Download PDF by G. K. Batchelor: An Introduction to Fluid Dynamics

By G. K. Batchelor

ISBN-10: 0521663962

ISBN-13: 9780521663960

First released in 1967, Professor Batchelor's vintage paintings continues to be one of many top-rated texts on fluid dynamics. His cautious presentation of the underlying theories of fluids continues to be well timed and acceptable, even today of virtually unlimited desktop strength. This reissue guarantees new iteration of graduate scholars studies the attractiveness of Professor Batchelor's writing.

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Extra resources for An Introduction to Fluid Dynamics

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In other words, we have a specification for the distribution of density of fluid which can take the place of the body. 4] 17 Mechanical equilibrium of a fluid where the integral is taken over the region which was occupied by the body, and this force is balanced by the contact force at the boundary A, which is unchanged by the replacement of the body by fluid. Thus the 'buoyancy' force on an immersed body due to the action of a volume force on the surrounding fluid (at rest) is JpV'Y dV, = - JpF dV, where the density p at a point within the region occupied by the body is determined by continuation of the distribution in the surrounding fluid in the manner described above.

_-- ........ 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.

It is evident that molecular transport will still lead to a net transfer across an element of surface in the material when the distribution of intensity in the neighbourhood of the surface element is non-uniform, but, instead of representing this local non-uniformity as a difference between the values of the intensity on the two sides of the element, we must take a more general point of view and represent it as a vector gradient of intensity at the position of the surface element. The linear relation between flux and the gradient of a scalar intensity Consider first the cases in which the relevant intensity is a scalar quantity (viz.

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An Introduction to Fluid Dynamics by G. K. Batchelor


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