HydrodynamicsUniversity Press, 1916 - 708 pages |
Contents
| 149 | |
| 158 | |
| 188 | |
| 194 | |
| 208 | |
| 215 | |
| 223 | |
| 233 | |
| 239 | |
| 241 | |
| 253 | |
| 264 | |
| 277 | |
| 283 | |
| 302 | |
| 316 | |
| 341 | |
| 352 | |
| 361 | |
| 367 | |
| 384 | |
| 401 | |
| 407 | |
| 419 | |
| 426 | |
| 432 | |
| 505 | |
| 517 | |
| 523 | |
| 563 | |
| 576 | |
| 586 | |
| 588 | |
| 593 | |
| 606 | |
| 610 | |
| 615 | |
| 628 | |
| 632 | |
| 634 | |
| 635 | |
| 639 | |
| 647 | |
| 653 | |
| 659 | |
| 668 | |
| 677 | |
| 691 | |
| 694 | |
| 697 | |
| 702 | |
| 704 | |
Other editions - View all
Common terms and phrases
amplitude angular velocity approximately assume axes axis boundary centre circle co-ordinates coefficients condition const constant corresponding cosh Crelle curve cylinder denote depth distance disturbance dx dy dz ellipsoid equation of continuity expression extraneous forces finite fluid formula free surface function given Green's Theorem harmonic Hence impulse infinity integral investigation irrotational irrotational motion kinetic energy liquid Math normal obtained origin oscillations parallel particle Phil plane positive pressure problem Proc quadratic function radius ratio Rayleigh region result rotation satisfied shewn shews simply-connected 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 260 - ... declination, and the consequent variations in it indicate a fortnightly (or, in the case of the sun, a semi-annual) tide. There is also introduced a diurnal tide whose sign depends on the declination. The reader will have no difficulty in examining these points, by means of the general value of Q given in the Appendix. 184. In the case of a uniform canal encircling the globe (Arts. 181, 182) there is necessarily everywhere exact agreement (or exact opposition) of phase between the tidal elevation...
Page 343 - Thus a particle moving in a circle about a centre of force varying inversely as the cube of the distance...
Page 13 - It is to be remarked that the quantities a, b, c need not be restricted to mean the initial co-ordinates of a particle ; they may be any three quantities which serve to identify a particle, and which vary continuously from one particle to another.
Page xv - 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 190 - Putting then <©=EW, (24) and remarking that E is independent of the coordinates of the movable solids, we may put — W in place of <© in the equations * Proposition I. of article " On the Forces experienced by Solids immersed in a Moving Liquid,
Page 567 - Considering the very wide range of values of the rates of distortion over which these experiments extend, we can hardly hesitate to accept the equations in question as a complete statement of the laws of viscosity.
Page 565 - Pa ................ (2) Hence the arithmetic mean of the normal pressures on any three mutually perpendicular planes through the point P is the same. We shall denote this mean pressure by p*. Again, resolving parallel to y, we obtain the third of the following symmetrical system of equations : These shew that Pn = Pn> Pxx = Pa, P*v = Pvx, as was proved independently in Art.
Page 600 - The pressure of the cylinder on the fluid continually tends to increase the quantity of fluid which it carries with it, while the friction of the fluid at a distance from the cylinder continually tends to diminish it. In the case of a sphere, these two causes eventually counteract each other, and the motion becomes uniform. But in the case of a cylinder, the increase in the quantity of fluid carried continually gains on the decrease due to the friction of the surrounding fluid, and the quantity carried...
Page 50 - The motion of a liquid moving irrotationally within an (n + 1)ply continuous space is determinate when the normal velocity at every point of the boundary, and the values of the circulations in the n circuits, are given. This is proved by an application of Green's extended formula (7) of § 57, showing, as the simple formula (1) of the same section showed us in § 61 for simply continuous space, that the difference of the velocity potentials of two motions...
Page 25 - Differentiating the first of these with respect to y, and the second with respect to x and subtracting, we eliminate p, and find (2) The fluid therefore rotates as a whole about the axis of z with constantly accelerated angular velocity, except in the particular case when B=B'.