Equation and Its Applications 117 5.1 Linear Momentum Equation 117 5.2 The Moment of Momentum Equation 119 Worked Examples 121 Objective Questions 132 Problems 135 Chapter 6 Dimensional Analysis and Similitude 139 6.1 Introduction 139 6.2 Common Variables in Fluid Flow 139 6.3 Dimensional Homogeneity 139 6.4 Dimensional Analysis 140 6.5 Similitude 140 6.6 Important Dimensionless How Parameters 141 6.7 Model Scales 141 6.8 Distorted Models 142 Worked Examples 142 Objective Questions 152 Problems 153 Chapter 7 Laminar Flow 158 7.1 Introduction 158 7.2 Basic Equations 158 7.3 Viscometers 161 Worked Examples 161 Objective Questions 169 Problems 172 Contents VI Chapter 8 Boundary Layer Concepts 175 8.1 Introduction 175 8.2 Boundary Conditions 176 8.3 Laminar Boundary Layer Over a Hat Plate 176 8.4 Karman Momentum Integral Formulation 176 8.5 Boundary Conditions for a Proper 0(r1) 177 8.6 Transition from Laminar Boundary Layer 177 8.7 Turbulent Boundary Layer 177 8.8 Laminar Sublayer 178 8.9 Establishment of Flow in a Pipe 178 8.10 Boundary Layer Separation 179 Worked Examples 180 Objective Questions 188 Problems 191 Chapter 9 Drag and Lift on Immersed Bodies 194 9.1 Introduction 194 9.2 Drag 194 9.3 Lift 196 Worked Examples 198 Objective Questions 205 Problems 207 Chapter 10 Turbulent Pipe Flow 210 10.1 Turbulent Flow 210 10.2 Pipe Flow 210 10.3 Commercial Pipes 212 10.4 Aging of Pipes 213 10.5 Simple Pipeline Design Problems 213 10.6 Velocity Distribution in the Neighbourhood of Hat Surfaces 215 Reference 215 Worked Examples 216 Objective Questions 225 Problems 228 Chapter 11 Pipe Flow Systems 232 11.1 Introduction 232 11.2 Minor Losses 232 11.3 Simple Pipe Problems 233 11.4 Pipe Network 237 11.5 Miscellaneous Problems 238 Worked Examples 238 Objective Questions 263 Problems 265 viii Contents Chapter 12 Flow in Open Channels 271 12.1 Open Channel Flow 271 12.2 Classification 271 12.3 Uniform How 271 12.4 Rapidly Varied How 274 12.5 Gradually Varied How 275 12.6 Flow Measurement 276 Reference 277 Worked Examples 277 Objective Questions 300 Problems 304 Chapter 13 Flow Measurement 314 13.1 Introduction 314 13.2 Orifices 314 13.3 Orifice Meter 315 13.4 Venturimeter 316 13.5 Pitot Tube 317 13.6 Weirs 318 13.7 Rotameter 320 Worked Examples 320 Objective Questions 338 Problems 342 Chapter 14 Unsteady Flow 349 14.1 Introduction 349 14.2 Surges in Open Channels 349 14.3 Water Hammer 350 14.4 Establishment of How 352 Worked Examples 353 Objective Questions 364 Problems 366 Chapter 15 Compressible Flow 370 15.1 Introduction 370 15.2 Thermodynamic Principles 370 15.3 Basic Definitions 371 15.4 Basic Equations for Compressible Fluid Flow 372 15.5 Application of Energy Equation 372 15.6 Sonic Velocity 372 15.7 Flow in a Nozzle Discharging from a Tank 373 15.8 Normal Shock Wave 375 References 376 Worked Examples 376 Contents iX Objective Questions 386 Problems 388 Chapter 16 Fluid Flow Machines 391 16.1 Fluid How Machines 391 16.2 Turbines 391 16.3 Rotodynamic Pumps 395 16.4 Reciprocating Pump 399 Worked Examples 404 Objective Questions 426 Problems 429 Appendices 436 Appendix A Multiple-Choice Objective Questions 436 Appendix B-1 Answers to Objective Questions 450 Appendix B-2 Answers to Multiple-Choice Objective Questions of Appendix A 452 Index 453