A Guide to Fluid Mechanics

✍ Scribed by Hongwei Wang, Yan Zhang

• Publisher: Cambridge University Press
• Year: 2023
• Tongue: English
• Leaves: 322
• Category: Library

✦ Table of Contents

FLUID MECHANICS
A Guide to Fluid Mechanics
A Guide to Fluid Mechanics
HONGWEI WANG
YAN ZHANG
Notation
Letters
Symbols
Subscripts
1 Fluids and Fluid Mechanics
1.1 Fluids: Basic Concepts
1.2 Some Properties of Fluids
1.2.1 Viscosity of Fluids
1.2.2 Surface Tension of Liquids
1.2.3 Equation of State for Gases
1.2.4 Compressibility of Gases
Thermal Conductivity of Gases
1.3 The Concept of Continuum
1.4 Forces in a Fluid
Expanded Knowledge
States of Matter
Compressibility of Water
Compressibility of Solids
Questions
2 Forces in a Static Fluid
2.1 Analysis of Forces in a Static Fluid
2.2 Pressure in a Static Fluid under the Action of Gravity
2.3 Pressure in a Fluid under the Action of Inertial Forces
2.4 Differences and Similarities in the Transfer of Force by Fluids and Solids
Expanded Knowledge
Atmospheric Pressure
Pressure Measurement
Questions
3 Description of Fluid Motion
3.1 Methods of Describing Fluid Motion
■ ■ (d r |
r = r (X, t); V = 1 — 1 ; a = Id t J x
3.2 Pathlines and Streamlines
3.3 Velocity, Acceleration, and Substantial Derivative
DO
dO
= + (V-V)O.
3.4 Reynolds Transport Theorem
3.5 Relationship between the Reynolds Transport Theorem and Substantial Derivative
// ( V ■ n) dA = J/fV-(V )dB,
v-(^V ) = (V-v)^+^(v-V).
jjjB + v V)| dB
d- + -(V.V )| dB ' +(V.V)' + -(V.V )|dB.
3.6 The Incompressibility Hypothesis
3.7 Motion and Deformation of a Fluid Element
Linear Deformation of a Fluid Element
= V-V
3.7.2 Rotation of a Fluid Element
WAB — —; — —7 — 7T .
o x o x dx
3.7.3 Angular Deformation of a Fluid Element
Expanded Knowledge
Streaklines and Their Applications
Streamline Coordinates
Questions
4 Basic Equations of Fluid Dynamics
4.1 Integral and Differential Approach
4.2 Continuity Equation
4.2.1 Continuity Equation: Integral Form
4.2.2 Conversion from Integral to Differential Equation
Differential Equation for an Elemental Control Volume
d( ru) ru + dx
ddr+v.( rV )=0.
dr+v-( rV ) = dr+(v -v) r + r (v-V ) = Dr+r (v-V), d t ' d d t d t \ /
4.3 Momentum Equation
4.3.1 Integral Form of the Momentum Equation
4.3.2 Differential Momentum Equation
\ /
F=
dx 3 v 7
tzz=2M - M(V-V)-p.
d z 3 v '
4.4
Bernoulli’s Equation
4.5 Angular Momentum Equation
4.5.1 Integral Angular Momentum Equation
ET = —///(r x V)rdB + //(r x V?)p (V?■ n)dA. (4.30)
Differential Angular Momentum Equation
( 1 d J
Energy Equation
Integral Energy Equation
( Y
Y |.
>.
4.6.2 Differential Energy Equation
L d T ^
= — [2 — | + — 2— I — 1^—1 + r<q dxdydz. dx[ dx] dy[ dy J dz^ dz}
dz[ d z
7
d zl d z
d L uiui 1 d / \ d L, dT
Ty—=- P (V- V )+ 0v- dxi v '
+ M +, + MI n“+n“l
- p (v-V),
d w d v 12 dU u d w -TT + ^r + g k- + -?F [oy d z J [ d z dx
4.6.3 Equations of Enthalpy, Entropy, Total Enthalpy, and Shaft Work
11 1 1 d
-|0v - p (V-V) +-— rL /J r dXi
1 / 1 1 d L, dT
-|FV-p(v-V)l + -— %- + C
r1 v /J r dxi ^ dxi J
+p pp-(v-V) + F +-— £— + C .
v-V =
4.7 Solution of the Governing Equations
4.7.1 Boundary Conditions
= fb —Vp +—V2 V + -—V(V- V); and
Ld T1
4.7.2 Some Analytical Solutions of N-S Equations
Expanded Knowledge
A Comparison between Constitutive Equations for Fluids and Solids
■^“+
Mathematical Properties of N-S Equations
Solving Flow Problems
Questions
5 Inviscid Flow and Potential Flow Method
5.1 Characteristics of Inviscid Flow
c d[V(x2+y2)] d[V(x2+y2 )] 2 dx dy
Vorticity Generated by Viscous Force
5.2.2 Vorticity Generation in Baroclinic Flow
5.2.3 Vorticity Generation with Nonconservative Body Forces
Irrotational Flow and Velocity Potential
Vx V = 0.
VxV0 = 0.
%++!2=0.
5.4 Planar Potential Flow
5.4.1 Uniform Flow
5.4.2 Point Source and Point Sink
5.4.3 Point Vortex
5.4.4 Dipole
Uniform Flow Around a Circular Cylinder
1+T" \ /
/
\ /
5.5 Complex Potential
5.5.1 A More Concise Expression
5.5.2 Conformal Transformations
5.5.3 The Method of Images
5.6 Engineering Applications of Potential Flow and Its Current Status
Expanded Knowledge
Complex Variable Functions and Fluid Mechanics
Questions
127
Questions
6 Viscous Shear Flow
Shearing Motion and Flow Patterns of Viscous Fluids
6.2 Laminar Boundary Layer
6.2.1 Prandtl’s Boundary Layer Equations for Two-Dimensional Flows
d u , d v
6.2.2 Boundary Layer Thickness
^1 u I
6.2.3 Integral Approach for Solving Boundary Layer Problems
dx \ /
L , 1 d'\ I, d6 .
dp rrd U
6.3 Turbulent Boundary Layer
u = u + u = _ + _w = w + w'.
Pipe Flow
6.4.1 Entrance Region
L 1
6.4.2 Fully Developed Region
u(r)=
T = Apr.
6.5 Jets and Wakes
6.5.1 Jets
6.5.2 Wake
Boundary Layer Separation
2x
6.7 Drag and Losses
6.7.1 Drag
6.7.2 Flow Losses
f d u I2
. [d r)
J
Expanded Knowledge
The Theory of Homogeneous Isotropic Turbulence
( 3 W4
Numerical Computation of Turbulent Flows
Turbulent Boundary Layer Separation
Questions
7 Fundamentals of Compressible Flow
7.1 Sound Speed and Mach Number
7.1.1 Speed of Sound
7.1.2 Mach Number
7.2 Steady Isentropic Flow Equations
7.2.1 Static and Total Parameters
7.2.2 Critical State and Coefficient of Velocity
Tt = T + = T +
[ 2 1 k-1 I k+1J
(k + 1)-(k-1)A2,
7.2.3
Gasdynamic Functions
= 1-
k [1— k — ^2 ]k-1 I k + 1 )
I k + 1 )
f k + 11 k-1
Expansion Wave, Compression Wave, and Shock Wave
7.3.1 Pressure Waves in Fluids
Normal Shock Wave
Oblique Shock Wave
7.4 Isentropic Flow in a Variable Cross-Section Pipe
7.4.1 Converging Nozzle
Laval Nozzle
Expanded Knowledge
Aerodynamic Heating
Shock Wave-Boundary Layer Interaction
Questions
8 Similarity and Dimensional Analysis
8.1 The Concept of Flow Similarity
8.2 Dimensionless Numbers
8.2.1 Reynolds Number
8.2.2 Mach Number
8.2.3 Strouhal Number
8.2.4 Froude Number
8.2.5 Euler Number
8.2.6 Weber Number
8.3 Governing Equations in Dimensionless Form
= [pfx]-
u + V —— Eu 1 — + — .
8.4 Flow Modeling and Analysis
8.4.1 Low-Speed Incompressible Flow
8.4.2 High-Speed Compressible Flow
8.4.3 A Real-Life Example: A Milk Drop
Expanded Knowledge
Flows at Extremely Low Reynolds Numbers
Questions
9 Analysis of Some Flow Phenomena
9.1 What Are the Shapes of Objects in Outer Space? Properties of Fluids
9.2 Upside-Down Cup of Water: Incompressibility of Liquids
9.3 Air Blockage: Compressibility of Gases
9.4 How Balloons Create Thrust: Momentum Theorem
9.5 Thrust of a Water Rocket: Independent of Working Substance
Turbojet Engine Thrust: On Which Components?
9.7 Total Pressure and Its Measurement: Not a Property of Fluids
Why Does a Converging Flow Accelerate? Balance of Basic Laws
9.9 Impulsive Force and Stagnation Pressure: Relationship between the Momentum Equation and Bernoulli’s Equation
9.10 Pressure of Jet Flow: A Pressure-Dominated Flow
Faucet Flow Control: Total Pressure Determines Jet Speed
Squeeze the Outlet of a Hose to Increase Velocity: Total Pressure Determines Jet Speed
9.13 Suction and Blow: Pressure-Dominated Flows
9.14 Wind Near Buildings: Complex Three-Dimensional Unsteady Flow
9.15 Coanda Effect: Viscous Effect is Indispensable
9.16 Shape of a Raindrop: Surface Tension and Pressure Distribution
9.17 Vacuum Effects in Racing Cars Related to Incoming Flow Velocity
9.18 Larger in Size, Longer in Range: Scale Effect
9.19 Meandering of Rivers: Pressure-Dominated Channel Vortex
9.20 Tea Leaves Gather in the Middle of the Cup: Another Channel Vortex
Iron Ox Moves Upstream: Pressure-Dominated Horseshoe Vortex
9.22 Pressure Change by a Passing Train: Not Just Bernoulli’s Equation
How Lift Is Created: The Coanda Effect is the Key
9.24 Principle of Heat Engines: Working Substance Must be Compressible
Q = A J + W,
9.25 Principle of Compressors: Work Done by Unsteady Pressure Forces
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