A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 12
... infinite pressure would involve an infinite density ; whereas no change of density can occur during the infinitely short time of the impulse . Hence , in applying ( 19 ) to the case of a gas we must put = 0 , whence u ' - u = X ' , v ...
... infinite pressure would involve an infinite density ; whereas no change of density can occur during the infinitely short time of the impulse . Hence , in applying ( 19 ) to the case of a gas we must put = 0 , whence u ' - u = X ' , v ...
Page 22
... infinite velocity at all points of the intersection . 28 . Steady Motion . When at every point the velocity at that point is constant in magnitude and direction , i . e . when du dt = 0 , dv dt dw = 0 , = 0 ....... dt everywhere , the ...
... infinite velocity at all points of the intersection . 28 . Steady Motion . When at every point the velocity at that point is constant in magnitude and direction , i . e . when du dt = 0 , dv dt dw = 0 , = 0 ....... dt everywhere , the ...
Page 35
... infinite number of infinitely small elements . The sum of the circulations round the boundaries of these elements , taken all in the same sense , is equal to the circu- lation round the original boundary of the surface ( supposed for ...
... infinite number of infinitely small elements . The sum of the circulations round the boundaries of these elements , taken all in the same sense , is equal to the circu- lation round the original boundary of the surface ( supposed for ...
Page 46
... infinite distance from the internal boundary , it is constant throughout the region . For otherwise would be a maximum or a minimum at some point of the region . We infer , exactly as in Art . 49 , that if o be given arbitrarily over ...
... infinite distance from the internal boundary , it is constant throughout the region . For otherwise would be a maximum or a minimum at some point of the region . We infer , exactly as in Art . 49 , that if o be given arbitrarily over ...
Page 47
... infinite . 52. The theorem stated at the end of Art . 50 is now obvious . For , under the conditions there stated , no stream - lines can begin or end on the internal boundary . Hence , any stream - lines which exist must come from an ...
... infinite . 52. The theorem stated at the end of Art . 50 is now obvious . For , under the conditions there stated , no stream - lines can begin or end on the internal boundary . Hence , any stream - lines which exist must come from an ...
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Common terms and phrases
angle angular velocity Ave Maria Lane axes axis C. J. CLAY Cambridge University Press centre Christ's College circle circuit CLAY & SONS co-ordinates component constant corresponding Crown 8vo cyclic Demy 8vo denote direction dT dT dx dx dx dy dz dy dy dydz Edited element equation of continuity equations of motion Fellow finite fluid forces formula formulæ given Green's Theorem Hence independent circuits infinitely small infinity integral internal boundary irrotational motion liquid LL.D mass moving Notes obtain origin P. G. TAIT parallel particle perpendicular plane xy portion Professor quantities radius RENDEL HARRIS satisfied shews side simply-connected solid sphere St John's College stream-lines surface theorem theory Thomson Trans Trinity College University of Cambridge University Press Warehouse velocity-potential vortex waves zero аф
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