Basics of Fluid Mechanics

✍ Scribed by Genick Bar-Meir

• Publisher: Potto Project Publishing
• Year: 2022
• Tongue: English
• Leaves: 835
• Series: Open textbook library
• Edition: 6
• Category: Library

✦ Table of Contents

Please Update
Abstract
Why Abstract
Short Abstract
Long Abstract
Prologue For This Book
Version 0.6.7 July 5, 2022
pages 831 size 13.3M
Version 0.6.2 April 13, 2022
pages 795 size 12.0M
Version 0.6.0 March 22, 2022
pages 773 size 11.8M
Version 0.5.5 March 17, 2022
pages 767 size 12M
Version 0.5.2 July 11, 2021
pages 743 size 11M
Version 0.4 April 6, 2020
pages 749 size 11M
Version 0.3.2.0 March 18, 2013
pages 617 size 4.8M
Version 0.3.0.5 March 1, 2011
pages 400 size 3.5M
Version 0.1.8 August 6, 2008
pages 189 size 2.6M
Version 0.1 April 22, 2008
pages 151 size 1.3M
How to contribute to this book
Credits
Steven from artofproblemsolving.com
Dan H. Olson
Richard Hackbarth
John Herbolenes
Eliezer Bar-Meir
Henry Schoumertate
Your name here
Typo corrections and other "minor" contributions
Change Log
Nomenclature
GNU Free Documentation License
APPLICABILITY AND DEFINITIONS
2. VERBATIM COPYING
3. COPYING IN QUANTITY
4. MODIFICATIONS
5. COMBINING DOCUMENTS
6. COLLECTIONS OF DOCUMENTS
7. AGGREGATION WITH INDEPENDENT WORKS
8. TRANSLATION
9. TERMINATION
10. FUTURE REVISIONS OF THIS LICENSE
ADDENDUM: How to use this License for your documents
How This Book Was Written
2022 Version
2021 Version
Initial
Properties
Turbulence
Inviscid Flow
Machinery
Internal Viscous Flow
Open Channel Flow
Introduction to Fluid Mechanics
What is Fluid Mechanics?
Brief History
Kinds of Fluids
Shear Stress
Viscosity
General Discussion
Non–Newtonian Fluids
Kinematic Viscosity
Estimation of The Viscosity
Fluid Properties
Fluid Density
Bulk Modulus
Surface Tension
Wetting of Surfaces
Review of Thermodynamics
Introductory Remarks
Basic Definitions
Thermodynamics First Law
Thermodynamics Second Law
Review of Mechanics
Introductory Remarks
Kinematics of of Point Body
Center of Mass
Actual Center of Mass
Approximate Center of Area
Change of Centroid Location Due to Added/Subtracted Area
Change of Mass Centroid Due to Addition or Subtraction of Mass in 3D
Centroid of Segment
Moment of Inertia
Moment of Inertia for Mass
Moment of Inertia for Area
Examples of Moment of Inertia
Product of Inertia
Principal Axes of Inertia
Newton's Laws of Motion
Angular Momentum and Torque
Tables of geometries
Fluids Statics
Introduction
The Hydrostatic Equation
Pressure and Density in a Gravitational Field
Constant Density in Gravitational Field
Pressure Measurement
Varying Density in a Gravity Field
The Pressure Effects Due To Temperature Variations
Gravity Variations Effects on Pressure and Density
Liquid Phase
Fluid in a Accelerated System
Fluid in a Linearly Accelerated System
Angular Acceleration Systems: Constant Density
Fluid Statics in Geological System
Fluid Forces on Surfaces
Fluid Forces on Straight Surfaces
Forces on Curved Surfaces
Buoyancy and Stability
Stability
Application of GM-.4
Surface Tension
Rayleigh–Taylor Instability
Qualitative questions
I Integral Analysis
Mass Conservation
Introduction
Control Volume
Continuity Equation
Non Deformable Control Volume
Constant Density Fluids
Reynolds Transport Theorem
Examples For Mass Conservation
The Details Picture – Velocity Area Relationship
More Examples for Mass Conservation
Momentum Conservation
Momentum Governing Equation
Introduction to Continuous
External Forces
Momentum Governing Equation
Momentum Equation in Acceleration System
Momentum Equation For Steady State and Uniform Flow
Momentum Equation Application
Momentum for Unsteady State and Uniform Flow
Momentum Application to Unsteady State
Conservation Moment Of Momentum
More Examples on Momentum Conservation
Qualitative Questions
Energy Conservation
The First Law of Thermodynamics
Limitation of Integral Approach
Approximation of Energy Equation
Energy Equation in Steady State
Energy Equation in Frictionless Flow and Steady State
Energy Equation in Accelerated System
Energy in Linear Acceleration Coordinate
Linear Accelerated System
Energy Equation in Rotating Coordinate System
Simplified Energy Equation in Accelerated Coordinate
Energy Losses in Incompressible Flow
Examples of Integral Energy Conservation
Qualitative Questions
II Differential Analysis
Differential Analysis
Introduction
Mass Conservation
Mass Conservation Examples
Simplified Continuity Equation
Conservation of General Quantity
Generalization of Mathematical Approach for Derivations
Examples of Several Quantities
Momentum Conservation
Derivations of the Momentum Equation
Boundary Conditions and Driving Forces
Boundary Conditions Categories
Examples for Differential Equation (Navier-Stokes)
Interfacial Instability
Dimensional Analysis
Introductory Remarks
Brief History
Theory Behind Dimensional Analysis
Dimensional Parameters Application for Experimental Study
The Pendulum Class Problem
Buckingham—-Theorem
Construction of the Dimensionless Parameters
Basic Units Blocks
Implementation of Construction of Dimensionless Parameters
Similarity and Similitude
Nusselt's Technique
Summary of Dimensionless Numbers
The Significance of these Dimensionless Numbers
Relationship Between Dimensionless Numbers
Examples for Dimensional Analysis
Abuse of Dimensional Analysis
Summary
Appendix summary of Dimensionless Form of Navier–Stokes Equations
Supplemental Problems
External Flow
Introduction
Boundary Layer Theory
Non–Circular Shape Effect
Internal Flow
Introduction
Colebrook-White equation for Friction Factor, f
Entry Problem
Non–Circular Shape Effect
Losses in Conduits Connections and Other Devices
Minor Loss
Flow Meters (Flow Measurements)
Nozzle Flow Meter
Flow Network
Series Conduits Systems
Parallel Pipe Line Systems
Potential Flow
Introduction
Inviscid Momentum Equations
Potential Flow Function
Streamline and Stream function
Compressible Flow Stream Function
The Connection Between the Stream Function and the Potential Function
Potential Flow Functions Inventory
Flow Around a Circular Cylinder
Complex Potential
Complex Potential and Complex Velocity
Blasius's Integral Laws
Forces and Moment Acting on Circular Cylinder.
Conformal Transformation or Mapping
Unsteady State Bernoulli in Accelerated Coordinates
Qualitative questions
Additional Example
Added Mass and Transfer Properties
Introduction
History
What is the Added Mass?
The Added Mass Matrix of a Body
Added Moment of Inertia Coefficients
Calculations of the Added Mass
Transfer Mechanisms and Transfer Properties
History of Transfer Properties
Introduction
Transfer Linear Motion to Rotating Motion
The Parallel Axes Theorem for Added Mass
Experimental Observation
Added Mass and Transfer Properties
Added Moment of Inertia
Introduction
III Compressible Flow
Compressible Flow One Dimensional
What is Compressible Flow?
Why Compressible Flow is Important?
Speed of Sound
Introduction
Speed of Sound in Ideal and Perfect Gases
Speed of Sound in Almost Incompressible Liquid
Speed of Sound in Solids
The Dimensional Effect of the Speed of Sound
Isentropic Flow
Stagnation State for Ideal Gas Model
Isentropic Converging–Diverging Flow in Cross Section
The Properties in the Adiabatic Nozzle
Isentropic Flow Examples
Mass Flow Rate (Number)
Isentropic Tables
The Impulse Function
Normal Shock
Solution of the Governing Equations
Prandtl's Condition
Operating Equations and Analysis
The Moving Shocks
Shock or Wave Drag Result from a Moving Shock
Qualitative questions
Tables of Normal Shocks, k=1.4 Ideal Gas
Isothermal Flow
The Control Volume Analysis/Governing equations
Dimensionless Representation
The Entrance Limitation of Supersonic Branch
Supersonic Branch
Figures and Tables
Isothermal Flow Examples
Fanno Flow
Introduction
Non–Dimensionalization of the Equations
The Mechanics and Why the Flow is Choked?
The Working Equations
Examples of Fanno Flow
Working Conditions
The Pressure Ratio, .P2 / P1, effects
Practical Examples for Subsonic Flow
The Practical Questions and Examples of Subsonic branch
Subsonic Fanno Flow for Given 4fLD and Pressure Ratio
Subsonic Fanno Flow for a Given M1 and Pressure Ratio
More Examples of Fanno Flow
The Table for Fanno Flow
Rayleigh Flow
Introduction
Governing Equations
Rayleigh Flow Tables and Figures
Examples For Rayleigh Flow
Compressible Flow 2–Dimensional
Introduction
Preface to Oblique Shock
Oblique Shock
Solution of Mach Angle
When No Oblique Shock Exist or the case of D>0
Application of Oblique Shock
Prandtl-Meyer Function
Introduction
Geometrical Explanation
Alternative Approach to Governing Equations
Comparison And Limitations between the Two Approaches
The Maximum Turning Angle
The Working Equations for the Prandtl-Meyer Function
d'Alembert's Paradox
Flat Body with an Angle of Attack
Examples For Prandtl–Meyer Function
Combination of the Oblique Shock and Isentropic Expansion
IV Special Topics
Multi–Phase Flow
Introduction
History
What to Expect From This Chapter
Kind of Multi-Phase Flow
Classification of Liquid-Liquid Flow Regimes
Co–Current Flow
Multi–Phase Flow Variables Definitions
Multi–Phase Averaged Variables Definitions
Homogeneous Models
Pressure Loss Components
Lockhart Martinelli Model
Solid–Liquid Flow
Solid Particles with Heavier Density S>L
Solid With Lighter Density S< and With Gravity
Counter–Current Flow
Horizontal Counter–Current Flow
Flooding and Reversal Flow
Multi–Phase Conclusion
Open Channel Flow
What is Open Channel Flow?
Introduction
Open Channel ``Intuition'
Energy Line
Energy conservation
Some Design Considerations
Expansion and Contraction
Summery
Hydraulic Jump
Poor Man Dimensional Analysis
Velocity Profile
Cross Section Area
Introduction
Energy For Non–Rectangular Cross–Section
Triangle Channel
General Points that Needed to be Mentioned
Qualitative Questions
Additional Examples
Mathematics For Fluid Mechanics
Vectors
Vector Algebra
Differential Operators of Vectors
Differentiation of the Vector Operations
Ordinary Differential Equations (ODE)
First Order Differential Equations
Variables Separation or Segregation
Non–Linear Equations
Second Order Differential Equations
Non–Linear Second Order Equations
Third Order Differential Equation
Forth and Higher Order ODE
A general Form of the Homogeneous Equation
Partial Differential Equations
First-order equations
Trigonometry
Index
Bibliography