Fluid Mechanics (Civil & Structural Engineering) Civil Engineering (CE) Notes | EduRev

Civil Engineering (CE) : Fluid Mechanics (Civil & Structural Engineering) Civil Engineering (CE) Notes | EduRev

 Page 1


Fluid Mechanics 
Dr. C. Caprani 1
  
 
 
Fluid Mechanics 
2nd Year 
Civil & Structural Engineering 
 
 
Semester 2 
2006/7 
 
 
 
Dr. Colin Caprani 
Chartered Engineer 
 
Page 2


Fluid Mechanics 
Dr. C. Caprani 1
  
 
 
Fluid Mechanics 
2nd Year 
Civil & Structural Engineering 
 
 
Semester 2 
2006/7 
 
 
 
Dr. Colin Caprani 
Chartered Engineer 
 
Fluid Mechanics 
Dr. C. Caprani 2
Contents 
1. Introduction ......................................................................................................... 7 
1.1 Course Outline ............................................................................................... 7 
Goals .............................................................................................................. 7 
Syllabus.......................................................................................................... 8 
1.2 Programme..................................................................................................... 9 
Lectures.......................................................................................................... 9 
Assessment..................................................................................................... 9 
1.3 Reading Material.......................................................................................... 10 
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 
Further Reading ........................................................................................... 21 
2.3 Properties ..................................................................................................... 22 
Further Reading ........................................................................................... 22 
Mass Density................................................................................................ 22 
Page 3


Fluid Mechanics 
Dr. C. Caprani 1
  
 
 
Fluid Mechanics 
2nd Year 
Civil & Structural Engineering 
 
 
Semester 2 
2006/7 
 
 
 
Dr. Colin Caprani 
Chartered Engineer 
 
Fluid Mechanics 
Dr. C. Caprani 2
Contents 
1. Introduction ......................................................................................................... 7 
1.1 Course Outline ............................................................................................... 7 
Goals .............................................................................................................. 7 
Syllabus.......................................................................................................... 8 
1.2 Programme..................................................................................................... 9 
Lectures.......................................................................................................... 9 
Assessment..................................................................................................... 9 
1.3 Reading Material.......................................................................................... 10 
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 
Further Reading ........................................................................................... 21 
2.3 Properties ..................................................................................................... 22 
Further Reading ........................................................................................... 22 
Mass Density................................................................................................ 22 
Fluid Mechanics 
Dr. C. Caprani 3
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 
Pressure Head............................................................................................... 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 
Page 4


Fluid Mechanics 
Dr. C. Caprani 1
  
 
 
Fluid Mechanics 
2nd Year 
Civil & Structural Engineering 
 
 
Semester 2 
2006/7 
 
 
 
Dr. Colin Caprani 
Chartered Engineer 
 
Fluid Mechanics 
Dr. C. Caprani 2
Contents 
1. Introduction ......................................................................................................... 7 
1.1 Course Outline ............................................................................................... 7 
Goals .............................................................................................................. 7 
Syllabus.......................................................................................................... 8 
1.2 Programme..................................................................................................... 9 
Lectures.......................................................................................................... 9 
Assessment..................................................................................................... 9 
1.3 Reading Material.......................................................................................... 10 
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 
Further Reading ........................................................................................... 21 
2.3 Properties ..................................................................................................... 22 
Further Reading ........................................................................................... 22 
Mass Density................................................................................................ 22 
Fluid Mechanics 
Dr. C. Caprani 3
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 
Pressure Head............................................................................................... 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 
Fluid Mechanics 
Dr. C. Caprani 4
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 
Comments .................................................................................................... 74 
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 
Page 5


Fluid Mechanics 
Dr. C. Caprani 1
  
 
 
Fluid Mechanics 
2nd Year 
Civil & Structural Engineering 
 
 
Semester 2 
2006/7 
 
 
 
Dr. Colin Caprani 
Chartered Engineer 
 
Fluid Mechanics 
Dr. C. Caprani 2
Contents 
1. Introduction ......................................................................................................... 7 
1.1 Course Outline ............................................................................................... 7 
Goals .............................................................................................................. 7 
Syllabus.......................................................................................................... 8 
1.2 Programme..................................................................................................... 9 
Lectures.......................................................................................................... 9 
Assessment..................................................................................................... 9 
1.3 Reading Material.......................................................................................... 10 
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 
Further Reading ........................................................................................... 21 
2.3 Properties ..................................................................................................... 22 
Further Reading ........................................................................................... 22 
Mass Density................................................................................................ 22 
Fluid Mechanics 
Dr. C. Caprani 3
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 
Pressure Head............................................................................................... 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 
Fluid Mechanics 
Dr. C. Caprani 4
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 
Comments .................................................................................................... 74 
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 
Fluid Mechanics 
Dr. C. Caprani 5
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 
Nikuradse’s Experiments........................................................................... 117 
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 
Local Head Losses ..................................................................................... 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 
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