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Prandtl L., Tietjens O.G. Fundamentals of Hydro- And Aeromechanics

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Prandtl L., Tietjens O.G. Fundamentals of Hydro- And Aeromechanics
McGraw Hill Book Company, 1934. — 283 p. — ISBN 0486603741.

The author’s pioneering experiments laid the basis for the use of theoretical hydromechanics and hydrodynamics in practical engineering problems. This volume presents Tietjens' famous expansion of the author’s lectures: statics and kinematics of liquids and gases, dynamics of non-viscous liquids. Proofs use vector analysis.
Introduction
The statics of liquids and gases
Equilibrium and stability
The Conditions under Which Liquids and Gases Can Be Treated as Continua
The Concept of Fluid Pressure
Relation between Pressure Distribution and Volume Force
Stable, Unstable, and Neutral Equilibrium
Equation of Hydrostatic Pressure
Applications of the Pressure Equation; Communicating Vessels
Hydrostatic Pressure on Walls and Floors
Hydrostatic Lift and Stability
Calculation of the Metacentric Height
Application of the pressure equation to permanent gases. Stability of air masses
Equation of State for Permanent Gases
Uniform Atmosphere
Isothermal Atmosphere
Polytropic Atmosphere
Determination of the Exponent n of the Poly trope
Significance of the Temperature Gradient in Relation to the Stability of Air Masses
Influence of Humidity
Concept of Potential Temperature
Origin of Clouds
Static lift on gas-filled aircraft
Pressure on the Balloon Wall
Lift of a Gas-filled Balloon
Effect of Temperature on Lift
Equilibrium of Forces on a Balloon
Stability of a Balloon in Taut State under Adiabatic Conditions
Stability of a Balloon in the Limp State under Adiabatic Conditions
Effect of Temperature Changes at Constant Pressure on a Balloon in the Taut State
Effect of Temperature Changes at Constant Pressure on a Balloon in the Limp State
Causes of Heat Changes; Behavior of Balloon during Travel
Surface tension
Physical Basis
Relation between Surface Tension and Pressure Difference across a Surface
Surface Tension at Place of Contact between Several Media
Surface Effects under the Action of Gravity
Capillarity
Kinematics of liquids and gases
Methods of description
Lagrangian Method
Eulerian Method and Its Connection with That of Lagrange
Streamlines and Paths of Particles; Steady Flow
Streak Lines
Significance of System of Reference in Interpretation of the Form of Motion
Construction of Path and Streak Lines
Stream Tubes
Geometry of the Vector Field
Linear Vector Function of Position
Geometrical Significance of the Individual Quantities of a Matrix Characterizing a Velocity Field
Shearing and Rotating Velocities
The Concept of the Tensor
Splitting a Tensor into a Symmetrical and Antisymmetrical Part
Stokes's Theorem
Gauss's Theorem
Introduction of the Operator V
Acceleration of a Fluid Particle
Velocity Change of a Fluid Particle as a Function of the Time and the Velocity Field
The Substantial Differential Is the Sum of the Local and Convective Differentials
Kinematic Boundary Conditions; Theorem of Lagrange.
Liquids and Gases Are Not to Be Considered as Ideal Media but as Quasi-continua
Equation of Continuity
Incompressible Homogeneous Fluids
Eulerian Derivation of the Continuity Equation for Gases.
The General Lagrangian Equation of Continuity
The dynamics of non-viscous fluids
The Eulerian Equation and Its Integration along a Streamline
General Remarks on the Action of Fluid Viscosity
Euler's Equation
Integration of Euler's Equation along a Streamline
Bernoulli's Equation
Applications of the Bernoulli Equation
Potential Motion
Simplification of Euler's Equation and Integration on Assuming a Velocity Potential
Connection between the Integral of Euler's Equation for Potential Motion and the Corresponding Integral along a Streamline
Equations Defining Potential and Pressure Functions
The Potential Function for Incompressible Fluids
The Potential Function When the Velocity w Is Very Small.
The Potential Function for Steady Motion
The Potential Function for the One-dimensional Problem
Simple Examples of Potential Motion for Incompressible Fluids
The Source and Sink Potential
Description of Motion about a Body of Revolution by the Method of Sources and Sinks
The Motion about a Sphere; Doublets
The Potential of a Rectilinear Vortex
Difference between Potential Motion with Circulation and a Motion with Rotation
The Interpretation of Potential as Impulsive Pressure
Two-dimensional Potential Motion
The Real and Imaginary Parts of an Analytic Function of Complex Argument Are Solutions of Laplace's Differential Equation
The Cauchy-Riemann Differential Equations and Their Physical Interpretation
The Stream Function
Examples of the Application of the Stream Function F(z) to Simple Problems of Motion in Two Dimensions
The Motion Round a Straight Circular Cylinder
The Fundamentals of Conformal Transformation
Applications of Conformal Transformation
The Hodograph Method
Discontinuous Fluid Motions
Vortex Motion
The Kinematics of Vortex Motion
Thomson's Theorem on the Permanence of Circulation
Extension of Thomson's Theorem to the Case of Non-homogeneous Fluids by V. Bjerkness
The Dynamics of Vortex Motion
The Vortex Theorems of Helmholtz
The Velocity Field in the Neighborhood of an Isolated Vortex; the Law of Biot and Savart
Simplified Construction of a Vortex Line by Assuming a Core of Constant Rotation
The Motion and Mutual Influence of Single Vortices
Pressure Distribution in the Neighborhood of a Rectilinear Vortex
The Relation between Vortex Motion and the Surface of Discontinuity or Separation
The Formation of Surfaces of Discontinuity
Instability of the Surface of Discontinuity
The Influence of Conpressibility
General Remarks about the Justification for Treating Gases as Incompressible Fluids
Compressibility in Bernoulli's Equation
The Effect of Compressibility on the Formula for Stagnation Pressure
Compressibility in the Equation of Continuity
The Effect of Compressibility on the Streamlines When the Velocity Is Less than That of Sound
Theorems of Energy and Momentum
The Momentum Theorem for Steady Motion
Extension of the Momentum Theorem to Fluid Motion with a Steady Mean Flow
Applications of the Theorem of Momentum
The Energy Theorem for Non-steady Motion of Incompressible Fluids
The Equation of Navier-Stokes for Viscous Fluids
The Fundamental Equation of Fluid Mechanics
Decomposition of the Total Surface Force into the Elements of a Stress Tensor
Relation of the Elements of the Stress Tensor to the Corresponding Rates of Change of Deformation
Relation between the Stress Tensor and the Velocity Tensor
The Equation of Navier-Stokes
Discussion of the Navier-Stokes Equation
The Differential Equation of Creeping Motion
Oseen's Improvement of the Theory
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