A Collection of Problems in Illustration of the Principles of Theoretical Hydrostatics and Hydrodynamics |
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Page 48
... position on a horizontal plane : to find the least weight of the vessel that the fluid may not escape from under it . Least weight of the vessel twice the weight of the fluid . = CHAPTER IV . EQUILIBRIUM OF SOLID BODIES FLOATING FREELY ...
... position on a horizontal plane : to find the least weight of the vessel that the fluid may not escape from under it . Least weight of the vessel twice the weight of the fluid . = CHAPTER IV . EQUILIBRIUM OF SOLID BODIES FLOATING FREELY ...
Page 50
... position of equilibrium , provided that be less σ than 1 and greater than . Taking ( 1 ) and ( 3 ) we have 50 EQUILIBRIUM OF SOLID BODIES FLOATING FREELY .
... position of equilibrium , provided that be less σ than 1 and greater than . Taking ( 1 ) and ( 3 ) we have 50 EQUILIBRIUM OF SOLID BODIES FLOATING FREELY .
Page 52
... positions of equilibrium . Should all the points of intersection of the hyperbolæ be such that x is greater than a or y than b , the lamina will not rest in any position with only one angle immersed . COR . 1. If the triangle be ...
... positions of equilibrium . Should all the points of intersection of the hyperbolæ be such that x is greater than a or y than b , the lamina will not rest in any position with only one angle immersed . COR . 1. If the triangle be ...
Page 53
... position of equilibrium , the plane of the lamina being vertical . Adhering to the diagram and notation of the preceding problem , it is plain that , BB'C'C being in the fluid and B'AC ' being in vacuum , whence or BB'C ' Cσ = BAC . p ...
... position of equilibrium , the plane of the lamina being vertical . Adhering to the diagram and notation of the preceding problem , it is plain that , BB'C'C being in the fluid and B'AC ' being in vacuum , whence or BB'C ' Cσ = BAC . p ...
Page 54
... positions of equilibrium . COR . 2. There will be three positions of equilibrium , A being without the fluid , if the triangle be equilateral , provided that σ 7 be greater than and less than 16 " 8 16 Bossut Traité d ' Hydrodynamique ...
... positions of equilibrium . COR . 2. There will be three positions of equilibrium , A being without the fluid , if the triangle be equilateral , provided that σ 7 be greater than and less than 16 " 8 16 Bossut Traité d ' Hydrodynamique ...
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Common terms and phrases
ABCD Albert Girard altitude angular velocity aperture axis axis of revolution axis vertical base Bernoulli Bossut Traité Cambridge centre of gravity centre of pressure cone constant quantity cos² Daniel Bernoulli denote the density denote the length denote the radius depth determine distance dx dy Edition elastic equal equation filled with fluid floating fluid displaced free surface given hemisphere Hence humidum inclination incompressible fluid integrating James Bernoulli John Bernoulli lamina latus rectum mass motion oscillation parabola paraboloid of revolution parallel particles Phoronomia portion position of equilibrium position of rest problem ratio represent right angles sesquialterum sin² small orifice solid cylinder specific gravity sphere supposed Traité d'Hydrodynamique Treatise triangle tube vertex volume w³y² weight whole pressure
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