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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