Гидродинамика

484 CONTENTS C h a p t e r II. Elliptic Cavity. 59 s 12. Ellipsoidal cavity. Elliptic motion 59 Cylindrical Cavities 65 § 13. Directions of the principal axes of inertia of the equi ­ valent body 65 § 14. General formulae for the relative velocities of par ­ ticles of the liquid and for the moments of inertia of equivalent bodies, in the case of a rotation about an axis parallel t o the g e ­ nerators of the cylinder . 66 § 15. Cavities bavins' the shape of an elhptic cylinder and of a triangular prism . . 68 § 16. Cavities of wh l c b the cross- section has tbe shape of two confocal ellipses . . . 71 § 17. Cavities of which the cross- section bas the shape of a circular sector. . . . 76 •1; 18. General formulae for the velocities of particles of the hquid and for the mo ­ ments of inertia of the equivalent bodies in the case of rotation about an axis at right angles to the generators 79 ^ 19. Cavity having the shape of a rectang-ular parallele­ piped 8 2 § 20. Cavity having the shape of a circular cylinder . . 81 Cavities Having tbe Shape of Solids of Revolution . . . . 90 § 21. Rotation about the axis of the cavity. Rotation about the axis at right angles to the axis of the cavity. The velocity poten ­ tial. Differential equations of the lines of flow and the moments of inertia of equivalent bodies. Equati­ ons for the associated spherical functions of the first kind and some of their properties 90 § 22. Conical cavity 96 § 23. Singly-connected and tho- roidal cavities bounded b y hyperbololds 101 24. Semispherlcal cavity . . . 105 Multiply-connected Cavities . . 112 § 25. Geometrical Interpretation of the motion about a fi ­ xed point of a solid with a gyroscope attached t o i t . 112 § 26. A note, on the determina ­ tion of the projections of the principal moment of momentum of particles of a liquid 117 § 27. Infinitely thin closed tube of arbitrary shape and cross-section 117 § 28. Cavities of revolution . . 121 C h a p t e r III. Case of a Vor ­ tex Motion of a Liquid Within the Cavities of a Moving Body. 122 § 29. Determination of velocities of particles of the hquid when the body Is fixed . . 122 § 30. Internal motion of the h- quid in the case of a rota ­ ting cavity. Differential equations of the problem . 124 § 31. Determination of the hyd- rodynamical pressure wi ­ thin the cavity 130 § 32. Cyhndrical cavity rotating about an axis parallel to the generators 132