By G. K. Batchelor
First released in 1967, Professor Batchelor's vintage paintings remains to be one of many premier texts on fluid dynamics. His cautious presentation of the underlying theories of fluids remains to be well timed and acceptable, even today of virtually unlimited desktop energy. This reissue guarantees new iteration of graduate scholars reviews the beauty of Professor Batchelor's writing.
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Additional info for An Introduction to Fluid Dynamics
_-- ........ Equilibrium position of a uniform sphere - ...... ' ---- - - - - - - - ,,~ " ,,,,'''',,,,,~' ",'" , ~,, ' .... ,_..... -.... , ........ 1. Non-uniform fluid at rest under the action of gravity and centrifugal force. Fluid at rest under grOlVity The case in which gravity is the only volume force acting on the fluid is both important and simple. Two extreme situations may be distinguished. In the first one, the mass of fluid concerned is large and isolated so that the gravitational attraction of other parts of the fluid provides the volume force on any element of the fluid, as in the case of a gaseous star.
The same is true of a sphere at a free surface of rotating liquid, since this is simply a particular distribution of density with respect to 'Y. On the other hand, if the sphere is sufficiently non-uniform in density, say by being weighted on one side, it is clearly possible for the total centrifugal force on the sphere to be greater than that on displaced fluid of the same total mass, in which case the sphere moves outward on a paraboloid of revolution until it meets the wall of the vessel. &.
At the other extreme, the mass of fluid concerned is much smaller than that of neighbouring matter and the gravitational field is approximately uniform over the region occupied by the fluid. 4. 6) G being the constant of gravitation. 3) for the pressure in a fluid at rest, we obtain V. (;') = -41TGp. 7) It is also necessary, as found earlier, that the level-surfaces of 'Y, p and p coincide. 4] Mechanical equilibrium of a fluid 19 of p coincide with one set of parametric surfaces, we see that the kinds of solution are severely restricted.