A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 3
... occupied by the fluid , for all instants ; or we may seek to determine the history of each individual particle . The equations obtained on these two plans are conveniently designated , as by German mathematicians , the Eulerian ' and ...
... occupied by the fluid , for all instants ; or we may seek to determine the history of each individual particle . The equations obtained on these two plans are conveniently designated , as by German mathematicians , the Eulerian ' and ...
Page 5
... integral of the normal velocity outwards , taken all over the boundary . If the region in question be that occupied by the matter which at time t fills the rectangular element of Art . 6 , the parts of this 5-8 . ] 5 EULERIAN EQUATIONS .
... integral of the normal velocity outwards , taken all over the boundary . If the region in question be that occupied by the matter which at time t fills the rectangular element of Art . 6 , the parts of this 5-8 . ] 5 EULERIAN EQUATIONS .
Page 13
... occupied a rectangular paral- lelepiped having the corner nearest the origin at the point ( a , b , c ) , and its edges dr , db , dc parallel to the axes . At the time t the same element forms an oblique parallelepiped . The corner cor ...
... occupied a rectangular paral- lelepiped having the corner nearest the origin at the point ( a , b , c ) , and its edges dr , db , dc parallel to the axes . At the time t the same element forms an oblique parallelepiped . The corner cor ...
Page 19
... occupied may , in the course of the motion , come to be occupied by matter which did not originally possess this property , and which therefore cannot have acquired it . The above theorem , stated in an imperfect form by Lagrange in ...
... occupied may , in the course of the motion , come to be occupied by matter which did not originally possess this property , and which therefore cannot have acquired it . The above theorem , stated in an imperfect form by Lagrange in ...
Page 37
... occupied by irrotationally - moving fluid , we see from ( 6 ) that the circulation is zero in every circuit which can be filled up by a continuous surface lying wholly in the region , or in other words capable of being contracted to a ...
... occupied by irrotationally - moving fluid , we see from ( 6 ) that the circulation is zero in every circuit which can be filled up by a continuous surface lying wholly in the region , or in other words capable of being contracted to a ...
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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 formulę 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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