A Treatise on Hydromechanics: Part I. Hydrostatics, Part 1 |
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action angular velocity atmospheric attraction axes axis vertical barometer body centre of gravity centre of pressure co-ordinates cone constant cos² curvature curved surface cylinder density depth determine displaced fluid distance dx dy dy dx dy dz elastica equal pressure equation equilibrium equilibrium is stable film floats fluid displaced fluid pressure free surface given homogeneous liquid horizontal hyperbola immersed lamina latus rectum liquid films mercury metacentre obtain oscillation parabola paraboloid parallel particles perfect differential perpendicular piston plane of floatation portion position of equilibrium prove quantity radius ratio resultant pressure rotation shew sin² solid solid of revolution sphere spherical spheroid supposed surface of revolution surfaces of equal tangent temperature vapour varies vertex vertical angle vertical plane vessel volume weight whole pressure λ²
Popular passages
Page 65 - ... the centres of gravity of the body and of the fluid displaced must be in the same vertical line. 4-31. When a solid of mean density p floats in a fluid of density p' (> p) only the fraction p/p
Page 29 - Fluid is a substance, such that a mags of it can be very easily divided in any direction, and of which portions, however small, can be very easily separated from the whole mass...
Page 210 - How do you account for the remarkable effect of wind on the intensity of sound ? 16. Find the attraction of a prolate spheroid on an internal particle. A mass of homogeneous fluid is subject to the mutual gravitation of its particles, and to a repulsive force tending from a plane through its centre of gravity and varying as the perpendicular distance from that plane ; shew that the conditions of equilibrium will be satisfied if the surface be a prolate spheroid of a certain ellipticity, provided...
Page 83 - ... horizontal: if 2a be the vertical angle of the cone, and /3 the angle between the plane base and the shortest generating line, shew that cot /3 = cot 4a - } cosec 4a.
Page 36 - He also demonstrates that if a globe consist of particles each of which attracts with a force varying inversely as the square of the distance...
Page 36 - A rigid spherical shell is filled with homogeneous inelastic fluid, every particle of which attracts every other, with a force varying inversely as the square of the distance...
Page 226 - If the Earth be completely covered by a sea of small depth, prove that the depth in latitude I is very nearly equal to H(1 — c sin2 1) where II is the depth at the equator, and e the ellipticity of the Earth.
Page 130 - We have shewn that the pressure of a fluid at rest is the same at all points of the same horizontal plane : hence the pressure at C is equal to the pressure of the mercury at Q.