Fluid Mechanics For Engineers

173 Pages·2011·11.774 MB·English

by  M. Galal Rabie, Ibrahim Saleh

Fluid Mechanics
For Engineers

Ibrahim Saleh M. Galal Rabie
Professor of Mechanical Professor of Mechanical
Engineering Engineering
This book is published by the authors. The hardcopy is for free distribution to
the authors' students while the electronic book is for free download and free
distribution.
No part of this publication may be reproduced for the purpose of re-
publishing, without the prior written permission of one of the authors.

ISBN 978-977-5092-00-7, 2011

٢٠١١/٥٤٦٤ :ةيرصملا بتكلا رادب عاديلإا مقر
To Fatema and Fatema,
To sons, daughters, grandsons and grand daughters
Ibrahim SALEH and M. Galal RABIE, FLUID MECHANICS FOR ENGINEERS
INTRODUCTION
A fluid is a substance that deforms continuously under shear stress; that is why a
fluid at rest has the shape of its containing vessel. Fluids include liquids, gases, and
plasmas. A fluid at rest has no shear stress.
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can
be divided into fluid statics, fluid kinematics and fluid dynamics. Fluid statics is the
study of fluids at rest. Fluid kinematics is the study of fluid motion without considering
the forces acting on them, while fluid dynamics is the study of the effect of forces on
fluid motion.
Fluid mechanics is a branch of continuum mechanics. It models matter from a
macroscopic viewpoint rather than from a microscopic viewpoint.
The study of fluid mechanics goes back at least to the days of ancient Greece, when
Archimedes investigated fluid statics and buoyancy and formulated his famous
Archimedes Principle. Rapid advancement in fluid mechanics began with Leonardo
da Vinci (observation and experiment), Evangelista Torricelli (barometer), Isaac
Newton (viscosity) and Blaise Pascal (hydrostatics). It was continued by Daniel
Bernoulli with the introduction of mathematical fluid dynamics in his book
Hydrodynamica (1738). Inviscid flow was further analyzed by various
mathematicians: Leonhard Euler, d'Alembert, Lagrange, Laplace, Poisson and
others. Viscous flow was explored by a multitude of engineers including Poiseuille
and Gotthilf Heinrich Ludwig Hagen. Further mathematical justification was provided
by Claude-Louis Navier and George Gabriel Stokes in the Navier–Stokes equations.
Boundary layers were investigated (Ludwig Prandtl), while various scientists
advanced the understanding of fluid viscosity and turbulence: Osborne Reynolds,
Andrey Kolmogorov and Geoffrey Ingram Taylor.
This book is prepared as a basic course in fluid mechanics for engineers, arranged in
six chapters:
Chapter 1: properties of fluids
Chapter 2: fluid statics
Chapter 3: fluid kinematics
Chapter 4: fluid dynamics
Chapter 5: steady incompressible real flow in hydraulic conduits
Chapter 6: dimensional analysis and similarity

Cover Design
The authors are indebted to the graphic designer Rehab Rabie, MSc.
i
Ibrahim SALEH and M. Galal RABIE, FLUID MECHANICS FOR ENGINEERS
THE AUTHORS

Prof. Dr. Ibrahim Saleh Mostafa
Birth date & place: 27 November 1945, Cairo, EGYPT
Degrees Hold:
PhD Field: Rheology, Multi-phase Flow.
Awarded by: ENSEEIHT Toulouse & Paul Sabatier Univ., Toulouse, France, Sept., 1980
MSc Field: Hydraulic Engineering
Awarded by: VUT, Brno, CSSR, , July,1976
BSc Field: Mechanical Engineering (Power & Energy)
Awarded by: Faculty of Engineering, Cairo University, Egypt, 1968
Previous occupations and Experience
Professor in Mechanical engineering, title awarded by the supreme council of the Military
Technical College (MTC), Cairo, April.1992
Author or co-author of more than 50 papers published in local and international journals and
conferences n and supervisor of 45 PhD & MSc Thesis.
Current Institution: Military Technical College, Cairo, Egypt.

Prof. Dr. Mahmoud Galal El-Din Mohamed RABIE
Birth date & place: 19 April 1946, Dakahlia, EGYPT
Degrees Hold:
PhD Field: Automatic Control and Computer Science Applied to Industrial Systems
Awarded by: INSA Lyon & Claud Bernard Univ., Lyon, France, Oct., 1980
MSc Field: Mechanical Engineering
Awarded by: Military Technical College, Cairo, Jan.,1977
BSc Field: Mechanical Engineering (Aircraft Engines)
Awarded by: Military Technical College, Cairo, 1968
Previous occupations and Experience
Professor in Mechanical engineering, title awarded by the supreme council of the Military
Technical College (MTC), Cairo, Nov.1991
Author of: M Galal Rabie, Fluid Power Engineering, McGraw-Hill, NY, May 18, 2009.
Author or co-author of 57 papers published in local and international journals and conferences n
and supervisor of 25 PhD & MSc Thesis
Current Institution: Modern Academy for Engineering and Technology, Cairo, Egypt.

ii
Ibrahim SALEH and M. Galal RABIE, FLUID MECHANICS FOR ENGINEERS
Content

CHAPTER 1: PROPERTIES OF FLUIDS 1
1.1 INTRODUCTION 1
1.2 BASIC PROPERTIES OF FLUIDS 2
1.2.1 Density 2
1.2.2 Compressibility and Elasticity 4
1.2.3 Viscosity 7
1.2.4 Surface Tension 12
1.2.5 Vapor Pressure 15
1.3 EXERCISE 17

CHAPTER 2: FLUID STATICS 21
2.1 INTRODUCTION 21
2.2 CONTROL VOLUME AND CONTROL SURFACE 21
2.3 SURFACE AND BODY FORCES 22
2.4 PRESSURE AND PASCAL’S LAW 22
2.5 EULER’S EQUATIONS OF FLUID STATICS 24
2.6 APPLICATIONS OF EULER’S EQUATION OF FLUID STATICS 26
2.6.1 Pressure Difference Between Two Points in a Gravity Field 26
2.6.2 Pressure Measuring Devices 28
2.6.2.1 Mercury barometer 28
2.6.2.2 Piezometer - Piezo-manometer 29
2.6.2.3 U-Tube Manometer 30
2.6.3 Pressure Forces on Submerged Surfaces 36
2.6.3.1 Pressure Forces on Plane Surfaces 36
2.6.3.3 Pressure force on curved surfaces 40
2.7 BUOYANCY AND STABILITY OF FLOATING BODIES 45
2.7.1 Buoyancy Forces 45
2.7.2 Stability of Submerged Bodies 46
2.7.3 Stability of Floating Bodies 47
2.8 RELATIVE EQUILIBRIUM IN LINEAR AND ROTARY MOTIONS 51
iii
Ibrahim SALEH and M. Galal RABIE, FLUID MECHANICS FOR ENGINEERS
2.8.1 Relative Equilibrium, Linear Motion 51
2.8.2 Relative Equilibrium, Rotary Motion 53
2.9 EXERCISE 55

CHAPTER 3: FLUID KINEMATICS 63
3.1 INTRODUCTION 63
3.2 BASIC CONCEPTS OF FLUID FLOW 64
3.2.1 Uniform and Steady Flow 64
3.2.2 One, Two and Three-Dimensional Flow 65
3.2.3 Rotational and Irrotational Flow 66
3.3 MOTION AND DEFORMATION OF A FLUID ELEMENT 67
3.3.1 Fluid Element Translation, Velocity and Acceleration 67
3.3.2 Fluid Element Rotation about its Own Axis- Spin 69
3.3.3 Angular Deformation of Fluid Element 71
3.3.4 Linear Deformation of a Fluid Element 72
3.4 STREAMLINES, PATH LINES AND STREAK LINES 72
3.5 STREAM AND POTENTIAL FUNCTIONS 75
3.5.1 Stream Function  75
3.5.2 Velocity Potential Function φ 78
3.5.3 Flow net 80
3.5.3.1 Uniform flow in x- direction 80
3.5.3.2 Source and sink 81
3.5.3.3 Vortex 82
3.5.3.4 Combination of a source and a uniform flow in x-direction 82
3.5.3.5 Combined source-sink 83
3.5.3.6 Doublet 83
3.6 EXERCISE 84

CHAPTER 4: FLUID DYNAMICS 85
4.1. INTRODUCTION 85
4.2. MASS CONSERVATION - Continuity Equation 85
4.2.1 Discharge and mean velocity 85
iv
Ibrahim SALEH and M. Galal RABIE, FLUID MECHANICS FOR ENGINEERS
4.2.2 Continuity Equation 86
4.2.3 Momentum Equation 90
4.4. ENERGY CONSERVATION, BERNOULLI’s EQUATION 91
4.5. FLUID DYNAMICS, APPLICATIONS OF BASIC EQUATIONS 93
4.5.1. Applications on Continuity equation 94
4.5.2. Mass flow rate 95
4.5.3. Volume flow rate: Discharge 96
4.5.4. Orifice Flow 96
4.5.5. Application of the Momentum Equation 100
4.5.6 Applications of Bernoulli’s equation 102
4.5.6.1 Free jet flow 103
4.5.6.2 Flow from a reservoir 103
4.5.6.3 Flow in a conduit 104
4.5.6.4 Pressure head, velocity head, potential head and total head 105
4.5.6.5 Piezo-meter and Pitot tube 107
4.5.6.6 Venturi Meter 109
4.5.6.7 Flow over notches and weirs 112
4.5.6.8 Empting of tanks 114
4.8 EXERCISE 116

CHAPTER 5: STEADY INCOMPRESSIBLE REAL FLOW IN HYDRAULIC CONDUITS 121
5.1. INTRODUCTION 121
5.2. REAL FLOW IN CONDUITS 121
5.3. HYDRAULIC LOSSES IN PIPES 122
5.4. FRICTION LOSSES IN PIPELINES 122
5.4.1. Laminar Flow in Pipelines 123
5.4.2 Flow between two parallel plates 128
5.4.3 Internal Leakage in Hydraulic Elements 130
5.4.4. Friction Losses in Turbulent Flow Pipelines 131
5.5 LOCAL LOSSES IN HYDRAULIC CONDUITS 134
5.6. APPLICATIONS ON HYDRAULIC LOSSES IN PIPES 137
5.6.1 Head Loss for a Given Flow Rate 137
5.6.2 Flow Rate for a Given Head Loss 139
v
Ibrahim SALEH and M. Galal RABIE, FLUID MECHANICS FOR ENGINEERS
5.6.3 Selecting a Pipe Diameter 141
5.6.4 Total Head Loss 142
5.6.5 Fluid Pumping 143
5.6.6 Complex Networks 145
5.7 EXERCISE 147

CHAPTER 6: DIMENSIONAL ANALYSIS AND SIMILARITY 151
6.1. INTRODUCTION 151
6.2. BASIC PRINCIPLES 152
6.3. BUCKINGHAM PI () THEOREM 153
6.4 SIMILARITY AND NON-DIMENSIONAL ANALYSIS 156
6.4.1. Geometric Similarity 158
6.4.2. Kinematic Similarity 158
6.4.3. Dynamic Similarity 159
6.5. EXERCISE 163

vi