KEY EQUATIONS F (1-1) PRESSURE fJ = - A WEIGHT-MASS RELATIONSHIP w = mg (1-2) -!lp (1-4) BULK MOOULUS E = (!lV)/ V DENSITY p = m/ V (1-5) SPECIFIC WEIGHT 1' = w/ V (1-6) 'l's Ps (1-7) SPECIFIC GRAVITY sg = = 1 ... @ 4°C p., CONTINUITY EQUATION FOR ANY FLUID P1A 1V1 = P2A2Vi (6--4) CONTINUITY EQUATION FOR A1V1 = A1V2 (6-5) LIQUIDS BERNOULLI'S EQUATION Pi vy P2 v~ (6-9) - + Zi + - = - + Z2 + - 'Y 2g 'Y 2g TORRICELLI'S THEOREM (6-16) Vi = V2iii TIME REQUIRED TO DRAIN A TANK 2(A,/ Aj) if2 i/2 (6-26) 12 - Ii = '\/h (hi - h2 ) 2g GENERAL ENERGY EQUATION Pi V?j P2 V2 (7-3) - + : i + - + hA - hR - hl = + :2 + - 'Y 2g 'Y 2g POWER ADDED TO A FLUID BY PA = hAW = h,aQ (7-5) A PUMP PUMP EFFICIENCY eM = Power delivered to flu id P11 (7-6) Power put into pump P1 POWER REMOVED FROM A FLUID BY A MOTOR PH = hRW = hRyQ (7-8) MOTOR EFFICIENCY Power output from motor Po (7-9) eM = Power delivered by fluid PR REYNOLDS NUMBER-CIRCULAR vDp vD (8-1) NR = -= - SECTIONS 1/ v DARCY'S EQUATION L v2 (8-3) FOR ENERGY LOSS hl =f X - X - D 2g HAGEN-POISEUILLE EQUATION 321)LV (8-4) hl= -- yD2 FRICTION FACTOR 64 (8-5) J=- FOR LAMINAR FLOW NR FRICTION FACTOR FOR 0.25 (8-7) f= TURBULENT FLOW [ ( I 5.74) J2 log 3.7(D I € ) + N'ti9 HAZEN-WILLIAMS FORMULA - U.S. CUSTOMARY UNITS v = 1.32 ch R0·63s0·54 (8-8) CONTENTS Preface xi 3 Pressure Measurement 38 Acknowledgments xv The Big Picture 38 3.1 Objectives 39 1 The Nature of Fluids and the Study 3.2 Absolute and Gage Pressure 39 of Fluid Mechanics 1 3.3 Relationship between Pressure and The Big Picture 1 Elevation 40 1.1 Objectives 3 3.4 Development of the Pressure-Elevation 1.2 Basic Introductory Concepts 3 Relation 43 1.3 T he International System of Units (SI) 4 3.5 Pascal's Paradox 45 1.4 The U.S. Customary System 4 3.6 Manometers 46 I 1.5 Weigh t and Mass 5 3.7 Barometers 51 I 1.6 Temperature 6 3.8 Pressure Expressed as the Height of a 1.7 Consistent Units in an Equation 6 Column of Liquid 52 1.8 The Definition of Pressure 8 3.9 Pressure Gages and Transducers 53 References 55 1.9 Compressibility 10 Internet Resources 55 1.10 Density, Specific Weight, and Specific Gravity 11 Practice Problems 55 1.11 Surface Tension 14 References 15 4 Forces Due to Static Fluids 63 Internet Resources 15 The Big Picture 63 Practice Problems 15 4.1 Objectives 65 Computer Aided Engineer ing Assignments 18 4.2 Gases Under Pressure 65 4.3 Horizontal Flat Surfaces Under 2 Viscosity of Fluids 19 Liquids 66 The Big Picture 19 4.4 Rectangular Walls 67 2.1 Objectives 20 4.5 Submerged Plane Areas- General 69 2.2 Dynamic Viscosity 21 2.3 Kinematic Viscosity 22 4.6 Development of the General Procedure for Forces on Submerged Plane Areas 72 2.4 Newtonian Fluids and Non-Newtonian Fluids 23 4.7 Piezometric Head 73 2.5 Variation of Viscosity with Temperature 25 4.8 Distribution of Force on a Submerged I' Curved Surface 74 2.6 Viscosity Measurement 27 4.9 Effect of a Pressure above the Fluid 2.7 SAE Viscosity Grades 32 Surface 78 2.8 ISO Viscosity Grades 33 4.10 Forces on a Curved Surface with Fluid 2.9 Hydraulic Fluids for Fluid Power Systems 33 Below It 78 References 34 4.11 Forces on Curved Surfaces with Fluid Above Internet Resources 35 and Below 79 Practice Problems 35 Practice Problems 80 Computer Aided Engineering Assignments 37 Computer Aided Engineering Assignments 92 vii viii Contents 5 Buoyancy and Stability 93 8 Reynolds Number, Laminar Flow, Turbulent Flow, and Energy Losses The Big Picture 93 Due to Friction 178 5.1 Objectives 94 5.2 Buoyancy 94 The Big Picture 178 5.3 Buoyancy Materials 101 8.1 Objectives 181 5.4 Stability of Completely Submerged 8.2 Reynolds Number 181 Bodies 102 8.3 Critical Reynolds Numbers 182 5.5 Stability of Floating Bodies 103 8.4 Darcy's Equation 183 5.6 Degree of Stability 107 8.5 Friction Loss in Laminar Flow 183 Reference 108 8.6 Friction Loss in Turbulent Flow 184 Internet Resources 108 8.7 Use of Software for Pipe Flow Problems 190 Practice Problems 108 8.8 Equations for the Friction Factor 194 Stability Evaluation Projects 116 8.9 Hazen-Williams Formula for Water Flow 195 8.10 Other Forms of the Hazen- Williams 6 Flow of Fluids and Bernoulli's Formula 196 Equation 117 8.11 Nomograph for Solving the Hazen-Williams Formula 196 The Big Picture 117 References 198 6.1 Objectives 118 Internet Resources 198 6.2 Fluid Flow Rate and the Con tinuity Practice Problems 198 Equation 118 Computer Aided Engineering Assignments 204 6.3 Commercially Available Pipe and Tubing 122 6.4 Recommended Velocity of Flow in Pipe and 9 Velocity Profiles for Circular Sections Tubing 124 and Flow in Noncircular Sections 205 6.5 Conservation of Energy- Bernoulli's The Big Picture 205 Equation 127 9.1 Objectives 206 6.6 Interpretation of Bernoulli's Equation 128 9.2 Velocity Profiles 207 6.7 Restrictions on Bernoulli's Equation 129 9.3 Velocity Profile for Laminar Flow 207 6.8 Applications of Bernoulli's Equation 129 9.4 Velocity Profile for Turbulent Flow 209 6.9 Torricelli's Theorem 137 9.5 Flow in Noncircular Sections 212 6.10 Flow Due to a Falling Head 140 9.6 Computational Fluid Dynamics 216 References 142 References 218 Internet Resources 142 Internet Resources 218 Practice Problems 143 Practice Problems 218 Analysis Projects Using Bernoulli's Equation and Torricelli's Theorem 153 Computer Aided Engineering Assignments 224 7 General Energy Equation 154 10 Minor Losses 225 The Big Picture 154 The Big Picture 225 7.1 Objectives 155 10.1 Objectives 227 7.2 Energy Losses and Additions 156 10.2 Resistance Coefficient 227 7.3 Nomenclature of Energy Losses and 10.3 Sudden Enlargement 228 Additions 158 10.4 Exit Loss 23 1 7.4 General Energy Equation 158 10.5 Gradual Enlargement 231 7.5 Power Required by Pumps 162 10.6 Sudden Contraction 233 7.6 Power Delivered to Fluid Motors 165 10.7 Gradual Contraction 236 Practice Problems 167 10.8 Entrance Loss 237 Contents ix 10.9 Resistance Coefficients for Valves and 13.3 Types of Pumps 320 Fittings 238 13.4 Positive-Displacement Pumps 320 10.10 Application of Standard Valves 244 13.S Kinetic Pumps 326 10.11 Pipe Bends 246 13.6 Performance Data for Centrifugal Pumps 330 10.12 Pressure Drop in Fluid Power Valves 248 13.7 Affinity Laws for Centrifugal Pumps 332 10.13 Flow Coefficients for Valves Using Cv 251 13.8 Manufacturers' Data for Centrifugal 10.14 Plastic Valves 252 Pumps 333 10.15 Using K-Factors in PIPE-FLO® Software 253 13.9 Net Positive Suction Head 341 References 258 13.10 Suction Line Details 346 Internet Resources 258 13.11 Discharge Line Details 346 Practice Problems 258 13.12 The System Resistance Curve 347 Computer Aided Analysis and Design 13.13 Pump Selection and the Operating Point for Assignments 263 the System 350 13.14 Using PIPE-FLO® for Selection of 11 Series Pipeline Systems 264 Commercially Available Pumps 352 The Big Picture 264 13.15 Alternate System Operating Modes 356 I I.I Objectives 265 13.16 Pump Type Selection and Specific Speed 361 11.2 Class I Systems 265 13.17 Life Cycle Costs for Pumped Fluid Systems 363 11.3 Spreadsheet Aid for Class I Problems 270 References 364 11.4 Class II Systems 272 Internet Resources 365 11.5 Class III Systems 278 Practice Problems 366 11.6 PIPE-FLO® Examples for Series Pipeline Systems 281 Supplemental Problem (PIPE-FLO® Only) 367 11.7 Pipeline Design for Structural Integrity 284 Design Problems 367 References 286 Design Problem Statements 368 Internet Resources 286 Comprehensive Design Problem 370 Practice Problems 286 Computer Aided Analysis and Design 14 Open-Channel Flow 372 Assignments 295 The Big Picture 372 14.1 Objectives 373 12 Parallel and Branching Pipeline 14.2 Classification of Open-Channel Flow 374 Systems 296 14.3 HydrauJic Radius and Reynolds Number in The Big Picture 296 Open-Channel Flow 375 I , 12.1 Objectives 298 14.4 Kinds of Open-Channel Flow 375 12.2 Systems with Two Branches 298 14.5 Uniform Steady Flow in Open 12.3 Parallel Pipeline Systems and Pressure Channels 376 Boundaries in PIPE-FLO® 304 14.6 The Geometry of Typical Open I 12.4 Systems with Three or More Branches- Channels 380 Networks 307 14.7 The Most Efficient Shapes for Open References 314 Channels 382 Internet Resources 314 14.8 Critical Flow and Specific Energy 382 Practice Problems 314 14.9 Hydraulic Jump 384 Computer Aided Engineering Assignments 317 14.10 Open-Channel Flow Measurement 386 References 390 13 Pump Selection and Application 318 Digital Publications 390 The Big Picture 318 Internet Resources 390 13.1 Objectives 319 Practice Problems 391 13.2 Parameters Involved in Pump Selection 320 Computer Aided Engineering Assignments 394