Fluid Mechanics for Civil and Environmental Engineers by Ahlam I. Shalaby
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Fluid Mechanics for Civil and Environmental Engineers written by
Ahlam I. Shalaby
Excellent books exist on physics at an introductory college level so why a new one ? Why so many books exist at the same level, in the first place, and why each of them is highly appreciated. It is because each of these books has the previlege of having an author or authors who have experienced physics and have their own method of communicating with the students. During my years as a physics teacher, I have developed a somewhat different methodology of presenting physics to the students. Concepts of Physics is a translation of this methodology into a textbook.
The book presents a calculus-based physics course which makes free use of algebra, trigonometry and co-ordinate geometry. The level of the latter three topics is quite simple and high school mathematics is sufficient. Calculus is generally done at the introductory college level and I have assumed that the student is enrolled in a concurrent first calculus course. The relevant portions of calculus have been discussed in Chapter-2 so that the student may start using it from the beginning. Almost no knowledge of physics is a prerequisite. I have attempted to start each topic from the zero level. A receptive mind is all that is needed to use this book.
Basic philosophy of the book. The motto underlying the book is physics is enjoyable. Being a description of the nature around us, physics is our best friend from the day of our existence. I have extensively used this aspect of physics to introduce the physical principles starting with common clay occurrences and examples. The subject then appears to be friendly and enjoyable. I have taken care that numerical values of different quantities used in problems correspond to real situations to further strengthen this approach.
cover the following topics.
Fluid Mechanics for Civil and Environmental Engineers written by
Ahlam I. Shalaby
cover the following topics.
1. Introduction
1.1 Introduction.
1.2 Fundamental Principles of Fluid Mechanics
1.3 Types of Fluid Flow.
1.4 Dimensions and Units
1.4.1 Primary and Secondary Dimensions
1.4.1.1 Dimensions for the British Gravitational (BG) System
1.4.1.2 Dimensions for the International System (SI)
1.4.2 System of Units
1.4.2.1 Units for the British Gravitational (BG) System
1.4.2.2 Units for the International System (SI)
1.5 Pressure Scales
1.6 Standard Atmosphere
1.7 Standard Reference for Altitude, Pressure, Latitude, and Temperature
1.7.1 Standard Atmospheric Pressure for Fluid Properties
1.7.2 Variation in Temperature for Fluid Properties
1.7.3 Standard Temperature Assumed for the Reference Fluid
1.8 Newton’s Second Law of Motion
1.8.1 Acceleration due to Gravity for the British Gravitational (BG) System
1.8.2 Acceleration due to Gravity for the International System (SI)
1.9 Dynamic Forces Acting on a Fluid Element
1.10 Physical Properties of Fluids
1.10.1 Mass Density
1.10.2 Specific Gravity
1.10.3 Specific Weight
1.10.4 Viscosity
1.10.4.1 Laminar versus Turbulent Flow
1.10.4.2 Shear Stress Distribution/Profile for Laminar or Turbulent Pipe Flow
1.10.4.3 Newton’s Law of Viscosity for Laminar Flow
1.10.4.4 Dynamic Viscosity versus Kinematic Viscosity
1.10.4.5 Newton’s Law of Viscosity: Theoretically Derived Expression for Shear Stress for Laminar Flow
1.10.4.6 Empirically Derived Expression for Shear Stress for Turbulent Flow
1.10.5 Surface Tension
1.10.5.1 Definition of Surface Tension
1.10.5.2 The Formation of a Droplet in the Atmosphere
1.10.5.3 The Formation of a Droplet on a Solid Surface and Capillarity
1.10.5.4 The Formation of a Droplet on a Solid Surface
1.10.5.5 Capillarity
1.10.6 Vapor Pressure
1.10.6.1 Partial Pressure, Atmospheric Pressure, and Vapor Pressure
1.10.6.2 Evaporation, Condensation, Boiling Point, and Vapor Pressure of a Liquid
1.10.6.3 Cavitation
1.10.7 Elasticity, Compressibility, or Bulk Modulus of Elasticity
1.10.7.1 Definition of Bulk Modulus of Elasticity
1.10.7.2 Ideal Gas Law: Definition of Gas Constant and Molecular Weight
1.10.7.3 First Law of Thermodynamics: Definition of Specific Heat and Specific Heat Ratio
1.10.7.4 Determination of Bulk Modulus of Elasticity for Gases
1.10.7.5 Definition of the Sonic (Acoustic) Velocity for Fluids
1.10.7.6 Definition of the Mach Number for Fluids: A Measure of Compressibility
End-of-Chapter Problems
2. Fluid Statics
2.1 Introduction.
2.2 The Principles of Hydrostatics
2.2.1 Pascal’s Law: The Hydrostatic Pressure at a Point
2.2.2 The Hydrostatic Pressure Equation: Variation of Pressure from Point to Point
2.2.3 The Hydrostatic Pressure Head
2.2.4 The Hydrostatic Pressure Distribution
2.2.5 Application of the Principles of Hydrostatics
2.3 Measurment of Hydrostatic Pressure at a Point
2.3.1 Pressure Scales
2.3.1.1 Standard Atmospheric Pressure
2.3.2 Methods of Pressure Measurement
2.3.3 Barometers
2.3.4 Manometers
2.3.4.1 Manometry
2.3.5 Piezometer Columns/Tubes: Simplest Manometers
2.3.6 Open U-Tube Manometers: Simple Manometers
2.3.6.1 Single-Fluid Simple Manometer
2.3.6.2 Multifluid Simple Manometer
2.3.7 Differential Manometers
2.3.7.1 Single-Fluid Differential Manometer within a Single Pipe
2.3.7.2 Single-Fluid Differential Manometer between Two Pipes.
2.3.7.3 Multifluid Differential Manometer between Two Pipes
2.4 Hydrostatic Forces on Submerged Surfaces
2.4.1 The Variation of the Hydrostatic Pressure along a Surface
2.4.1.1 Variation of the Pressure Prism for a Surface Submerged in a Gas
2.4.1.2 Variation of the Pressure Prism for a Surface Submerged in a Liquid Open to the Atmosphere
2.4.1.3 Variation of the Pressure Prism for a Surface Submerged in a Liquid, Enclosed, and Pressurized
2.4.2 Magnitude and Location of the Hydrostatic Force for Plane Surfaces.
2.4.2.1 Magnitude of the Resultant Hydrostatic Force on Plane Surfaces
2.4.2.2 Location of the Resultant Hydrostatic Force on Plane Surfaces
2.4.3 Planes Submerged in a Gas
2.4.4 Planes Submerged in a Liquid Open to the Atmosphere
2.4.4.1 Submerged (h = H) Horizontal Plane (Open)
2.4.4.2 Submerged (h = yo) Vertical Plane (Open)
2.4.4.3 Submerged (h = yo sin a) Sloping Plane (Open)
2.4.5 Planes Submerged in an Enclosed and Pressurized Liquid
2.4.5.1 Submerged (h = H) Horizontal Plane (Enclosed)
2.4.5.2 Submerged (h = 0) Vertical Plane (Enclosed)
2.4.5.3 Submerged (h = yo) Vertical Plane (Enclosed)
2.4.5.4 Submerged (h = yo sin a) Sloping Plane (Enclosed)
2.4.6 Submerged Nonrectangular Planes
2.4.6.1 Submerged (h = H) Horizontal Nonrectangular Plane
2.4.6.2 Submerged (h = H) Horizontal Circular Plane
2.4.6.3 Submerged (h = H) Horizontal Triangular Plane
2.4.6.4 Submerged (h = yo) Vertical Nonrectangular Plane.
2.4.6.5 Submerged (h = yo) Vertical Circular Plane
2.4.6.6 Submerged (h = yo) Vertical Triangular Plane
2.4.6.7 Submerged (h = yo sin a) Sloping Nonrectangular Plane
2.4.6.8 Submerged (h = yo sin a) Sloping Circular Plane
2.4.6.9 Submerged (h = yo sin a) Sloping Triangular Plane
2.4.7 Magnitude and Location of the Hydrostatic Force for Curved Surfaces
2.4.7.1 Magnitude and Location of the Horizontal Component of Force on Curved Surfaces
2.4.7.2 Magnitude and Location of the Vertical Component of Force on Curved Surfaces
2.4.7.3 Magnitude and Location of the Resultant Force on Curved Surfaces
2.4.8 Magnitude and Location of the Hydrostatic Force for Surfaces Submerged in a Multilayered Fluid
2.4.8.1 Magnitude and Location of the Resultant Force Acting in First Fluid
2.4.8.2 Magnitude and Location of the Resultant Force Acting in Second Fluid
2.4.8.3 Magnitude and Location of the Resultant Force Acting in Multilayer Fluid
2.5 Buoyancy and Stability of a Floating or a Neutrally Buoyant Body
2.5.1 Buoyancy and Archimedes Principle
2.5.1.1 Magnitude and Location of the Buoyant Force
2.5.1.2 Buoyancy of a Completely Submerged Sinking Body
2.5.1.3 Buoyancy of a Completely Submerged Neutrally Buoyant Body
2.5.1.4 Buoyancy of a Partially Submerged Floating Body
2.5.1.5 The Role of the Buoyant Force in Practical Applications
2.5.2 Stability of a Floating or a Neutrally Buoyant Body
2.5.2.1 Vertical Stability of a Floating or Neutrally Buoyant Body
2.5.2.2 Rotational Stability of a Floating or Neutrally Buoyant Body
2.5.2.3 Rotational Stability of Neutrally Buoyant/Suspended Bodies
2.5.2.4 Rotational Stability of Floating Bodies
2.5.2.5 Maximum Design Angle of Rotation for a Top-Heavy Floating Body
2.5.2.6 Metacentric Height for a Top-Heavy Floating Body
2.5.2.7 Computation of the Metacentric Height and the Resulting Moment (Restoring, Overturning, or Zero) for a Top-Heavy Floating Body
End-of-Chapter Problems
3. Continuity Equation
3.1 Introduction
3.2 Fluid Kinematics
3.3 Types of Fluid Flow
3.3.1 Internal versus External Flow
3.3.2 Pressure versus Gravity Flow
3.3.3 Real versus Ideal Flow.
3.3.3.1 Laminar versus Turbulent Flow
3.3.4 Compressible versus Incompressible Flow
3.3.5 Spatially Varied (Nonuniform) versus Spatially Uniform Flow
3.3.6 Unsteady versus Steady Flow.
3.3.7 One-, Two-, and Three-Dimensional Flows
3.4 Flow Visualization/Geometry
3.4.1 Path Lines
3.4.2 Streamlines
3.4.3 Stream Tubes
3.5 Describing and Observing the Fluid Motion
3.5.1 Definition of a Fluid System: The Lagrangian Point of View
3.5.1.1 Definition of the Fluid Particle Velocity in the Lagrangian Point of View
3.5.2 Definition of a Control Volume: The Eulerian Point of View
3.5.2.1 Definition of the Fluid Particle Velocity in the Eulerian Point of View.
3.5.2.2 Fixed versus Moving Control Volume in the Eulerian Point of View.
3.5.3 Deriving One View from the Other
3.5.4 Application of the Lagrangian View versus Application of the Eulerian View
3.6 The Physical Laws Governing Fluid in Motion
3.6.1 Statement of the Governing Physical Laws Assuming a Fluid System
3.6.1.1 Extensive and Intensive Fluid Properties
3.6.2 The Reynolds Transport Theorem.
3.6.3 Statement of the Assumptions Made for the Type of Fluid Flow
3.6.3.1 The Assumption of Spatial Dimensionality of the Fluid Flow
3.6.3.2 The Modeling of Two-Dimensional Flows
3.6.3.3 The Modeling of One-Dimensional Flows
3.6.3.4 A Comparison of Velocity Profiles for Various Flow Types
3.7 Conservation of Mass: The Continuity Equation
3.7.1 The Continuity Equation
3.7.1.1 The Continuity Equation for a Fluid System
3.7.1.2 The Continuity Equation for a Control Volume
3.8 Measurement of the Volume Flowrate
End-of-Chapter Problems
4. Energy Equation .
4.1 Introduction
4.2 Fluid Dynamics
4.3 Derivation of the Energy Equation
4.4 Conservation of Momentum Principle: Newton’s Second Law of Motion
4.4.1 Newton’s Second Law of Motion for a Fluid System
4.4.2 Newton’s Second Law of Motion for a Control Volume
4.5 The Energy Equation Based on Newton’s Second Law of Motion
4.5.1 The Energy Equation for a Fluid System
4.5.2 The Energy Equation for a Control Volume
4.5.2.1 Definition of the Terms in the Energy Equation
4.5.2.2 Practical Assumptions Made for the Energy Equation
4.5.2.3 Application of the Energy Equation for Pressure Flow versus Open Channel Flow . 376
4.5.3 The Bernoulli Equation
4.5.3.1 Applications of the Bernoulli Equation
4.5.3.2 The Pitot-Static Tube: Dynamic Pressure Is Modeled by a Pressure Rise
4.5.3.3 Ideal Flow Meters, Ideal Gradual Channel Contractions, and Ideal Flow from a Tank: Dynamic Pressure Is Modeled by a Pressure Drop
4.5.3.4 The Energy Grade Line (EGL) and the Hydraulic Grade Line (HGL)
4.5.3.5 The Hydraulic Grade Line (HGL) and Cavitation
4.5.4 Application of the Energy Equation in Complement to the Momentum Equation
4.5.4.1 Application of the Governing Equations
4.5.4.2 Modeling Flow Resistance: A Subset Level Application of the Governing Equations
4.5.5 Application of the Energy and Momentum Equations for Real Internal Flow
4.5.5.1 Evaluation of the Major and Minor Head Loss Terms
4.5.5.2 Evaluation of the Pump and Turbine Head Terms
4.5.5.3 Applications of the Governing Equations for Real Internal Flow
4.5.5.4 Application of the Energy Equation for Real Pipe Flow
4.5.5.5 Application of the Energy Equation for Real Open Channel Flow
4.5.6 Application of the Energy and Momentum Equations for Ideal Internal Flow and Ideal Flow from a Tank
4.5.6.1 Evaluation of the Actual Discharge
4.5.6.2 Applications of the Governing Equations for Ideal Internal Flow and Ideal Flow from a Tank
4.5.6.3 Application of the Bernoulli Equation for Ideal Pipe Flow
4.5.6.4 Application of the Bernoulli Equation for Ideal Open Channel Flow
4.5.6.5 Applications of the Bernoulli Equation for Ideal Flow from a Tank
4.5.7 Application of the Energy and Momentum Equations for Ideal External Flow
4.5.7.1 Evaluation of the Drag Force
4.5.7.2 Applications of the Governing Equations for Ideal External Flow
4.5.7.3 Applications of the Bernoulli Equation for Ideal External Flow
4.5.8 Application of the Energy and Momentum Equations for a Hydraulic Jump
4.5.8.1 Applications of the Governing Equations for a Hydraulic Jump
4.5.8.2 Application of the Energy Equation for a Hydraulic Jump
4.6 Conservation of Energy Principle: First Law of Thermodynamics
4.6.1 Total Energy
4.6.1.1 Total Energy for a Fluid Flow System
4.6.1.2 Dimensions and Units for Energy
4.6.2 Energy Transfer by Heat.
4.6.3 Energy Transfer by Work
4.7 The Energy Equation Based on the First Law of Thermodynamics
4.7.1 The Energy Equation for a Fluid System
4.7.2 The Energy Equation for a Control Volume
4.7.2.1 The Energy Equation Expressed in Power Terms
4.7.2.2 Pump and Turbine Losses Are Modeled by Their Efficiencies
4.7.2.3 Pump, Turbine, and System Efficiencies
4.7.2.4 The Energy Equation Expressed in Energy Head Terms.
4.7.2.5 Definition of the Terms in the Energy Equation
4.7.2.6 Practical Assumptions Made for the Energy Equation.
4.7.3 Application of the Energy Equation in Complement to the Momentum Equation
4.7.4 Application of the Energy Equation for Real Internal Flow with a Pump or a Turbine
4.7.4.1 Dimensions and Units for the Pump and Turbine Head Terms
4.7.4.2 Applications of the Energy Equation for Real Internal Flow with a Pump
4.7.4.3 Applications of the Energy Equation for Real Internal Flow with a Turbine
End-of-Chapter Problems
5. Momentum Equation
5.1 Introduction
5.2 Derivation of The Momentum Equation
5.2.1 The Momentum Equation for a Fluid System: Differential Form of the Momentum Equation
5.2.1.1 Differential Form of the Momentum Equation
5.2.1.2 Application of the Differential Form of the Momentum Equation
5.2.2 The Momentum Equation for a Control Volume: Integral Form of the Momentum Equation
5.2.2.1 Fixed versus Moving Control Volume in the Eulerian (Integral) Point of View
5.2.2.2 Application of the Integral Form of the Momentum Equation
5.3 Application of the Energy Equation in Complement to the Momentum Equation
5.3.1 Application of the Governing Equations
5.3.2 Modeling Flow Resistance: A Subset Level Application of the Governing Equations
5.3.3 Application of the Energy and Momentum Equations for Real Internal Flow
5.3.3.1 Evaluation of the Major and Minor Head Loss Terms
5.3.3.2 Evaluation of the Pump and Turbine Head Terms
5.3.3.3 Applications of the Governing Equations for Real Internal Flow
5.3.3.4 Applications of the Governing Equations for Real Internal Flow: Differential Fluid Element
5.3.3.5 Applications of the Governing Equations for Real Internal Flow: Finite Control Volume
5.3.4 Application of the Energy and Momentum Equations for Ideal Internal Flow and Ideal Flow from a Tank
5.3.4.1 Evaluation of the Actual Discharge
5.3.4.2 Applications of the Governing Equations for Ideal Internal Flow and Ideal Flow from a Tank
5.3.4.3 Applications of the Governing Equations for Ideal Pipe Flow
5.3.4.4 Applications of the Governing Equations for Ideal Open Channel Flow
5.3.4.5 Applications of the Governing Equations for Ideal Flow from a Tank
5.3.5 Application of the Energy and Momentum Equations for Ideal External Flow
5.3.5.1 Evaluation of the Drag Force
5.3.5.2 Applications of the Governing Equations for Ideal External Flow
5.3.6 Application of the Energy and Momentum Equations for a Hydraulic Jump
5.3.6.1 Applications of the Governing Equations for a Hydraulic Jump
End-of-Chapter Problems
6. Flow Resistance Equations
6.1 Introduction
6.1.1 Modeling Flow Resistance: A Subset Level Application of the Governing Equations
6.1.2 Derivation of the Flow Resistance Equations and the Drag Coefficients
6.1.2.1 Empirical Evaluation of the Drag Coefficients and Application of the Flow Resistance Equations
6.1.3 Modeling the Flow Resistance as a Loss in Pump and Turbine Efficiency in Internal Flow
6.2 Types of Flow.
6.2.1 Internal Flow versus External Flow
6.2.2 Pipe Flow versus Open Channel Flow.
6.2.3 Real Flow versus Ideal Flow.
6.2.4 Ideal Flow. 649
6.2.4.1 Ignoring the Flow Resistance in Ideal Flow
6.2.4.2 Subsequently Modeling the Flow Resistance in Ideal Flow
6.2.4.3 The Pitot-Static Tube: Dynamic Pressure Is Modeled by a Pressure Rise
6.2.4.4 The Venturi Meter: Dynamic Pressure Is Modeled by a Pressure Drop.
6.2.5 Real Flow 654
6.2.5.1 Directly and Subsequently Modeling the Flow Resistance in Real Flow
6.2.5.2 Directly Modeling the Flow Resistance in Real Flow.
6.2.5.3 Laminar Flow versus Turbulent Flow
6.2.5.4 The Velocity Profiles for Laminar and Turbulent Internal Flows
6.2.5.5 Developing Flow versus Developed Flow
6.3 Modeling the Flow Resistance as a Drag Force in External Flow.
6.3.1 Evaluation of the Drag Force
6.3.2 Application of the Bernoulli Equation: Derivation of the Ideal Velocity
6.3.3 Application of the Momentum Equation and Dimensional Analysis: Derivation of the Actual Velocity, Drag Force Equation, and the Drag Coefficient
6.3.4 Modeling the Drag Force in the Momentum Equation
6.3.4.1 Submerged Stationary Body in a Stationary Real or Ideal Fluid
6.3.4.2 Submerged Moving Body in a Stationary Ideal Fluid
6.3.4.3 Submerged Moving Body in a Stationary Real Fluid.
6.3.5 Supplementing the Momentum Equation with Dimensional Analysis: Derivation of the Drag Force and the Drag Coefficient
6.4 Modeling the Flow Resistance as a Major Head Loss in Internal Flow.
6.4.1 Evaluation of the Major Head Loss
6.4.2 Application of the Energy Equation: Derivation of the Head Loss.
6.4.3 Application of the Momentum Equations and Dimensional Analysis: Derivation of the Pressure Drop, Shear Stress, and the Drag Coefficient.
6.4.4 Application of the Governing Equations to Derive the Major Head Loss Equations for Laminar and Turbulent Flow
6.5 Laminar and Turbulent Internal Flow Characteristics
6.5.1 Determining the Variation of Shear Stress with Radial Distance for Laminar and Turbulent Flow
6.5.2 The Variation of the Velocity with Time for Laminar and Turbulent Flow
6.5.3 The Variation of the Velocity, Pressure Drop, and the Wall Shear Stress with Length of Pipe for Laminar and Turbulent Flow: Developing versus Developed Flow
6.5.3.1 The Extent of Developing Flow in the Pipe Length
6.5.3.2 The Variation of the Velocity Profile with Pipe Length
6.5.3.3 The Variation of the Pressure Drop and the Wall Shear Stress with Pipe Length
6.5.3.4 Laminar versus Turbulent Flow
6.6 Derivation of the Major Head Loss Equation for Laminar Flow
6.6.1 Application of the Integral Form of the Momentum Equation: Deriving the Velocity Profile for Laminar Flow
6.6.2 Application of the Differential form of the Continuity Equation: Deriving Poiseuille’s Law
6.6.3 Substituting Poiseuille’s Law into the Integral Form of the Energy Equation: Deriving the Major Head Loss Equation for Laminar Flow (Poiseuille’s Law)
6.6.4 Interpretation of Poiseuille’s Law Expressed in Terms of the Pressure Drop
6.7 Derivation of the Major Head Loss Equation for Turbulent Flow
6.7.1 Application of the Integral Momentum Equation: Deriving an Expression for the Pressure Drop
6.7.2 Application of the Differential Momentum Equation: Interpreting the Friction Slope in Turbulent Flow
6.7.3 Application of Dimensional Analysis: Empirically Interpreting Friction Slope (Empirically Deriving an Expression for Wall Shear Stress) in Turbulent Flow
6.7.3.1 Derivation of an Empirical Expression for the Wall Shear Stress as a Function of the Velocity
6.7.3.2 Derivation of the Chezy Equation and Evaluation of the Chezy Coefficient, C
6.7.3.3 Application of the Chezy Equation.
6.7.4 Substituting the Chezy Equation into the Integral Form of the Energy Equation: Deriving the Major Head Loss Equation for Turbulent Flow
6.7.5 The Darcy–Weisbach Equation
6.7.5.1 Derivation of the Darcy–Weisbach Friction Coefficient, f
6.7.5.2 Evaluation of the Darcy–Weisbach Friction Coefficient, f
6.7.5.3 The Darcy–Weisbach Head Loss Equation
6.7.6 Manning’s Equation
6.7.6.1 Derivation and Evaluation of the Manning’s Roughness Coefficient, n
6.7.6.2 Manning’s Equation
6.7.6.3 Manning’s Head Loss Equation
6.7.7 The Hazen–Williams Equation
6.7.7.1 The Hazen–Williams Equation.
6.7.7.2 Evaluation of the Hazen–Williams Equation Roughness Coefficient, Ch
6.7.7.3 The Hazen–Williams Head Loss Equation
6.7.8 The Relationship between the Drag Coefficient, CD; the Chezy Coefficient, C; the Darcy–Weisbach Friction Factor, f; and Manning’s Roughness Coefficient, n.
6.7.9 A Comparison between Laminar and Turbulent Flow Using the Darcy–Weisbach Head Loss Equation
6.7.9.1 The Darcy–Weisbach Head Loss Equation and the Reynolds Number, R for Noncircular Pipes
6.7.9.2 Evaluating the Darcy–Weisbach Friction Coefficient, f for Laminar Pipe Flow
6.7.9.3 A Comparison between Laminar and Turbulent Flow Using the Darcy–Weisbach Head Loss Equation
6.7.10 Determining the Velocity Profile for Turbulent Flow
6.7.10.1 A Comparison between the Velocity Profiles for Laminar Flow and Turbulent Flow
6.7.10.2 The Role of the Boundary Roughness in Laminar Flow and Turbulent Flow
6.7.11 Application of the Major Head Loss Equation for Open Channel Flow
6.7.11.1 Application of the Chezy Equation for Open Channel Flow
6.8 Modeling the Flow Resistance as a Minor Head Loss in Pipe Flow
6.8.1 Evaluation of the Minor Head Loss
6.8.2 Application of the Energy Equation: Derivation of the Head Loss
6.8.3 Application of the Momentum Equation and Dimensional Analysis: Derivation of the Pressure Drop, Shear Stress, and the Drag Coefficient
6.8.4 Analytical Derivation of the Minor Head Loss Equation due to a Sudden Pipe Expansion
6.8.5 Empirical Derivation of the Minor Head Loss Equation due to Pipe Components in General
6.8.5.1 Application of the Energy Equation: Derivation of the Head Loss
6.8.5.2 Application of the Momentum Equation and Dimensional Analysis: Derivation of the Pressure Drop, Shear Stress, and the Drag Coefficient
6.8.5.3 Evaluation of the Minor Head Loss Coefficient, k
6.9 Modeling the Flow Resistance as a Loss in Flowrate in Internal Flow
6.9.1 Evaluation of the Actual Discharge
6.9.2 Application of the Bernoulli Equation: Derivation of the Ideal Velocity
6.9.3 Application of the Continuity Equation: Derivation of the Ideal Discharge and the Actual Discharge
6.9.4 Application of the Momentum Equation and Dimensional Analysis: Derivation of the Actual Velocity, Actual Area, Actual Discharge, and the Discharge Coefficient
6.9.4.1 Supplementing the Momentum Equation with Dimensional Analysis: Derivation of the Reduced/Actual Discharge Equation for Pipe Flow
6.9.4.2 Supplementing the Momentum Equation with Dimensional Analysis: Derivation of the Reduced/Actual Discharge Equation for Open Channel Flow
6.9.5 A Comparison of the Velocity Profiles for Ideal and Real Flows
6.10 Modeling the Flow Resistance as a Loss in Pump and Turbine Efficiency in Internal Flow
6.10.1 Evaluation of the Efficiency of Pumps and Turbines
6.10.1.1 Supplementing the Momentum Equation with Dimensional Analysis: Derivation of the Efficiency of Pumps and Turbines
End-of-Chapter Problems
7. Dimensional Analysis
7.1 Introduction.749
7.1.1 The Role of Dimensional Analysis in the Modeling of Fluid Flow
7.1.2 The Role of Dimensional Analysis in the Empirical Modeling of Flow Resistance in Real Fluid Flow
7.1.2.1 Modeling of Flow Resistance in Real Fluid Flow
7.1.2.2 Using Dimensional Analysis in the Empirical Modeling of Flow Resistance in Real Fluid Flow
7.1.3 Flow Types and Dimensional Analysis
7.1.4 Internal Flow versus External Flow
7.1.5 Modeling Flow Resistance: A Subset Level Application of the Governing Equations
7.1.6 Supplementing the Momentum Theory with Dimensional Analysis
7.1.7 Derivation of the Flow Resistance Equations and the Drag Coefficients
7.1.7.1 Empirical Evaluation of the Drag Coefficients and Application of the Flow Resistance Equations
7.1.8 Derivation of the Efficiency of Pumps and Turbines
7.2 Dimensional Analysis of Fluid Flow
7.2.1 Dynamic Forces Acting on a Fluid Element
7.2.2 Two-Dimensional Systems
7.2.3 Deriving a Functional Relationship/Dimensionless Numbers
7.2.4 Main Pi Terms. 761
7.2.5 The Definition of New Pi Terms
7.2.6 Guidelines in the Derivation of the Flow Resistance Equations and the Drag Coefficients
7.2.7 The Definition of the Drag Coefficient
7.2.8 Guidelines in the Derivation of the Efficiency of Pumps and Turbines
7.2.9 The Definition of the Pump (or Turbine) Efficiency
7.2.10 Specific Guidelines and Summary in the Application of Dimensional Analysis for Example Problems and End-of-Chapter Problems
7.3 Modeling the Flow Reistance as a Drag Force in External Flow
7.3.1 Evaluation of the Drag Force
7.3.2 Application of the Bernoulli Equation: Derivation of the Ideal Velocity
7.3.3 Application of the Momentum Equation and Dimensional Analysis: Derivation of the Actual Velocity, Drag Force Equation, and the Drag Coefficient
7.3.3.1 Application of Dimensional Analysis: Derivation of the Drag Force and the Drag Coefficient
7.3.3.2 Application of Dimensional Analysis to Derive the Drag Force and Drag Coefficient for More Specific Assumptions of External Flow
7.3.4 Derivation of the Lift Force and the Lift Coefficient . 791
7.4 Modeling the Flow Resistance as a Major Head Loss in Internal Flow
7.4.1 Evaluation of the Major Head Loss
7.4.2 Application of the Energy Equation: Derivation of the Head Loss
7.4.3 Application of the Momentum Equations and Dimensional Analysis: Derivation of the Pressure Drop, Shear Stress, and the Drag Coefficient
7.4.4 Derivation of the Major Head Loss Equation for Laminar Flow
7.4.5 Derivation of the Major Head Loss Equation for Turbulent Flow
7.4.5.1 Application of Dimensional Analysis: Derivation of the Wall Shear Stress and Drag Coefficient in Turbulent Flow
7.4.5.2 Derivation of the Chezy Equation and Evaluation of the Chezy Coefficient, C 804
7.4.5.3 Substituting the Chezy Equation into the Energy Equation: Deriving the Major Head Loss Equation for Turbulent Flow
7.4.6 The Darcy–Weisbach Equation
7.4.6.1 Derivation of the Darcy–Weisbach Friction Coefficient, f
7.4.6.2 Evaluation of the Darcy–Weisbach Friction Coefficient, f
7.4.6.3 The Darcy–Weisbach Head Loss Equation.
7.4.6.4 Evaluating the Darcy–Weisbach Friction Coefficient, f for Laminar Pipe Flow
7.4.7 Manning’s Equation
7.4.7.1 Derivation and Evaluation of the Manning’s Roughness Coefficient, n
7.4.7.2 Manning’s Equation
7.4.7.3 Manning’s Head Loss Equation
7.4.8 Application of the Major Head Loss Equation for Open Channel Flow
7.4.8.1 Interpretation of the Results of Dimensional Analysis for Open Channel Flow
7.4.8.2 Application of the Chezy Equation for Open Channel Flow
7.4.8.3 Application of the Darcy–Weisbach Equation for Open Channel Flow
7.4.8.4 Application of Manning’s Equation for Open Channel Flow
7.4.9 Application of Dimensional Analysis to Derive the Wall Shear Stress and Drag Coefficient for More Specific Assumptions of Internal Flow
7.5 Modeling the Flow Resistance as a Minor Head Loss in Pipe Flow
7.5.1 Evaluation of the Minor Head Loss
7.5.2 Application of the Energy Equation: Derivation of the Head Loss.
7.5.3 Application of the Momentum Equation and Dimensional Analysis: Derivation of the Pressure Drop, Shear Stress, and the Drag Coefficient
7.5.4 Analytical Derivation of the Minor Head Loss Equation due to a Sudden Pipe Expansion
7.5.5 Empirical Derivation of the Minor Head Loss Equation due to Pipe Components in General.
7.5.5.1 Application of Dimensional Analysis: Derivation of the Pressure Drop and Drag Coefficient for Pipe Components in General
7.5.5.2 Substituting the Pressure Drop into the Energy Equation: Deriving the Minor Head Loss Equation for Pipe Components in General
7.5.5.3 Evaluation of the Minor Head Loss Coefficient, k
7.5.5.4 Application of Dimensional Analysis to Derive the Pressure Drop and Drag Coefficient for More Specific Assumptions for Pipe Flow Components
7.6 Modeling the Flow Resistance as a Loss in Flowrate in Internal Flow
7.6.1 Evaluation of the Actual Discharge
7.6.2 Application of the Bernoulli Equation: Derivation of the Ideal Velocity
7.6.3 Application of the Continuity Equation: Derivation of the Ideal Discharge and the Actual Discharge
7.6.4 Application of the Momentum Equation and Dimensional Analysis: Derivation of the Actual Velocity, Actual Area, Actual Discharge, and the Discharge Coefficient
7.6.4.1 Application of Dimensional Analysis: Derivation of the Reduced/Actual Discharge and Drag Coefficient for Pipe Flow Measuring Devices
7.6.4.2 Application of Dimensional Analysis: Derivation of the Reduced/Actual Discharge and Drag Coefficient for Open Channel Flow-Measuring Devices
7.6.4.3 Application of Dimensional Analysis to Derive the Reduced/Actual Discharge and Drag Coefficient for More Specific Assumptions for Open Channel Flow-Measuring Devices
7.7 Modeling the Flow Resistance as a Loss in Pump and Turbine Efficiency in Internal Flow
7.7.1 Evaluation of the Efficiency of Pumps and Turbines
7.7.1.1 Application of Dimensional Analysis: Derivation of the Efficiency of Pumps and Turbines
7.7.1.2 Application of Dimensional Analysis to Derive the Efficiency of Pumps and Turbines for More Specific Flow Assumptions
7.8 Experimental Formulation of Theoretical Equations
End-of-Chapter Problems 901
8. Pipe Flow
8.1 Introduction
8.2 Application of the Eulerian (Integral) versus Lagrangian (Differential) Forms of the Governing Equations
8.2.1 Eulerian (Integral) Approach for Pipe Flow Problems
8.2.2 Lagrangian (Differential) Approach for Pipe Flow Problems
8.3 Modeling Flow Resistance in Pipe Flow: A Subset Level Application of the Governing Equations
8.4 Application of the Governing Equations in Pipe Flow
8.4.1 Application of the Governing Equations for Real Pipe Flow
8.4.1.1 Integral Approach for Real Pipe Flow Problems
8.4.1.2 Evaluation of the Major and Minor Head Loss Terms
8.4.1.3 Evaluation of the Pump and Turbine Head Terms
8.4.1.4 Differential Approach for Real Pipe Flow Problems
8.4.1.5 Applications of the Governing Equations for Real Pipe Flow Problems
8.4.2 Application of the Governing Equations for Ideal Pipe Flow
8.4.2.1 Evaluation of the Actual Discharge
8.4.2.2 Applications of the Governing Equations for Ideal Pipe Flow
8.5 Single Pipes: Major Head Loss in Real Pipe Flow
8.5.1 Evaluation of the Major Head Loss Term in the Energy Equation
8.5.1.1 Laminar Pipe Flow: Poiseuille’s Law
8.5.1.2 Turbulent Pipe Flow: The Chezy Equation
8.5.2 Turbulent Pipe Flow Resistance Equations and Their Roughness Coefficients
8.5.2.1 A Comparison of the Three Standard Empirical Flow Resistance Coefficients
8.5.2.2 A Comparison between Manning’s and Hazen–Williams Roughness Coefficients
8.5.2.3 Turbulent Pipe Flow Resistance Equations
8.5.3 The Darcy–Weisbach Friction Coefficient, f and the Darcy–Weisbach Equation
8.5.3.1 Evaluation of the Darcy–Weisbach Friction Coefficient, f
8.5.3.2 Application of the Darcy–Weisbach Equation
8.5.4 Manning’s Roughness Coefficient, n and Manning’s Equation
8.5.4.1 Application of Manning’s Equation
8.5.5 The Hazen–Williams Roughness Coefficient, Ch and the Hazen–Williams Equation
8.5.5.1 Application of the Hazen–Williams Equation
8.6 Pipes with Components: Minor Head Losses and Reaction Forces in Real Pipe Flow
8.6.1 Evaluation of the Minor Head Loss Term in the Energy Equation
8.6.1.1 Evaluation of the Minor Head Loss
8.6.1.2 Derivation of the Minor Head Loss Coefficient, k
8.6.1.3 Evaluation of the Minor Head Loss Coefficient, k
8.6.2 Alternative Modeling of the Minor Head Loss Term in the Energy Equation
8.6.3 Evaluation of the Minor Head Loss due to Pipe Components
8.6.4 Minor Losses in Valves and Fittings (Tees, Unions, Elbows, and Bends)
8.6.4.1 Valves
8.6.4.2 Fittings (Tees, Unions, Elbows, and Bends)
8.6.5 Minor Losses in Entrances, Exits, Contractions, and Expansions
8.6.5.1 Pipe Entrances
8.6.5.2 Pipe Exists
8.6.5.3 Sudden Pipe Expansions
8.6.5.4 Sudden Pipe Contractions
8.6.5.5 Gradual Pipe Expansions
8.6.5.6 Gradual Pipe Contractions
8.6.6 Reaction Forces on Pipe Components
8.7 Pipe Systems: Major and Minor Head Losses in Real Pipe Flow
8.7.1 Single Pipes
8.7.2 Pipes with Components
8.7.3 Pipes with a Pump or a Turbine
8.7.4 Pipes in Series
8.7.5 Pipes in Parallel
8.7.6 Branching Pipes
8.7.6.1 Branching Pipes Connected to Three Reservoirs
8.7.6.2 Branching Pipes Connected to a Water Supply Source under Pressure
8.7.7 Pipes in a Loop
8.7.8 Pipe Networks
8.7.8.1 Continuity Principle
8.7.8.2 Energy Principle
8.7.8.3 Momentum Principle
8.7.8.4 Summary of Governing Equations for Pipe Networks
8.8 Pipe Flow Measurement and Control Devices: Actual Flowrate in Ideal Flow Meters
8.8.1 Evaluation of the Actual Flowrate for Ideal Flow Meters in Pipe Flow
8.8.1.1 Derivation of the Discharge Coefficient, Cd
8.8.1.2 Evaluation of the Discharge Coefficient, Cd
8.8.2 Evaluation of the Actual Flowrate for a Pitot-Static Tube
8.8.3 Evaluation of the Actual Flowrate for Orifice, Nozzle, and Venturi Meters
8.8.3.1 Evaluation of the Actual Flowrate for an Orifice, a Nozzle, or a Venturi Meter
8.8.3.2 Actual Flowrate for an Orifice Meter
8.8.3.3 Actual Flowrate for a Nozzle Meter
8.8.3.4 Actual Flowrate for a Venturi Meter
8.8.3.5 Evaluation of the Minor Head Loss due to an Orifice, a Nozzle, or a Venturi Meter
End-of-Chapter Problems
9. Open Channel Flow
9.1 Introduction
9.2 Application of the Eulerian (Integral) versus Lagrangian (Differential) Forms of the Governing Equations
9.2.1 Eulerian (Integral) Approach for Open Channel Flow Problems
9.2.2 Lagrangian (Differential) Approach for Open Channel Flow Problems
9.3 The Occurrence of a Major Head Loss in Open Channel Flow
9.4 Modeling Flow Resistance in Open Channel Flow: A Subset Level Application of the Governing Equations
9.5 Application of the Governing Equations in Open Channel Flow
9.5.1 Application of the Governing Equations for Real Open Channel Flow
9.5.1.1 Integral Approach for Real Open Channel Flow Problems
9.5.1.2 Evaluation of the Major Head Loss Term
9.5.1.3 Evaluation of the Pump and Turbine Head Terms
9.5.1.4 Differential Approach for Real Open Channel Flow Problems
9.5.1.5 Applications of the Governing Equations for Real Open Channel Flow
9.5.2 Application of the Governing Equations for Ideal Open Channel Flow
9.5.2.1 Evaluation of the Actual Discharge
9.5.2.2 Applications of the Governing Equations for Ideal Open Channel Flow
9.5.3 Application of the Governing Equations for a Hydraulic Jump
9.6 Major Head Loss due to Flow Resistance in Real Open Channel Flow
9.6.1 Uniform versus Nonuniform Open Channel Flow
9.6.2 Evaluation of the Major Head Loss Term in the Energy Equation
9.6.3 The Chezy Equation and Evaluation of the Chezy Coefficient, C
9.6.4 Turbulent Channel Flow Resistance Equations and Their Roughness Coefficients
9.6.5 Manning’s Equation and Evaluation of Manning’s Roughness Coefficient, n
9.7 Flow Type (State) and Flow Regime
9.7.1 The Role and Significance of Uniform Flow
9.7.2 The Definition of Flow Regimes for Uniform Flow
9.7.3 The Occurrence of Nonuniform Flow and Changes in the Flow Regime
9.8 Transitions and Controls in Open Channel Flow
9.8.1 The Definition of a Control in Open Channel Flow
9.8.1.1 The Occurrence of Critical Flow at Controls
9.8.2 The Definition of a Flow-Measuring Device in Open Channel Flow
9.9 Energy Concepts in Open Channel Flow
9.9.1 Hydrostatic Pressure Distribution
9.9.2 Deviation from a Hydrostatic Pressure Distribution
9.9.2.1 Sharp-Crested Weir and Free Overfall
9.9.3 Specific Energy in Open Channel Flow
9.9.4 Specific Energy for Rectangular Channel Cross Sections
9.9.4.1 The Specific Energy Curve for Rectangular Channel Sections
9.9.4.2 Derivation of Critical Flow for Rectangular Channel Sections
9.9.4.3 The Depth–Discharge Curve for Rectangular Cross Sections
9.9.5 Specific Energy for Nonrectangular Channel Cross Sections
9.9.5.1 Derivation of Critical Flow for Nonrectangular Channel Sections
9.9.6 Subcritical and Supercritical Flow
9.9.7 Analysis of the Occurrence of Critical Flow at Controls
9.9.7.1 Critical Flow at Controls due to an Abrupt/Maximum Vertical Constriction
9.9.7.2 Critical Flow at Controls due to an Abrupt/Maximum Horizontal Constriction
9.9.7.3 Critical Flow at Controls due to a Change in Channel Bottom Slope
9.9.8 Analysis of the Occurrence of Uniform Flow as a Control
9.10 Momentum Concepts in Open Channel Flow
9.10.1 The Momentum Function
9.10.1.1 The Use of Controls in the Formation of a Hydraulic Jump
9.10.1.2 Definition of the Momentum Function for Rectangular Channel Sections
9.10.1.3 The Momentum Function Curve for Rectangular Channel Sections
9.10.1.4 Definition of the Momentum Function for Nonrectangular Channel Sections
9.11 Geometric Properties of Some Common Channel Sections
9.11.1 Geometric Properties of Rectangular Channel Sections
9.11.2 Geometric Properties of Trapezoidal Channel Sections
9.11.3 Geometric Properties of Triangular Channel Sections
9.11.4 Geometric Properties of Partially Filled Circular Channel Sections
9.12 Flow Depth and Reaction Force for Short Channel Transitions in Open Channel Flow: Ideal Flow
9.12.1 Flow Depth for Gradual Channel Transitions: Not Controls
9.12.1.1 Flow Depth for a Gradual Upward Step
9.12.1.2 Flow Depth for a Gradual Decrease in Channel Width
9.12.2 Flow Depth for Abrupt Channel Transitions: Controls
9.12.2.1 Flow Depth for an Abrupt Upward Step
9.12.2.2 Flow Depth for an Abrupt Decrease in Channel Width
9.12.2.3 Flow Depth for Typical Flow-Measuring Devices
9.12.3 Reaction Force on Open Channel Flow Structures/Controls (Abrupt Flow Transitions and Flow-Measuring Devices)
9.13 Flow Depth and Major Head Loss for a Hydraulic Jump in Open Channel Flow
9.13.1 Critical Flow at the Hydraulic Jump
9.13.2 Derivation of the Hydraulic Jump Equations: Rectangular Channel Sections
9.13.3 Numerical Solution for a Hydraulic Jump: Nonrectangular Channel Sections
9.13.4 Computation of the Major Head Loss due to a Hydraulic Jump
9.14 Flow Depth and Major Head Loss in Uniform Open Channel Flow: Real Flow
9.15 Flow Depth and Major Head Loss in Nonuniform Open Channel Flow: Real Flow
9.16 Actual Flowrate in Flow Measrurement and Control Devices in Open Channel Flow: Ideal Flow Meters
9.16.1 Flow-Measuring Devices in Open Channel Flow
9.16.1.1 Ideal Flow Meters
9.16.1.2 Critical Depth Meters
9.16.2 Controls Serving as Flow Measurement Devices in Open Channel Flow
9.16.2.1 Determination of the Depth–Discharge Relationship for Controls Serving as Flow-Measuring Devices
9.16.2.2 Deviations from the Assumptions for Critical Flow in Controls Serving as Flow-Measuring Devices
9.16.2.3 Applied Depth–Discharge Relationship for Ideal versus Critical Flow Meters
9.16.3 Actual Flowrate for Ideal Flow Meters
9.16.4 Actual Flowrate for Critical Flow Meters
9.16.5 A Comparison between Ideal Flow Meters and Critical Depth Meters
9.16.5.1 Advantages of Critical Depth Meters
9.16.5.2 Disadvantages of Critical Depth Meters
9.16.5.3 Ideal Flow Meters: Typical Flow-Measuring Devices
9.17 Evaluation of the Actual Flowrate for Ideal Flow Meters in Open Channel Flow
9.17.1 Evaluation of the Actual Flowrate for Ideal Flow Meters
9.17.1.1 Application of the Bernoulli Equation
9.17.1.2 Application of the Continuity Equation, the Momentum Equation, and Dimensional Analysis
9.17.1.3 Derivation of the Discharge Coefficient, Cd
9.17.1.4 Evaluation of the Discharge Coefficient, Cd
9.17.2 Sluice Gates, Weirs, Spillways, Venturi Flumes, and Contracted Openings in Open Channel Flow
9.17.3 Evaluation of the Actual Flowrate for a Sluice Gate
9.17.4 Evaluation of the Actual Flowrate for a Sharp-Crested Weir
9.17.4.1 Rectangular Sharp-Crested Weir
9.17.4.2 Triangular Sharp-Crested Weir
9.17.4.3 A Comparison between a Rectangular and a Triangular Sharp-Crested Weir
9.17.5 Evaluation of the Actual Flowrate for a Spillway
9.17.6 Evaluation of the Actual Flowrate for a Broad-Crested Weir
9.17.7 Evaluation of the Actual Flowrate for the Parshall Flume (Venturi Flume)
9.17.8 Evaluation of the Actual Flowrate for a Contracted Opening
End-of-Chapter Problems
10. External Flow
10.1 Introduction
10.1.1 Occurrence and Illustration of the Drag Force and the Lift Force
10.2 Application of the Eulerian (Integral) versus Lagrangian (Differential) Forms of the Governing Equations
10.3 Modeling Flow Resistance in External Flow: A Subset Level Application of the Governing Equations
10.4 Application of the Governing Equations in External Flow
10.4.1 Application of the Governing Equations for Ideal External Flow
10.4.1.1 Evaluation of the Drag Force
10.5 The Drag Force and the Lift Force in External Flow
10.5.1 Evaluation of the Drag Force in External Flow
10.5.1.1 Modeling the Drag Force in the Momentum Equation
10.5.1.2 Derivation of the Drag Coefficient, CD
10.5.2 Determination of the Drag Coefficient, CD
10.5.3 Evaluation of the Drag Coefficient, CD
10.5.3.1 The Role of the Velocity of Flow
10.5.3.2 The Role of the Shape of the Body
10.5.3.3 Reducing the Total Drag Force by Optimally Streamlining the Body
10.5.3.4 The Occurrence of Flow Separation
10.5.3.5 Reducing the Flow Separation (Pressure Drag)
10.5.3.6 The Importance of the Reynolds Number, R
10.5.3.7 Creeping Flow (R = 1) for Any Shape Body, and Stokes Law for a Spherical Shaped Body
10.5.3.8 Laminar and Turbulent Flow for Any Shape Body except Round-Shaped Bodies
10.5.3.9 Laminar and Turbulent Flow for Round-Shaped Bodies (Circular Cylinder or Sphere)
10.5.3.10 Laminar and Turbulent Flow with Wave Action at the Free Surface for Any Shape
10.5.3.11 The Importance of the Relative Surface Roughness.1362
10.5.3.12 The Importance of the Mach Number, M
10.5.3.13 The Importance of the Froude Number, F
10.5.4 Evaluation of the Lift Force in External Flow
10.5.5 Evaluation of the Lift Coefficient
10.5.5.1 The Role of the Shape of the Body and the Angle of Attack
10.5.5.2 Optimizing the Shape of an Airfoil and the Angle of Attack
10.5.5.3 Optimizing the Performance of an Airfoil
10.5.5.4 Optimizing the Shape of an Airfoil by the Use of Flaps
10.5.5.5 Optimizing the Shape of an Airfoil by the Aspect Ratio
10.5.6 Estimating the Lift Force and Lift Coefficient for a Hot-Air Balloon
End-of-Chapter Problems
11. Dynamic Similitude and Modeling
11.1 Introduction
11.1.1 The Role of Dynamic Similitude in the Modeling of Fluid Flow
11.1.2 The Role of Dynamic Similitude in the Empirical Modeling of Flow Resistance in Real Fluid Flow
11.1.2.1 Using Dynamic Similitude in the Empirical Modeling of Flow Resistance in Real Fluid Flow
11.1.3 Developing and Applying the Laws of Dynamic Similitude to Design Geometrically Scaled Physical Models of Real Fluid Flow
11.2 Primary Scale Ratios
11.2.1 Geometric Similarity
11.2.2 Kinematic Similarity
11.2.3 Dynamic Similarity
11.3 Interpretation of the Main p Terms
11.3.1 The Euler Number
11.3.2 The Froude Number
11.3.3 The Reynolds Number
11.3.4 The Cauchy Number
11.3.5 The Weber Number
11.3.6 Implications of the Definitions of the Main p Terms
11.4 Laws Governing Dynamic Similirity: Secondary/Similitude Scale Ratios
11.4.1 Similitude Scale Ratios for Physical Quantities
11.4.2 Similitude Scale Ratios for Physical Properties of Fluids
11.5 The Role and the Relative Importance of the Dynamic Forces in Dynamic Similitude
11.6 Guidelines in the Application of the Laws Governing Dynamic Similarity
11.6.1 Definition of the Flow Resistance Prediction Equations (or Equations for Any Other Physical Quantity)
11.6.2 Definition of the Dynamic Similarity Requirements
11.6.3 “True Models” versus “Distorted Models”
11.6.4 General Guidelines in the Application of “Distorted Models”
11.7 Application of the Laws Governing Dynamic Similarity for Flow Resistance Equations and Efficiency of Pumps and Turbines
11.7.1 Specific Guidelines in the Application of “Distorted Models”
11.7.1.1 Geometry Similarity Requirements
11.7.1.2 Relative Roughness Similarity Requirements
11.7.1.3 “Pressure Model” Similarity Requirements
11.7.1.4 “Viscosity Model” Similarity Requirements
11.7.1.5 “Elastic Model” Similarity Requirements
11.7.1.6 “Gravity Model” Similarity Requirements
11.7.1.7 “Surface Tension Model” Similarity Requirements
11.7.1.8 “Viscosity Model” and “Elastic Model” Similarity Requirements
11.7.1.9 “Viscosity Model” and “Gravity Model” Similarity Requirements
11.7.1.10 “Viscosity Model” and “Surface Tension Model” Similarity Requirements
11.7.1.11 “Gravity Model,” “Viscosity Model,” and “Surface Tension Model” Similarity Requirements
11.7.2 Application of the Similitude Scale Ratios for the Drag Force in External Flow
11.7.2.1 Creeping Flow (R = 1) for Any Shape Body
11.7.2.2 Laminar Flow (R , 10,000) for Any Shape Body except Round-Shaped Bodies
11.7.2.3 Turbulent Flow (R . 10,000) for Any Shape Body except Round-Shaped Bodies
11.7.2.4 Laminar and Turbulent Flow for Round-Shaped Bodies (Circular Cylinder or Sphere)
11.7.2.5 Laminar and Turbulent Flow with Wave Action at the Free Surface for Any Shape Body
11.7.3 Application of the Similitude Scale Ratios for the Major Head Loss in Pipe Flow
11.7.3.1 Laminar Pipe Flow
11.7.3.2 Completely Turbulent Pipe Flow (Rough Pipes)
11.7.3.3 Transitional Pipe Flow
11.7.4 Application of the Similitude Scale Ratios for the Major Head Loss in Open Channel Flow
11.7.4.1 Turbulent Open Channel Flow
11.7.5 Application of the Similitude Scale Ratios for the Minor Head Loss in Pipe Flow
11.7.5.1 Turbulent Pipe Flow with Pipe Component
11.7.6 Application of the Similitude Scale Ratios for the Actual Discharge in Pipe Flow
11.7.6.1 Pipe Flow with a Flow-Measuring Device
11.7.7 Application of the Similitude Scale Ratios for the Actual Discharge in Open Channel Flow
11.7.7.1 Open Channel Flow with Sluice Gate or Venturi Meter
11.7.7.2 Open Channel Flow with Weir or Spillway with Large Head
11.7.7.3 Open Channel Flow with Weir or Spillway with Small Head
11.7.8 Application of the Similitude Scale Ratios for the Efficiency of Pumps and Turbines
11.7.8.1 Similitude Scale Ratios for the Efficiency of Pumps
11.7.8.2 Affinity Laws for the Efficiency of Homologous Pumps
11.7.8.3 Modeling of Scaling Effects for the Efficiency of Nonhomologous (“Distorted Models”) Pumps Using the Moody Equation
11.7.8.4 Similitude Scale Ratios for the Efficiency of Turbines
11.7.8.5 Affinity Laws for the Efficiency of Homologous Turbines
11.7.8.6 Modeling of Scaling Effects for the Efficiency of Nonhomologous (“Distorted Models”) Turbines
Using the Moody Equation
End-of-Chapter Problems
Appendix
A: Physical Properties of Common Fluids
B: Geometric Properties of Common Shapes
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