HydrodynamicsUniversity Press, 1916 - 708 pages |
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Common terms and phrases
amplitude angular velocity approximately axes axis boundary canal centre circle co-ordinates coefficients const constant corresponding cosh Crelle curve cylinder denote depth distance disturbance dx dy dz ellipsoid equation of continuity equipotential curves expression extraneous forces finite fluid formula free surface function given Green's Theorem harmonic Hence infinite infinity integral investigation irrotational irrotational motion kinetic energy liquid Math normal obtained origin oscillations parallel particle Phil plane pressure problem Proc radius ratio Rayleigh region result rotation satisfied shewn shews sin² sinh solid solid harmonic solution sphere spherical spherical harmonics steady motion stream-lines suppose theorem theory vanish velocity-potential viscosity vortex vortices wave-length waves whence whilst zero ΘΩ ат аф ди дп др дф дх ду
Popular passages
Page 621 - The second condition of wave motion is to be observed when the velocity of the wind acting on the smooth water has increased to two miles an hour. Small waves then begin to rise uniformly over the whole surface of the water; these are waves of the second order, and cover the water with considerable regularity. Capillary waves disappear from the ridges of these waves, but are to be found sheltered in the hollows between them, and on the anterior slopes of these waves. The regularity of the distribution...
Page 620 - A gentle zephyr flitting along the surface from point to point, may be observed to destroy the perfection of the mirror for a moment, and on departing, the surface remains polished as before ; if the air have a velocity of about a mile an hour, the surface of the water becomes less capable of distinct reflexion, and on observing it in such a condition, it is to be noticed that the diminution of this reflecting power is owing to the presence of those minute corrugations of the superficial film which...
Page 665 - On the Resistance of Plane Surfaces in a Uniform Current of Air,
Page 620 - ... in. per sec.) does not sensibly disturb the smoothness of the reflecting surface. A gentle zephyr flitting along the surface from point to point, may be observed to destroy the perfection of the mirror for a moment, and on departing, the surface remains polished as before ; if the air have a velocity of about a mile an hour, the surface of the water becomes less capable of distinct...
Page 445 - A steel globe of the same dimensions, without mutual gravitation of its parts, could scarcely oscillate so rapidly, since the velocity of plane waves of distortion in steel is only about 10,140 feet per second, at which rate a space equal to the earth's diameter would not be travelled in less than 1 h.
Page 621 - ... remarkable ; they begin with about an inch of amplitude, and a couple of inches long ; they enlarge as the velocity or duration of the wave increases ; by and by conterminal waves unite ; the ridges increase, and if the wind increase the waves become cusped, and are regular waves of the second order. They continue enlarging their dimensions; and the depth to which they produce the agitation increasing simultaneously with their magnitude, the surface becomes extensively covered with waves of nearly...
Page 375 - ... and therefore that the phase in question travels over the surface with a constant acceleration. The meaning of this somewhat remarkable result will appear presently (Art. 240). The series in (14) is virtually identical with one (usually designated by M*} which occurs in the theory of Fresnel's diffraction-integrals.
Page 1 - The fundamental property of a fluid is that it cannot be in equilibrium in a state of stress such that the mutual action between two adjacent parts is oblique to the common surface.
Page 192 - TO, , m2, ... are in the present problem equal to the fluxes xo , x0', • • • across the sections of the respective tubes, so that (10) corresponds to the form T0 of the * Maxwell, Electricity and Magnetism, Art. 573. •f The theorem of this paragraph was given by Kirchhoff, ie ante p. 52. See also Sir W. Thomson, "On the Forces experienced by Solids immersed in a Moving Liquid,
Page 369 - It has often been noticed that when an isolated group of waves, of sensibly the same length, is advancing over relatively deep water, the velocity of the group as a whole is less than that of the individual waves composing it. If attention be fixed on a particular wave, it is seen to advance through the group, gradually dying out as it approaches the front...