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Fluid Mechanics

Fluid mechanics is the branch of physics that studies the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. Fluid mechanics has a wide range of applications, including for mechanical engineering, chemical engineering, geophysics, astrophysics, and biology. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.

Civil Engineering Engineering

Author: Bar-Meir
Publisher: LibreTexts
Source: LibreTexts
License: GNU FDL
Language: EN

Read online Download PDF (open licence)

Contents· 254 sections

02: Review of Thermodynamics
2.1: Introductory Remarks
2.2: Basic Definitions
2.3: Thermodynamics First Law
2.4: Thermodynamics Second Law
03: Review of Mechanics
3.1: Introductory Remarks
3.2: Kinematics of a Point Body
3.3: Center of Mass
3.3.1: Actual Center of Mass
3.3.2: Aproximate Center of Area
3.4: Moment of Inertia
3.4.1 Moment of Inertia for Mass
3.4.2: Moment of Inertia for Area
3.4.2.1: General Discussion
3.4.2.2: The Parallel Axis Theorem
3.4.3: Examples of Moment of Inertia
3.4.4: Product of Inertia
3.4.5: Principal Axes of Inertia
3.5: Newton's Laws of Motion
3.6: Angular Momentum and Torque
3.6.1: Tables of geometries
04: Fluids Statics
4.1: Introduction
4.2: The Hydrostatic Equation
4.3: Pressure and Density in a Gravitational Field
4.3.1: Constant Density in Gravitational Field
4.3.2: Pressure Management
4.3.2.1: Measuring the Atmospheric Pressure
4.3.2.2: Pressure Measurement
4.3.2.3 Magnified Pressure Measurement
4.3.3 Varying Density in a Gravity Field
4.3.3.1: Gas Phase under Hydrostatic Pressure
4.3.3.2: Liquid Phase Under Hydrostatic Pressure
4.3.4: The Pressure Effects Due To Temperature Variations
4.3.4.1: The Basic Analysis
4.3.4.2 The Stability Analysis
4.3.5: Gravity Variations Effects on Pressure and Density
4.3.5.1: Ideal Gas in Varying Gravity
4.3.5.2: Real Gas in Varying Gravity
4.3.5.3: Liquid Under Varying Gravity
4.3.6 Liquid Phase
4.4: Fluid in an Accelerated System
4.4.1: Fluid in a Linearly Accelerated System
4.4.2 Angular Acceleration Systems: Constant Density
4.4.3: Fluid Statics in Geological System
4.5: Fluid Forces on Surfaces
4.5.1: Fluid Forces on Straight Surfaces
4.5.1.1: Pressure Center
4.5.1.2: Multiply Layers
4.5.2: Forces on Curved Surfaces
4.6: Buoyancy and Stability
4.6.1: Stability
4.6.1.1: Stability of Body with Shifting Mass Centroid
4.6.1.2: Metacentric Height, (overlineGM), Measurement
4.6.1.3 Stability of Submerged Bodies
4.6.1.4: Stability of None Systematical or ``Strange'' Bodies
4.6.1.5: Neutral frequency of Floating Bodies
4.6.2: Surface Tension
4.7: Rayleigh–Taylor Instability
4.8: Qualitative questions
05: The Control Volume and Mass Conservation
5.1: Introduction
5.2: Control Volume
5.3: Continuity Equation
5.3.1: Non Deformable Control Volume
5.3.2: Constant Density Fluids
5.3.2.1: Non Deformable Control Volume
5.3.2.2: Deformable Control Volume
5.3.2.3: One–Dimensional Control Volume
5.4: Reynolds Transport Theorem
5.5: Examples For Mass Conservation
5.6: The Details Picture Velocity Area Relationship
5.7: More Examples for Mass Conservation
06: Momentum Conservation for Control Volume
6.1: Momentum Governing Equation
6.1.1: Introduction to Continuous
6.1.2: External Forces
6.1.3: Momentum Governing Equation
6.1.4: Momentum Equation in Acceleration System
6.1.5: Momentum For Steady State and Uniform Flow
6.1.5.1: Momentum for For Constant Pressure and Frictionless Flow
6.2: Momentum Equation Application
6.2.1: Momentum for Unsteady State and Uniform Flow
6.2.2: Momentum Application to Unsteady State
6.3: Conservation Moment Of Momentum
6.4: More Examples on Momentum Conservation
6.4.1: Qualitative Questions
07: Energy Conservation
7.1: The First Law of Thermodynamics
7.2: Limitation of Integral Approach
7.3 Approximation of Energy Equation
7.3.1: Energy Equation in Steady State
7.3.2: Energy Equation in Frictionless Flow and Steady State
7.4: Energy Equation in Accelerated System
7.4.1: Energy in Linear Acceleration Coordinate
7.4.2: Linear Accelerated System
7.4.3: Energy Equation in Rotating Coordinate System
7.4.4: Simplified Energy Equation in Accelerated Coordinate
7.4.4.1: Energy Equation in Accelerated Coordinate with Uniform Flow
7.4.5: Energy Losses in Incompressible Flow
7.5: Examples of Integral Energy Conservation
7.6: Qualitative Questions
08: Differential Analysis
8.1: Introduction
8.2: Mass Conservation
8.2.1 Mass Conservation Examples
8.3: Conservation of General Quantity
8.3.1 Generalization of Mathematical Approach for Derivations
8.3.2 Examples of Several Quantities
8.3.2.1: The General Mass Time Derivative
8.4: Momentum Conservation
8.5: Derivations of the Momentum Equation
8.6: Boundary Conditions and Driving Forces
8.6.1 Boundary Conditions Categories
8.7: Examples for Differential Equation (Navier-Stokes)
8.7.1: Interfacial Instability
09: Dimensional Analysis
9.1 Introductory Remarks
9.1.1: Brief History
9.1.2: Theory Behind Dimensional Analysis
9.1.3: Dimensional Parameters Application for Experimental Study
9.1.4: The Pendulum Class Problem
9.2: Buckingham–π–Theorem
9.2.1: Construction of the Dimensionless Parameters
9.2.2: Basic Units Blocks
9.2.3: Implementation of Construction of Dimensionless Parameters
9.2.3.1: One Shot Method: Constructing Dimensionless Parameters
9.2.3.2: Building Blocks Method: Constructing Dimensional Parameters
9.2.3.3 Mathematical Method: Constructing Dimensional Parameters
9.2.4: Similarity and Similitude
9.3: Nusselt's Technique
9.4 Summary of Dimensionless Numbers
9.4.1: The Significance of these Dimensionless Numbers
9.4.2: Relationship Between Dimensionless Numbers
9.4.3: Examples for Dimensional Analysis
9.5 Summary
10: Inviscid Flow or Potential Flow
10.1 Introduction
10.1.1: Inviscid Momentum Equations
10.2
10.2.1: Streamline and Stream function
10.2.2: Compressible Flow Stream Function
10.2.2.1: Stream Function in a Three Dimensions
10.2.3: The Connection Between the Stream Function and the Potential Function
10.2.3.1: Existences of Stream Functions
10.3 Potential Flow Functions Inventory
10.3.1: Flow Around a Circular Cylinder
10.3.1.1: Adding Circulation to a Cylinder
10.4 Conforming Mapping
10.4.1: Complex Potential and Complex Velocity
10.5 Unsteady State Bernoulli in Accelerated Coordinates
11: Compressible Flow One Dimensional
11.01 What is Compressible Flow?
11.2 Why Compressible Flow is Important?
11.3 Speed of Sound
11.3.1: Introduction
11.3.2: Speed of Sound in Ideal and Perfect Gases
11.3.3: Speed of Sound in Almost Incompressible Liquid
11.3.4: Speed of Sound in Solids
11.3.5: The Dimensional Effect of the Speed of Sound
11.4 Isentropic Flow
11.4.1: Stagnation State for Ideal Gas Model
11.4.2: Isentropic Converging–Diverging Flow in Cross Section
11.4.3: The Properties in the Adiabatic Nozzle
11.4.3.1: The pressure Mach number relationship
11.4.3.2: Relationship Between the Mach Number and Cross Section Area
11.4.4: Isentropic Flow Examples
11.4.5: Mass Flow Rate (Number)
11.4.7: The Impulse Function
11.5 Normal Shock
11.5.1: Solution of the Governing Equations
11.5.1.1: The Star Conditions
11.5.2: Prandtl's Condition
11.5.3: Operating Equations and Analysis
11.6 Qualitative questions
11.7 Isothermal Flow
11.7: Fanno Flow
11.6.1: Introduction
11.7.05
11.7.5.1: Maximum Length for the Supersonic Flow
11.7.06: Working Conditions
11.7.6.1: Variations of The Tube Length ((ld)) Effects
11.7.6.2: Fanno Flow Supersonic Branch
P 1), effects
reduction
11.7.09: The Practical Questions and Examples of Subsonic branch
11.7.11: Subsonic Fanno Flow for a Given (M 1) and Pressure Ratio
11.7.12: More Examples of Fanno Flow
11.8: The Table for Fanno Flow
11.9: Rayleigh Flow
11.9.1: Introduction
11.9.2: Governing Equations
11.9.3: Rayleigh Flow Tables and Figures
11.9.4: Examples For Rayleigh Flow
11.70 Isothermal Flow
Governing equations
11.7.2: Dimensionless Representation
11.7.3: The Entrance Limitation of Supersonic Branch
11.7.4: Supersonic Branch
11.7.5: Figures and Tables
11.7.6: Isothermal Flow Examples
12: Compressible Flow 2Dimensional
12.1: Introduction
12.1.1: Preface to Oblique Shock
12.1.1.1: Introduction to Zero Inclination
12.2: Oblique Shock
12.2.1: Solution of Mach Angle
12.2.1.1: Upstream Mach Number, \(M 1\), and Deflection Angle, \(\delta\)
12.2.2: When No Oblique Shock Exist or the case of \(D>0\)
12.2.2.1: Large deflection angle for given, \(M 1\)
12.2.2.2: The case of \(D\geq 0\) or \(0 \geq\delta\)
12.2.2.3: Upstream Mach Number, \(M 1\), and Shock Angle, \(\theta\)
12.2.2.4: Given Two Angles, \(\delta\) and \(\theta\)
12.2.2.5: Flow in a Semi–2D Shape
12.2.2.6: Close and Far Views of the Oblique Shock
12.2.2.7: Maximum Value of Oblique shock
12.2.2.8: Oblique Shock Examples
12.2.3: Application of Oblique Shock
12.3: Prandtl-Meyer Function
12.3.1: Introduction
12.3.2: Geometrical Explanation
12.4: The Maximum Turning Angle
12.5: The Working Equations for the Prandtl-Meyer Function
12.6: d'Alembert's Paradox
12.7: Flat Body with an Angle of Attack
12.8: Examples For Prandtl–Meyer Function
12.9: Combination of the Oblique Shock and Isentropic Expansion
13: MultiPhase Flow
13.1: Introduction
13.2: History
13.3: What to Expect From This Chapter
13.4: Kind of Multi-Phase Flow
13.5: Classification of Liquid-Liquid Flow Regimes
13.5.1: Co–Current Flow
13.5.1.1: Horizontal Flow
13.5.1.2: Vertical Flow
13.5.1.3: Vertical Flow Under Micro Gravity
13.6: Multi–Phase Flow Variables Definitions
13.6.1: Multi–Phase Averaged Variables Definitions
13.7: Homogeneous Models
13.7.1: Pressure Loss Components
13.7.1.1: Friction Pressure Loss
13.7.1.2: Acceleration Pressure Loss
13.7.1.3: Gravity Pressure Loss
13.7.1.4: Total Pressure Loss
13.7.2: Lockhart Martinelli Model
13.8: Solid–Liquid Flow
13.8.1: Solid Particles with Heavier Density \(\rho S>\rho L\)
13.8.2: Solid With Lighter Density \(\rho S< \rho\) and With Gravity
13.91: Counter–Current Flow
13.9.1: Horizontal Counter–Current Flow
13.9.2: Flooding and Reversal Flow
13.99: Multi–Phase Conclusion