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Fluid Mechanics Contents
1. Introduction ......................................................................................................... 7
1.1 Course Outline ............................................................................................... 7
Goals .............................................................................................................. 7
Syllabus.......................................................................................................... 8
1.2 Programme..................................................................................................... 9
Lectures.......................................................................................................... 9
Assessment..................................................................................................... 9
Lecture Notes ............................................................................................... 10
Books ........................................................................................................... 10
The Web....................................................................................................... 10
1.4 Fluid Mechanics in Civil/Structural Engineering........................................ 11
2. Introduction to Fluids ....................................................................................... 12
2.1 Background and Definition.......................................................................... 12
Background .................................................................................................. 12
Definition ..................................................................................................... 13
Definition Applied to Static Fluids.............................................................. 13
Definition Applied to Fluids in Motion....................................................... 14
Generalized Laws of Viscosity .................................................................... 17
2.2 Units ............................................................................................................. 19
Dimensions and Base Units ......................................................................... 19
Derived Units ............................................................................................... 19
SI Prefixes.................................................................................................... 21
2.3 Properties ..................................................................................................... 22
Mass Density................................................................................................ 22
Specific Weight............................................................................................ 22
Relative Density (Specific Gravity)............................................................. 22
Bulk Modulus............................................................................................... 23
Viscosity....................................................................................................... 23
Problems - Properties................................................................................... 25
3. Hydrostatics ....................................................................................................... 26
3.1 Introduction.................................................................................................. 26
Pressure ........................................................................................................ 26
Pressure Reference Levels ........................................................................... 27
3.2 Pressure in a Fluid........................................................................................ 28
Statics of Definition ..................................................................................... 28
Pascal’s Law ................................................................................................ 29
Pressure Variation with Depth..................................................................... 31
Summary...................................................................................................... 33
Problems - Pressure...................................................................................... 34
3.3 Pressure Measurement ................................................................................. 36
Manometers.................................................................................................. 36
Problems – Pressure Measurement.............................................................. 41
3.4 Fluid Action on Surfaces ............................................................................. 43
Plane Surfaces.............................................................................................. 43
Plane Surface Properties .............................................................................. 46
Plane Surfaces – Example............................................................................ 47
Curved Surfaces ........................................................................................... 51
Curved Surfaces – Example......................................................................... 55
Problems – Fluid Action on Surfaces .......................................................... 57
4. Hydrodynamics: Basics..................................................................................... 59
4.1 General Concepts ......................................................................................... 59
Introduction.................................................................................................. 59
Classification of Flow Pattern...................................................................... 59
Visualization ................................................................................................ 60
Dimension of Flow ...................................................................................... 62
Fundamental Equations................................................................................ 63
Control Volume ........................................................................................... 64
4.2 The Continuity Equation.............................................................................. 65
Development ................................................................................................ 65
Mass Conservation – Example .................................................................... 68
4.3 The Energy Equation ................................................................................... 71
Development ................................................................................................ 71
Energy Equation – Example ........................................................................ 75
4.4 The Momentum Equation ............................................................................ 78
Development ................................................................................................ 78
Application – Fluid Striking a Flat Surface................................................. 79
Application – Flow around a bend in a pipe................................................ 81
Application – Force exerted by a firehose................................................... 83
4.5 Modifications to the Basic Equations .......................................................... 86
Flow Measurement – Small Orifices ........................................................... 86
Flow Measurement – Large Orifices ........................................................... 89
Discharge Measurement in Pipelines........................................................... 92
Velocity and Momentum Factors ................................................................ 94
Accounting for Energy Losses..................................................................... 96
Problems – Energy Losses and Flow Measurement.................................... 99
5. Hydrodynamics: Flow in Pipes ...................................................................... 100
5.1 General Concepts ....................................................................................... 100
Characteristics of Flow Types ................................................................... 103
Background to Pipe Flow Theory.............................................................. 104
5.2 Laminar Flow............................................................................................. 105
Steady Uniform Flow in a Pipe: Momentum Equation ............................. 105
Hagen-Poiseuille Equation for Laminar Flow........................................... 108
Example: Laminar Flow in Pipe ................................................................ 111
5.3 Turbulent Flow........................................................................................... 113
Description................................................................................................. 113
Empirical Head Loss in Turbulent Flow ................................................... 114
5.4 Pipe Friction Factor.................................................................................... 116
Laminar Flow............................................................................................. 116
Smooth Pipes – Blasius Equation .............................................................. 116
The von Karman and Prandlt Laws ........................................................... 118
The Colebrook-White Transition Formula ................................................ 119
Moody........................................................................................................ 120
Barr............................................................................................................. 121
Hydraulics Research Station Charts .......................................................... 122
Example ..................................................................................................... 124
Problems – Pipe Flows .............................................................................. 129
5.5 Pipe Design ................................................................................................ 130
Sudden Enlargement .................................................................................. 131
Sudden Contraction.................................................................................... 133
Example – Pipe flow incorporating local head losses ............................... 134
Partially Full Pipes..................................................................................... 136
Example ..................................................................................................... 138
Problems – Pipe Design............................................................................. 141
6. Hydrodynamics: Flow in Open Channels ..................................................... 142
6.1 Description................................................................................................. 142
Properties ................................................................................................... 143
6.2 Basics of Channel Flow ............................................................................. 145
Laminar and Turbulent Flow..................................................................... 145
Moody Diagrams for Channel Flow .......................................................... 146
Friction Formula for Channels................................................................... 147
Evaluating Manning’s n............................................................................. 149
Example –Trapezoidal Channel................................................................. 150
6.3 Varying Flow in Open Channels ............................................................... 152
The Energy Equation ................................................................................. 152
Flow Characteristics................................................................................... 154
Example – Open Channel Flow Transition ............................................... 157
Problems – Open Channel Flow ................................................................ 159