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1 ISBN 9783540024118
内容説明
343 Whilst this may be so it is also true that this in itself is not sufficient to deter- mine it completely. In fact the extent of the dead air region and the behaviour of the shear layer are also of prime importance and in short a unified treatment comprising external flow, boundary layer, shear layer and dead air region becomes necessary to complete the investigation. This would take us outside the scope of the present article and for the substantial progress that has been made towards such a treatment the reader is referred to a paper by HOLDER and GADD 1 and its comprehensive list of references. v. Heat transfer in incompressible boundary layers. 25. Introduction. The term fluid includes gases and liquids. Both gases and liquids are to some extent compressible but in many problems of fluid flow the density changes occurring are small. When they are small enough to be negligible we can regard the flow as incompressible. In Chap. IV we have established the equations for compressible flow of gases and these can of course be used to deter- mine when density changes in a gas flow are in fact negligible.
Broadly speaking this will be so when the temperature changes as determined by the energy equation are small enough.
目次
Physikalische Grundlagen der Stromungslehre.- I. Grundgleichungen in Integralform.- II. Stosswellen und Schallwellen.- III. Differentialform der Grundgleichungen in Eulerscher Darstellung.- IV. Kinematische Beziehungen und Deutungen.- V. Grundgleichungen fur reibungslose Stromungen.- VI. Wirbelsatze.- VII. Innere Reibung.- VIII. Stromungstypen.- IX. Potential- und Stromfunktionen.- X. Stromungskrafte.- XI. Potentialstromungen.- XII. Instabilitaten und Turbulenz.- Zusammenfassende Literatur.- Mathematical Principles of Classical Fluid Mechanics.- A. Preface and introductory remarks.- B. The equation of motion.- I. Kinematics and dynamics of fluid motion.- II. Energy and momentum transfer.- III. Transformation of coordinates.- IV. Variational principles.- C. Incompressible and barotropic perfect fluids.- I. General principles.- II. Irrotational motion.- III. Rotational motion.- D. Thermodynamics and the energy equation.- I. Thermodynamics of simple media.- II. The energy equation.- E. The perfect gas.- I. General principles.- II. Energy, entropy, and vorticity.- III. Special methods in two-dimensional flow.- IV. Subsonic potential flow.- V. Supersonic flow and characteristics.- VI. Special topics.- F. Shock waves in perfect fluids.- G. Viscous fluids.- I. The constitutive equations of a viscous fluid.- II. Dynamical similarity.- III. Incompressible viscous fluids.- Laminar Boundary Layers.- I. Two-dimensional incompressible boundary layers.- II. Three-dimensional boundary layers.- III. Limitations of the boundary layer approximation.- IV. The laminar boundary layer in compressible flow.- V. Heat transfer in incompressible boundary layers.- VI. Boundary layer control.- General works of reference.- Entstehung der Turbulenz.- I. Einige experimentelle Ergebnisse uber den Umschlag laminar-turbulent..- II. Grundlagen der Stabilitatstheorie der Laminarstromung.- III. Ergebnisse der Stabilitatstheorie fur die Grenzschicht an der langsangestromten ebenen Platte und fur das Poiseuillesche Parabelprofil.- IV. Vergleich der Stabilitatstheorie mit Versuchsergebnissen.- V. Einfluss des Druckgradienten auf den Umschlag.- VI. Einfluss der Absaugung auf den Umschlag laminar-turbulent.- VII. Einfluss eingepragter Krafte auf den Umschlag laminar-turbulent.- VIII. Einfluss des Warmeuberganges und der Kompressibilitat auf den Umschlag laminar-turbulent.- IX. Stabilitat gegen dreidimensionale Storungen.- X. Einfluss der Wandrauhigkeit auf den Umschlag laminar-turbulent.- Zusammenfassende Literatur.- Sachverzeichnis (Deutsch/Englisch).- Subject Index (English/German).
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3 ISBN 9783540025481
内容説明
Sect 2. 317 tinuity surfaces 1. This suggests that a wake pressure Pw be associated with each flow past a bluff body, and that a wake parameter (2. 4) which plays the same role as the cavitation parameter (2. 1), be defined for the flow. This idea has been made the basis of a modified wake theory (ef. Sect. 11) which proves to be in good qu- titative agreement with pressure and drag measurements. It should be emphasized, however, that un- h like the cavitation number, the wake parameter is a quantity which is not known a priori, and must be empirically determined in each case. (3) Jet flows. The problem of jet efflux from an orifice is one of the oldest in hydrodynamics and the first to be treated by Fig. 3a. the HELMHOLTZ free streamline theory. Of particular importance for engineering applications is the discharge coefficient Cd' which is defined in terms of the discharge Q per unit time, the pressure P, and the cross-sectional area A of the orifice, by the formula, (2. 5) where e is the fluid density. Two methods of measuring Cd have been most fre- quently adopted. In the first the liquid issues from an orifice in a large vessel under the influence of gravity _,- . , (Fig.
3 a), while in the second it 1 L is forced out of a nozzle or pipe under high pressure (Fig. 3 b).
目次
Analytical Theory of Subsonic and Supersonic Flows.- I. Physical and mathematical foundations.- II. Linearized theory.- III. The hodograph method.- IV. The analytical theory of two-dimensional subsonic flows.- V. The analytical theory of two-dimensional transonic flows.- General references and textbooks.- Theorie des ondes de choc.- A. Les equations des phenomenes de choc.- a) Introduction.- b) Demonstration des equations des phenomenes de choc.- c) Chocs stationnaires dans les ecoulements uniformes.- B. Les ondes de choc dans les ecoulements stationnaires.- I. La formation des ondes de choc.- II. Les ondes de choc detachees.- III. Les ondes de choc attachees dans les ecoulements plans.- a) Etude des chocs uniformes.- b) Ecoulement autour d'un obstacle termine par un diedre.- c) Ecoulement autour d'une ogive.- IV. Les ondes de choc attachees dans les ecoulements a trois dimensions.- a) Ecoulements coniques de revolution.- b) Ecoulements de revolution.- c) Ecoulements coniques.- C. Les ondes de choc dans les ecoulements non stationnaires.- I. Formation et propagation des ondes de choc planes.- a) Etude des chocs uniformes.- b) Exemples de chocs non uniformes.- c) La formation des chocs dans les tuyeres.- II. Rencontre d'une onde de choc plane et d'un diedre.- a) Cas de la reflexion reguliere.- b) Cas de la reflexion de Mach.- c) Etude de l'ecoulement apres le choc.- III. Etude des ondes de choc spheriques.- IV. Etude des translations rectilignes de vitesse variable.- Annexe. Propagation des chocs dans les gaz ionises.- Bibliographie.- Theory of Characteristics of Inviscid Gas Dynamics.- A. Introduction.- B. One-dimensional unsteady motion.- I. Homentropic motion.- a) Characteristic equations and simple waves.- b) Structure of the motion.- c) Solution of the general wave-interaction problem.- II. Motion with entropy variation.- C. Steady two-dimensional supersonic flow.- I. Homentropic irrotational flow.- a) Characteristic equations and simple waves.- b) Structure of the flow.- c) Analytical solution methods.- II. Flow with entropy variation.- D. Steady axially symmetrical supersonic flow.- References.- Linearized Theory of Unsteady Flow of a Compressible Fluid.- I. Formulation of the problem.- II. Explicit solutions.- a) Subsonic case.- b) Applications.- III. The method of integral equations.- IV. Reciprocity relations.- References.- Jets and Cavities.- I. Physical and mathematical foundations.- II. Particular flows.- a) The hodograph method.- b) The method of reflection.- c) Inverse and semi-inverse solutions.- d) Approximate theories.- III. Qualitative theory.- a) Geometric properties of free streamlines.- b) Comparison methods.- c) Variational principles.- IV. Existence and uniqueness theory.- a) Existence theory.- b) Uniqueness theory.- V. Numerical methods.- a) Plane flows past curved obstacles.- b) Axially symmetric flows.- General references.- Surface Waves.- A. Introduction.- B. Mathematical formulation.- 1. Coordinate systems and conventions.- 2. Equations of motion.- 3. Boundary conditions at an interface.- 4. Boundary conditions on rigid surfaces.- 5. Other types of boundary surfaces.- C. Preliminary remarks and developments.- 6. Classification of problems.- 7. Progressive waves and wave velocity-standing waves.- 8. Energy.- 9. Momentum.- 10. Expansion of solutions in powers of a parameter.- D. Theory of infinitesimal waves.- 11. The fundamental equations.- 12. Other boundary conditions.- 13. Some mathematical solutions.- 14. Some simple physical solutions.- 15. Group velocity and the propagation of disturbances and of energy.- 16. The solution of special boundary problems.- 17. Two-dimensional progressive and standing waves in unbounded regions with fixed boundaries.- 18. Three-dimensional progressive and standing waves in unbounded regions with fixed boundaries.- 19. Problems with steadily oscillating boundaries.- 20. Motions which may be treated as steady flows.- 21. Waves resulting from pressure distributions.- 22. Initial-value problems.- 23. Waves in basins of bounded extent.- 24. Gravity waves in the presence of surface tension.- 25. Waves in a viscous fluid.- 26. Stability of free surfaces and interfaces.- 27. Higher-order theory of infinitesimal waves.- E. Shallow-water waves.- 28. The fundamental equations for the first approximation.- 29. The linearized shallow-water theory.- 30. Nonlinear shallow-water theory.- 31. Higher-order theories and the solitary and cnoidal waves.- F. Exact solutions.- 32. Some general theorems.- 33. Waves of maximum amplitude.- 34. Explicit solutions.- 35. Existence theorems.- G. Bibliography.- Sachverzeichnis (Deutsch-Englisch).- Subject Index (English-German).- Table des matieres (Francais).
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